Can You Teach Risk Arbitrage?

I asked this question from my students in the mid-term exam at MDI today.

Risk Arbitrage Template # 1: Base case of risk-free open offer

Company A’s stock price is quoting at Rs 35 per share. Suddenly, a competitor of Company A makes an offer to buy out all the outstanding shares of the company at Rs 100 per share. The stock promptly zooms up to Rs 80, at which price you can buy a large quantity, if you wish.

You and your friend have evaluated this risk arbitrage opportunity. Here are your findings:

    1. The last date for a competitive bid has gone by, so the probability of a higher bid is zero.
    2. The bidder cannot, of its own accord, withdraw the bid and has deposited all the money required to fund the offer in an escrow account under the control of a highly reputed bank. Moreover the investment banker who has made the public offer is highly trustworthy.
    3. The offer is likely to be completed within 90 days if it’s approved by the Competition Commission of India (CCI). The deal is subject to approval by the CCI because the bidder is a competitor of Company A.
    4. In your estimate, the probability that the deal will get approved by the CCI is 80%.
    5. In the event of the deal not being approved by the CCI, the offer will be withdrawn.
    6. If the offer is withdrawn, the stock price will plummet back to Rs 35 level, which was the price in the market before the bid was announced. However, in your estimate, if such an eventuality arises, you should be able to sell all your shares in the market at an average price of Rs 50.

Questions on Template # 1

  1. Assume that you are looking for opportunities which are uncorrelated to the market, why should you invest in this one? (10 marks)
  2. How would you act if CCI approval was not granted and you have bought the shares? How would you psychologically respond to that situation? (10 marks)
  3. If your friend refuses to make this bet because of the loss scenario, what bias is he suffering from? (10 marks)
  4. How would you help him over-come this bias? (10 marks)

The Purpose behind this “experiment”

This is an experiment in teaching and learning from each other. Let’s see how it goes. If it goes well, I will repeat this experiment by introducing newer problems.

This current problem is a hypothetical one but serves as a really good basic template for working on risk arbitrage. In my view, risk arbitrage is an excellent building block for learning value investing because it requires a mindset of an unbiased, unemotional, and rational decision maker. Moreover, it does not require making long-term predictions about businesses, managements, or the economy.


This is an invitation to you to answer the questions listed above. I will accumulate the submitted answers over the next three days i.e. until 23 October 5:30pm. I won’t approve answers until the deadline has passed.

Once the deadline has passed, I will approve all the answers posted. Then, if needed, I will add more, complex questions. The process of questioning and answering will follow a method used by Socrates and which is called “Socratic Questioning”

Socratic questioning is disciplined questioning that can be used to pursue thought in many directions and for many purposes, including: to explore complex ideas, to get to the truth of things, to open up issues and problems, to uncover assumptions, to analyze concepts, to distinguish what we know from what we don’t know, to follow out logical implications of thought, or to control the discussion. The key to distinguishing Socratic questioning from questioning per se is that Socratic questioning is systematic, disciplined, and deep, and usually focuses on fundamental concepts, principles, theories, issues, or problems.

Hopefully, the process of Socratic questioning will produce some really good insights.

The person who submits the best answer and subsequent insights will be awarded a copy of “Thinking, Fast and Slow” by Daniel Kahneman. Just a small incentive for achieving a higher end. 🙂

Model Answers Template # 1

Many of you have given excellent answers. I will keep the answer brief because I want to spend time on the concept and also on taking the topic to the next template.

Answer 1

You should invest in this opportunity if you are looking for good bets which are not correlated to the market provided that it’s a small bet and it offers returns which are superior to a bond investment. As Ankur Jain (my ex-student and colleague) points out, we need to know the prevailing interest rates. The prospect of earnings Rs 10 on an investment of Rs 80 over a period of 90 days which translates into a flat return of 12.5% and an annualised return of about 51% looks very good because in the back of our mind we know that prevailing interest rates are much lower. But if India was going through hyper inflation and nominal interest rates were higher than 51% p.a., this would be a bad trade.

Answer 2

If CCI rejects the acquisition proposal then the offer stands cancelled and reason for owning the stock no longer exists. This sale will result in a loss but that is part of the (probabilistic) game we are playing. It would be foolish to anchor to cost (anchoring bias) or find new reasons to own the stock (commitment bias).

The correct psychological response to the loss scenario is to swallow your pride and to take the loss by “thinking like a trader.” You can console yourself by thinking “you win some, you lose some.” In other words, focus on process not outcome. Good processes in the probabilistic world of Fermat and Pascal sometimes result in bad outcomes. By keeping the eye on the process and being unemotional is the right psychological response.

Answer 3

If your friend refuses to make this bet, he is suffering from loss aversion. This is a very common bias and was discussed beautifully by Daniel Kahneman in his book “Thinking, Fast and Slow.” See this link titled “Samuelson’s Problem.” Risk arb teaches how to get out of loss aversion extremely well. If you don’t take losses which are going the occasional but inevitable outcomes of even good investment process, you won’t last very long in this game. That’s one huge reason why I consider doing risk arb as a great building block for other forms of value investing.

Answer 4

Kahneman also provides an elegant solution to the problem. Carefully read “Samuelson’s Problem” to find it. Many of you have referred to this “death bed problem” by using terms like “broad framing” and “loss aversion” in your answers. Those of you who have done this are bang on target.

Socratic Solitaire with Risk Arbitrage Template # 1

I talked about the idea of socratic solitaire in an earlier blog post. I will use that idea again over here by asking some questions and answer them myself.

Question: Why a small bet? Why not bet the bank on such bets? After all they have large, positive expected payoffs!

Answer: Because there is a scenario where you may lose Rs 30 on a Rs 80 investment. That’s a loss of 37.5% of the capital invested in the operation. Moreover, the probability of this scenario is not tiny. It’s 20%. That’s why you will never make large bets in these situations? Look at this way: If you invest your entire bankroll on a series of such bets then a day will come when you will lose 37.5% of your capital. That would be bad financially. It will also be psychologically devastating. You don’t want those outcomes.

Question: Ok, then what about another bet, which has the same expected return but the loss scenario isn’t there at all?

Answer: In that case, you should willing to invest a higher amount than you would in the previous bet.

Question: What about fundamentals? Don’t I need to worry about that?

Answer: For the most part, no. In later templates, maybe but not in Template 1.Why? Because the offer is for all the shares, you are effectively buying, not the stock of Company A, but the bonds of offerer. Your analysis of this situation is the functional equivalent of doing credit risk analysis on the offerer. (This, by the way, is a very good example of a situation when a stock becomes a bond and where you should focus on underlying economic realities and not titles. As Shakespeare wrote: “What’s in a name? A rose by any other name will smell just as sweet.”)

If CCI declines to approve the deal, the offer will fail. When that happens, the instrument will cease to be an effective bond of the offerer and will start trading like a stock — like it did before the offer was made. In other words, it will crash. But since you’ve already decided to get out if that happens, fundamentals won’t matter much won’t they?

But, what if the stock keeps on tanking limit down every day and you can’t get out? This can happen because there are other arbitrageurs like you who are rushing for the exits. To all of you fundamentals don’t really matter here.

However, if the stock keeps on falling, a time may come when you will have to start thinking about fundamentals. 🙂 Tough luck! Just think about this for a moment. You bought a stock at 80 to make Rs 20 on it. Your return is CAPPED. Now the deal has collapsed because the CCI said no. The stock is selling at limit down every day and you can’t get out. It’s now at 20. What will you do? No matter how unemotional you are being asked to think about the situation, you will have the temptation to dig out that annual report, calculate the book value, economic earnings etc and consider holding on to this stock.

The idea of capped small absolute returns combines with the possibility of large losses can be remembered with the help of a powerful metaphor of “picking up pennies in front of a steamroller.” The money you make if things go right is small, and the money you lose if they go wrong is large. Keep that in mind when you plunge into risk arbitrage.

Btw, metaphors are very powerful way of thinking about the world around you and just like multiple mental models, you need a multiple metaphor framework.

Question: Ok, now I am really scared. Why do risk arb at all?

Answer: Two big reasons. One, it has a role in portfolio management. Recall low or no correlation to markets. That’s very attractive. When there’s a bull market on and you can’t find good stocks to buy, risk arb comes handy. It’s like a high interest lending operation. Money goes out for a short while, earns a good return (averaged out, if you do it right) and then it comes back, by which time stock markets may be lower and you may find a longer-term home for your money. So, one may think of money invested in risk arb as a cash equivalent but there are exceptions to this rule, as we will discover in a later template.

Two, you may want to do only risk arb and nothing else. Some people do that. It’s a lot of fun, and open offers are just one type of a risk arb operation. There are several more. Graham used to call them “special situations.” You can read up about a few I have done long time ago from here and the original “special situations” article by Ben Graham from here.

Question: Ok, I am back in the game! But tell me what can go wrong.

Answer: Like I said, you are effectively picking up pennies in front of a steamroller. Remember this: most surprises in risk arb are bad ones (asymmetric payoffs). There may be good surprises (we will discover them in future templates), but bad ones outnumber good ones. So, you have to keep on worrying about what can go wrong, where is the risk etc. While doing so, it’s a good idea to keep Robert Rubin’s observation about risk in mind: Condoms aren’t completely safe. My friend was wearing one and he got hit by a bus. 🙂

That Rubin quote is very powerful advice on risk for risk arbs. Rubin, by the way, spent a good part of his earlier years in risk arb.

Question: Very funny! When should I sell out of this situation?

Answer: When you’re wrong, when something better comes along and you don’t have spare cash, or when you’ve made most of the money that you wre going to make in this trade. Here I have a rule of thumb. You bought it at 80. The max you can make is 100 so that’s 20 points. Now, let’s say 80% of those points are already in the bag. That is the stock price has risen to 96. From here onwards, out of a total 20 points, only 4 remain. For me, it’s a good idea to let someone else take the risk on those points. Keep Rubin’s advice in mind. If you hold on at 96 and some shit happens then you will lose the return and you may also lose your shirt. Why take the chance?

Question: Ok, makes sense. But who will buy from me?

Answer: Traders who want to buy today and tender in just a few days. Obviously if the stock has risen to Rs 96, this means that the offer is just about to close. The fellow who buys at 96 from you and sells it at 100 to the offerer makes 4 bucks on 96. That’s a 4.2% return. If he is going to make that return, say, in a week, then his annualised return comes to 217%. And you made a lower IRR in percentage terms, but look at it this way: who got most of the juice out of the trade? You! You let him have the rest of it because you figured that the remaining part of the return is just not worth the additional risk. There are two very important lessons here. One, don’t be fooled by a percentage.

And two, in risk arb there is no hold period. Either you are a buyer, or a seller. If the price has risen to 96 and you are not a buyer at this price, you should sell. That logic does not apply in buying long term equities where there is a price range for buying, holding, and selling. Now, I know many smart people who argue against this but that’s the way i feel about it. People who argue against this view are thinking like traders even for long term opportunities… But I diverge, so let’s get back to the topic.

Question: Ok, I understand that it’s rational to accept these types of bets because they are favourable bets, and they are small wagers so even if the loss scenario arises out of bad luck it won’t kill you. Why would someone reject such a bet then and still be rational?

Answer: Good question. The answer depends on how we define rationality. If we look purely at the investment merits, everyone who is looking for uncorrelated special situations should make this bet. But we have to think about incentives and perverse incentives. What if you are managing a fund in which if you get a bad outcome, it will look bad on you. Under such circumstances, in the interest of self-preservation, would it not be rational for the fund manager to reject such bets because they carry a not-insnificant loss scenario? So, on top of expected value framework, there is a “regret analysis” framework. Buffett ignores the “regret analysis” framework because over decades he has positioned himself in a manner which allows him this privilege. He does not care about short term performance, lumpy results. In his words, “we are willing to look foolish, so long as we are sure we have not acted foolishly.” Not many people have that privilege.

Risk Arbitrage Template # 2: Partial Offer

Ok, now we move to the next template where we increase the complexity a bit.

Company A’s stock price is quoting at Rs 35 per share. The promoters of the company, who hold 51% of the company’s shares sell out to a MNC at Rs 100 per share. The MNC makes a tender offer for an additional 26% at Rs 100. There is no regulatory risk like the CCI risk in template 1.

The stock has risen to Rs 60 per share. After the offer is over, you expect the stock price to fall back to the pre-offer level of Rs 35 which is also the price at which you will be able to liquidate your remaining shares. The offer will take 90 days to complete.


  1. What’s the expected return of this operation?
  2. Should you look at fundamentals of the target company? Why or why not?
  3. What is the likely acceptance ratio i.e. how many of your shares are likely to get accepted under the offer (theoretical vs. practical) and what key factors will govern that ratio?
  4. How can you use the “inversion” (invert, always invert) trick to estimate market’s assessment of the acceptance ratio?
  5. Should you borrow money to do this operation? Should you have done it in Template 1? Why or why not?

Try to answer these questions. This time, I will approve responses as they come in and give my own views in a while.

Then, we will go to the next template.

Model Answers Template # 2

Again, we have excellent answers in comments. Without being too repetitive, here are my thoughts.

Answer 1

If everyone who is eligible to tender, tenders, then the operation involves:

Buying 100 shares @ Rs 60 resulting in cash outflow of Rs 6,000

Tendering all shares, getting 53 (=(26/49)*100) accepted at Rs 100. Cash inflow Rs 5,300

Selling the remaining 47 shares @ 35, resulting in a cash inflow of Rs 1,645

Ignoring time value of money and taxes (you can easily factor the former by using XIRR function in Excel), we find that for laying out Rs 6,000 we get back Rs 6,945. Accounting pre-tax profit of Rs 945 translates into a return of 15.75% over 90 days which annualises to 64% p.a. Not bad at all.

The actual return will be higher because not every one who is eligible to tender will tender. That’s discussed below in Answer 3.

Answer 2

Since you’re going to end up with some shares, you have to think about fundamentals. What if underlying value is far below Rs 35 — the level at which the stock was selling before the offer. What’s the sanctity of this Rs 35 number? It’s just a number — an anchor. We need anchors but not the wrong ones. The right anchor here is the underlying value and not the price at which the stock was selling before the offer.

Another danger here is to think along these lines: Well the acquirer who is buying is not a fool and if it’s paying Rs 100, then I can assume the stock won’t fall below Rs 35. This maybe true and maybe not. So, don’t fall for the bias from over-influence of authority, unless you have very good prior evidence to support the belief that the acquirer is not a fool. For example, Ravi Purohit has cited examples of two acquisitions done by a group, which has a solid track record in M&A.

Answer 3

People have generally stated correctly that the actual acceptance ratio will be higher because not everyone will tender. Here it’s important to think in terms of base rates. There is plenty of statistical evidence on tender offers from where these base rates can be calculated. While studying any given offer, it makes sense to first start from base rate and only then adjust that base rate probability by taking into account the peculiarities of the situation you’re evaluating.

Many people discard the base rate and start modelling their excel sheets by assuming a much higher proportion of non-tenderers (called “brain dead” investors in Risk arb parlance because these people won’t tender at 100 but will sell in the after-market at 35). Excel is a dangerous tool. It allows you to insert what you want to believe, as if it’s a fact. So, if you want to believe that a particular institutional investor who holds 10% stake, will never tender because he bought it at a higher price than the offer price of Rs 100 (loss aversion), then your model will project a higher acceptance ratio than would be the case if you had assumed that he would tender. And that would make the trade look profitable at a higher price and you’ll go and buy and later find that he tendered and acceptance ratio was not as good as you had projected and you ended up with either much less profit or even a loss.

So you have to exercise caution when making predictions about acceptance ratios. The outcome of the trade is likely to be highly sensitive to your predictions of acceptance ratios. It makes sense to do a scenario analysis and the trade may become uninteresting in the pessimistic scenario. Now that won’t happen in our example above because even if everyone tenders, the trade still makes sense, but it will happen in other situations.

One thing I have learnt here is that it’s just stupid to assume that a fellow won’t tender because “its rational to not tender.” Think about this for a moment. As value investors, we make a living by trading against irrational people. We think the world consists of a large number of irrational people and institutions. And yet, when it comes to risk arb, we tend to fool ourselves into believing that people will be rational when it comes to tendering shares. They wont always be. So, don’t implicitly apply the human rationality assumption.

Answer 4

The inversion trick is a very powerful idea because it de-biases us. We want to believe that LIC won’t tender or HDFC won’t tender and that will make the acceptance ratio so much better so we want to buy. Why not invert and figure out what the market price is telling us about the likely acceptance ratio, and then see if we agree or disagree with the market? Without going into the details, here’s the procedure.
We already know the offer price (Rs 100) and the current stock price (Rs 60). We know the time to closure (90 days). We have estimated the likely exit price for remaining shares (Rs 35). We also know that risk arbs will do a trade by insisting upon a return which is higher than the risk free return. So, let’s say the risk-free return is 10% p.a. and risk arbs required return is 14% p.a. We can plug in the 14% p.a. return to figure out the acceptance ratio which will deliver that return. Once we have that ratio, we can then approach the problem more objectively. Inversion, or backward thinking accomplishes just that: it makes us more objective. By thinking forward (i.e by estimating acceptance ratios by studying shareholding patterns, and base rates), we are prone to making mistakes. By thinking backward, we create a sanity check on thinking forward. So, we must use both types of thinking — forward and backward.

What should you do if the “implied acceptance ratio” by reverse engineering it from the data we have turns out to be way more than what you estimated by thinking forwards (using base rates, and then adjusting for them with the peculiarities of the situation being examined)? You should walk away from the trade. You have arrived at a conclusion that people who are setting the price in the market are over-optimistic.

Could there be alternate explanations? Yes! You may be competing with people who don’t have to pay taxes and/or have much lower transaction costs than yours or have access to low cost borrowed funds. For such arbs, certain trades will make sense while they won’t make sense for you.

Regardless of explanation (overoptimism or low cost advantage), your conclusion will be the same: Walk away.

Answer 5

I agree with the conclusions given by most of the commentators. Borrowing in Template # 1 does not make sense because of a loss scenario. Borrowing in Template # 2, MAY make sense. I liked L.J’s comment that “We must also keep in mind the temperament of the investor. If borrowing money makes you uncomfortable and you have trouble sleeping at night, it might be better to avoid it.”

Socratic Solitaire withe Template # 2

Question: You have no clue whether an institutional investor will tender or not. How will you deal with that in your model?

Answer: I will toss a coin. In other words when I don’t know, I will simply be agnostic and assume a 50% chance of tender and in my model.

Question: How will you turn English words like “highly probable” “almost certain” “likely” “unlikely” etc into probability percentages?

Answer: I will use Sherman Kent’s framework and will do it routinely as a practise in applying Fermat/Pascal way of thinking to virtually everything in life.

Question: Should you use Template # 2, to create cheap shares in a stock you want to own?

Answer: Yes! L.J has mentioned this important point in his comment. So has Ashim. The idea is very simple. You love a stock at a price. There is an offer outstanding at a higher price. You can buy more shares, tender them in the offer and lock in a gain on shares accepted. The profit on shares accepted should be thought of as a reduction in the cost of the shares that are returned. Sometimes, this can result in a fantastic opportunities. This happened in the case of Eicher Motors a few years ago.

So, even if you are not a risk arb, but are a long-term investor, it makes sense to temporarily wear the hat of an arb…

Question: But my accounting cost won’t change, will it? If I buy 100 shares at 60 and tender them all in the offer at Rs 100 and 45 of them are accepted, then my accountant will record a gain of Rs 40 per share on 45 shares, and leave the cost of remaining shares unchanged. But if I think in terms of cash flow, then there is an initial cash outflow of Rs 6,000, then a cash inflow of Rs 4,500, then, ignoring taxes, I have a net cash outflow of Rs 1,500 and I am left with 55 shares, so my effective cost of creating those 55 shares is Rs 27. So, who is right — the accountant or the cash flow investor?

Answer: The cash flow investor. You should ignore accounting consequences, and compare effective cash cost of creating new shares (after considering taxes which for simplicity’s sake, I have ignored), with fundamental information like earnings and asset values. The prospect of creating the shares of a high quality company at a very low P/E or P/B is very attractive.

Risk Arbitrage Template # 3: Stock Trades in F&O Segment

Ok, let’s add some complexity.

Company A’s stock price is quoting at Rs 35 per share. The promoters of the company, who hold 51% of the company’s shares sell out to a competitor at Rs 100 per share. The acquirer makes a tender offer for an additional 26% at Rs 100. It’s offer is subject to approval by CCI. In your estimate, the probability that the deal will get approved by the CCI is 80%. In the event of the deal not being approved by the CCI, the offer will be withdrawn. If the offer is withdrawn, the stock price will plummet to Rs 30 but the average price at which you should be able to sell all your shares will be Rs 35.

CCI will take 6 months to approve or reject the deal and then the deal will go back to SEBI for approval. Since the acquirer is involved in some litigation with SEBI on an unrelated matter, you think the offer could take a long time to be approved by SEBI, but you are confident it won’t take longer than 90 days after CCI decision. Thereafter another 30 days will be needed to complete the offer.

The bidder cannot, of its own accord, withdraw the bid and has deposited all the money required to fund the offer in an escrow account under the control of a highly reputed bank. Moreover the investment banker who has made the public offer is highly trustworthy.

Immediately after the announcement, the stock of Company A rises to Rs 65 per share. This stock also trades in the F&O segment of NSE and while options are quite illiquid, the futures contracts for each of the next three months trade at a premium to spot, reflecting cost of carry of about 12% p.a.

There is another potential bidder who has been giving media interviews about a counter offer. However, it has not come forward with a formal offer yet, and the last date by which it can do so will be 25 days from now.

In your judgment, in the absence of a competitive bid, the acceptance ratio is likely to be 67% of all tendered shares based on shareholding pattern as of now, before the offer, but since arbs are moving in, and there is a possibility of a competitive bid, things may change…

After the offer is over, you expect the stock price to plummet to Rs 35 — the price at which you will be able to liquidate your remaining shares.


  1. Will you buy now and hedge your net long exposure using futures? Why or why not?
  2. How will your estimate of acceptance ratio change over time?
  3. What’s the worst case scenario, if you buy now and also hedge using futures?
  4. How will you deal with the possibility of a competitive bid?
  5. How will you deal with the CCI risk and the SEBI risk in terms of a probability chain? (Hint: How many things have to go right for you to make money?)
  6. What kind of deal-related (not market related) volatility can you expect in this transaction? How will you deal with that volatility?

Model Answers Template # 3

In Template # 3, we experienced complexity like in messy real life. In such situations, different people, acting rationally, can come up with slightly different conclusions. Keep this in mind while you read my model answers to template # 3. Also focus more on the underlying principles on which I will rely rather than on the actual answers.

Let’s look at the base case of expectation of no competitive bid, no hedging, and transaction completing in 10 months (6 months for CCI + 3 months for SEBI + 1 month for offer formalities).

Let’s first figure out the acceptance ratio. The offer is for 26% our of a total of 49%, so the absolute minimum acceptance ratio is 53% (26/49). In the problem I have stated two things: (1) if there is no competitive bid, and no change in shareholding pattern, the acceptance ratio should be 67%; (2) since arbs are buying shares the acceptance ratio will change.

So the first major lesson here is to not estimate acceptance ratios based on old shareholding patterns. That’s because when arbs buy, they buy either to tender or to sell to other arbs, who will tender. So the shareholding pattern starts changing immediately after the offer is announced and the stock effectively starts moving from investors to arbs. This means that the actual acceptance ratio should be lower than 67%? So we need to model a lower acceptance ratio. A 67% acceptance ratio implied 39% of shares being tendered (26/39=.67) which means brain dead investors of 10% (49%-39%). Let’s model 6% brain dead investors instead of 10% because of arbs moving in. If we do that, then number of shares tendered will be 49%-6%=43% and acceptance ratio will become 60% (26%/43%).

So the first thing I have done is to recognise the unfavourable change in ownership structure in my model.

Now, let’s look at the base case.

Trade Today: Buy 100 shares for Rs 65. Cost: Rs 6,500

Sell in 10 months in offer: 60 shares at Rs 100. Total receipt: Rs 6,000

Sell in 10 month returned shares in market. 40 shares sold for Rs 35. Money received: Rs 1,400.

Total money received: Rs 7,400. Total money invested: Rs 6,000. Total return: Rs 900. Flat return in 10 months: 13.85%. Annualised return: 16.62%

Not bad, but not terribly exciting either. I can’t spike this return by borrowing because of a loss scenario (If deal falls all shares will have to be liquidated at 35).

Now, with this base case in mind, let me address the question with the observations that I very largely agree with Ravi Purohit’s replies. So let me just my perspective to his replies.

Answer 1

Identifying a deal and deciding the time to enter is are two different things. They need not co-incide. The key question to ask when you identify a deal is not should I buy but rather how can I make money in this deal?

It may make sense to buy the long position now but it does not make sense to short now. Why? To answer that consider what all can go wrong if you short a stock for hedging purposes. One, there are 10 months and you don’t have a futures contract for a 10 month duration, so you have to use shorter period contracts all roll them over. This exposes you to asset liability mismatch. In this particular case, if the arb interest is very high then the presence of shorts may make rolling over quite expensive.

Second, there is a possibility of a competitive bid. That possibility will become reality or disappear in 25 days. If you short now, you can get screwed if a large competitive bid happens. Why? That’s because the stock will shoot up and your short position will lose money. Moreover, you will find that you have over-hedged your position because with two offers on the table, the need to be short won’t be there. Two offers of 26% – one at 100 and one above 100 and total shares with public being only 49% makes shorting now a bad idea.

The general idea I want to invoke here is the idea of “preserving optionality” I wrote about this long ago, here and here. There is no point burning your bridges when the situation is volatile and dynamic such as in risk arb. The twists and turns in any risk arb is just another manifestation of the idea of volatility in option valuation. And options are worth more if volatility is high than when it’s not. So, keeping your options open till the last moment makes sense in risk arb. In the current situation, this means that considering shorting before the 25 day time limit for a competitive bid is over is a bad idea. And as Ravi has pointed out, the risk of deal failure due to CCI rejection won’t be known for 6 months so what’s the point of hedging now?

Why not break the trade into long buy at one time and short expected returned shares at a different time?

Answer 2

I have already address this above.

Answer 3

The worst case scenario is this: You buy now and you short now. Then there is a competitive bid and stock soars and you have loss on short position but which is offset by profit on long position. But since need to hedge has gone away because of two offers (so you think), you square up the futures at a loss but keep the long position intact. Then CCI rejects the deal and the stock collapses to 35.

Answer 4

As Ashim has mentioned, you have think in terms of decision trees and scenario analysis and expected value under various scenarios. As time moves forward some branches of your decision tree will disappear and new ones will appear. It’s a dynamic process — the very reason I like risk arb as a stepping stone for learning value investing generally.

You may decide to do nothing right now and wait for 25 days and then once the uncertainty about the competitive bid is over, work out the expected value at that time and then decide whether or not you want to take a position.

Alternatively, you may decide to take small long position now and then hope for competitive bid to materialise and then react to a bid materialising or not after 25 days. If it does materialise you may buy more shares, at a higher price and even if those news shares will cost you more and the return you will make on them will be lower than the return you make on the original quantity you bought, those lower returns will also come with lower risk of loss. So, you have to think of risk arb not in terms of just buy or not buy now but also in terms how much to buy and when always keeping in mind the dynamics of the situation. The same logic applies around the date of CCI approval. If the approval comes, the stock should move up. At that time you have evaluate if it makes sense to buy more or to liquidate the position. When you make that decision you will base it on your estimate of expected return as per information available at that time.

Answer 5

I have partially addressed this in the above paragraph. You have to think in terms of a probability chain. How many things have to go right for you to make money in this deal? The deal has to be approved by CCI, then by SEBI. If CCI approval probability is 80% and thereafter SEBI approval probability is 90% (you never know so you should not model certainty of approval), then the probability of both approvals coming through is 72%. And by the way these numbers are not static. They change. And you will know they are changing if you sit though the proceedings of CCI or reviewed SEBI approval process. So you have to change these probabilities based on new information and that could make the trade not worth doing or worth doing even more. What’s important here is to remember that its a very dynamic process and you have to keep on adjusting your estimate of returns based on events as they unfold. And while you do that keep in mind that decision trees expand by creation of new branches and also contract because of collapse of a few branches.

Answer 6

As mentioned by others, deal related volatility will revolve around: (1) competitive bid; (2) CCI approval; and (3) SEBI approval.


The award for the answers I liked the best goes to Ravi Purohit. Congratulations Ravi! And thanks a lot to the others for participating in this experiment.

Two Few Additional questions on Risk Arb

You have a number of risk arb opportunities and they offer different expected returns. Some expected returns are below AAA bond yields. Others are well above.

  1. How will you determine which ones to choose to invest in?
  2. How would you think about position size?

91 thoughts on “Can You Teach Risk Arbitrage?”

  1. 1) EMV = Rs. 10 , so Yes I would Invest
    2) Sell the shares as my original purpose of buying the stock has been lost , if it falls below 35 at some time due to panic selling , buy more
    3)The Bias of weighing losses more than gains , even though the EMV is +ve
    4) This is not his last bet in life , if the deal doesn’t work out , they would sell and fight to live another day & Broad Framing – It is bet in which odds are in favour of us ,but it is should not be looked on as a single chance, life would present more such bets and even if this does not work out in long run if we continue taking such favorable bets we would emerge richer

  2. Sir,
    Here is how my answer sheet will look like-

    1)Assuming I am looking for Risk Arb, I will take part in this one because of its high return on risk adjusted basis.
    The expected price on risk adjusted basis is 80% * 100/- + 20% * 50/- = Rs 90/-. So I will make Rs 10 on Rs 80 that I had put in making it 12.5% return in a 3 month time frame. Annualizing it gives me 45% return (though annualizing carries a reinvestment risk), which beats my hurdle rate (15% CAGR). Hence, I will take this opportunity.

    2)In case CCI rejects the bid, I will SELL the stock. Though my System-1 will take me to Endowment Bias, Loss Aversion Bias, Psychological denial (stock will go up)and Regret. But my System-2 will jump in asking me to look at Process rather than Outcome; Broad Frame rather than Narrow (if my calculated probabilities were right, I will make money from this process over the long term) & sell immediately to aviod Opportunity Costs. Also, I will try to examine whether my process was right or was I suffering from WYSIATI & Overconfidence Bias & Availability Bias when I calculated the probabilities of 80:20 (will do this keeping Possibility of Hindsight Bias in mind).

    3)If friend says No, he is suffering from Loss Aversion Bias & is looking at the opportunity from a Narrow frame of mind (as if he is on his death bed & this is his last bet).

    4) I will try to help him by telling him to evaluate the situation with a probabilistic mind & not with worst case scenario, will get him to Broad Frame (from his Narrow frame), get him to look at process & not the result, & will get him to diversify.

    Thanks & Regards,

  3. 1. The bidder cannot withdraw the bid and I can make 20% return on this opportunity within 90 days.

    2. If CCI approval is not granted, I would sell the shares immediately. Psychologically it would not have any negative effect as the probability that CCI will not approve the bid was 20%.

    3. Friend is suffering from status quo bias.

    4. I will try to bring his attention to the fact that the bidder in no case has option to withdraw, so the deal failing due to bidders withdrawal is not a possibility and probability that the deal will get approved by the CCI is 80% is higher, than the deal not getting approved, which is 20%.

  4. Sir, Here are my answers:

    Q Assume that you are looking for opportunities which are uncorrelated to the market, why should you invest in this one? (10 marks)

    A. Considering the risk adjusted return of this deal, it has a positive return. The price of this share will not depend on market but on whether deal goes through or not and hence this deal is uncorrelated with market.
    Now considering the return, there is 80% chance of deal going through. In case deal goes through profit will be increase in share price from 80 to 100, i.e. Rs.20 Risk adjusted return will be 0.8*20=Rs.16
    Also, there is 20% chance of deal failing to happen. In that case loss will be (80-35)=Rs.45. Risk adjusted loss will be 0.2*45=Rs.9
    Net Return will be 16-9=Rs.+7
    So, considering net positive return one should invest in this one.

    Q. How would you act if CCI approval was not granted and you have bought the shares? How would you psychologically respond to that situation? (10 marks)

    A. If the approval is not granted then I would sell the shares as soon as I know about the information. This is because I was looking for an opportunity which was uncorrelated with market and once deal is withdrawn the share price will become correlated with market. Had I been looking at both correlated as well as uncorrelated opportunity, then I would evaluate what should be the price of stock according to its intrinsic value. If I find that price of stock A has fallen far below its intrinsic value, due to market overreaction, I will again purchase stock of A.
    My personal strategy is not to put all my eggs in one basket, so I won’t have invested a fortune in this deal even though expected outcome was positive. I would suffer some loss but knowing that I followed the correct approach, psychologically I would convince myself to move to look for next opportunity where this loss could be recovered!

    Q If your friend refuses to make this bet because of the loss scenario, what bias is he suffering from? (10 marks)

    He is suffering from loss-aversion bias. He feels pain from loss more than the happiness from same amount of gain.

    Q How would you help him over-come this bias? (10 marks)

    I think best way to overcome this bias is to look at numbers. The risk adjusted return that we calculated in Ques 1 of Rs. 7/share should be enough to convince him about the deal. Additional comfort can be achieved by only investing amount which he is comfortable losing in worst case scenario. For example, if his financial situation allows him to go in Rs. 10,000 loss then he could invest 10,000 in the stock. So even if due to unforeseeable circumstances stock drops below Rs. 35, possible hitting Rs. 0, then also the maximum loss is capped at Rs. 10,000. If he looks at the bet from this perspective, he would see the maximum loss is capped at his comfort level but in positive scenario he can make some money.
    No. of shares bought= 10000/80 = 125
    Profit = 20*125=2500
    A 25% return in case of positive scenario.

  5. Hello Sir,

    Thanks once again for the great initiative. Would love to think upon these kind challenges in future.

    Answers according to me.

    1) Expected value is positive. 80% chance of making Rs 20 versus 20% chance of losing Rs. 30. Hence expected value comes out to be Rs 10. Also the expected return of Rs 10 on Rs 80 is 12.5% return in 3 months time which when annualized comes to 50%. Even including transaction costs the return is very good. Hence I would invest.

    Next answers inspired by the article on ‘Samuelson’s Problem’ that you shared 🙂

    2) I would this as see as a one of many bets(ones with probability in my favour) that I would make in future instead of this bet to be singular. Also sometimes there are bad outcomes even from a good process and as you have pointed out many ‘Shit Happens’. Not much to be sad about.

    3) The friend would be suffering from Loss aversion and narrow framing.

    4) Explain him the importance of broad framing and to think like a trader (for a change :P). Phrases like “imagine yourself as a trader,” “you do this all the time,” and “treat it as one of many monetary decisions, which will sum together to produce a ‘portfolio. These should help him overcome the emotional reaction to losses and increase willingness to take risks.

    Manan Patel

  6. 1. We should invest in this opportunity because the expected returns we can earn here are truly uncorrelated to the market. On the one hand, because the competitive bid timeline has passed, our expected returns cannot be improved by an improving market, where we assume that an improving market correlates with more bidders in the process (because people psychologically feel better about the world and are thus inclined to bid at a more uneconomic level, and presumably drives a more competitive process that leads to even higher bids) if it were possible to still place a bid. On the other hand, because the current bidder has already put their money into an escrow account and cannot back away from the merger, our expected returns cannot be worsened by a worsening market, where we assume that the current bidder would be more likely to back away from the deal in a worsening market (due to psychological biases like herd mentality, where the bidder thinks that maybe he shouldn’t complete the acquisition because everyone is exiting the market) if he still had the ability to do so. Instead, the key driver of expected returns is the probability that the CCI approves the deal or does not approve the deal. I think it is fair to assume that the CCI’s decision is not correlated to the market in any way, meaning that our expected returns are truly uncorrelated to the market, and we should make an investment (taking into account our actual expected returns, which are discussed below).

    2. If the CCI approval is not granted, we would likely experience the loss aversion bias, as we will have endured a 37.5% multiple of money loss (falling from 80 to 50) and might even be subject to the status quo bias, where we illogically decide we want to hold the shares so that we do not have to “recognize” the loss and maybe hope that the deal resumes. However, these are all illogical responses based on the psychological biases of the mind. The correct thing to do is to sell the position. Our thesis was that the deal would go through. Since it did not go through, and we have no view about whether another deal might emerge for the company in the future, or even about the fundamental economic prospects for the company, we should ignore our psychological biases and sell immediately.

    3. Our friend is suffering from loss aversion bias, where he is more concerned with the magnitude of loss compared to the magnitude of gain (down 30 if the deal does not go through vs. up 20 if the deal does go through) than he is with the probabilities of the two events occurring (80% likelihood that the deal goes through vs. 20% likelihood that the deal does not go through).

    4. To cure our friend of this bias, I would show him the expected value returns from making this investment. Given that there is an 80% chance that our investment goes to 100, and a 20% chance that our investment goes to 50, the expected price of the stock should be Rs. 90, meaning that our expected multiple of money is 1.125 if we buy at 80 (or (90-80)/80)). On an IRR basis, given that we think the deal closes in 90 days, our expected IRR is ((90/80)^(1/0.25)-1)=60.2%. Thus, taking into account the probability of a loss, we have an expected annualized return of 60.2%. And of course, if the merger were to actually go through, our actual results would be much higher (multiple of money of 1.25x, annualized return of 144.1%). Coming back to question 1, not only are these expected returns uncorrelated to the market, but they are very attractive on a multiple of money and IRR basis, meaning that we should make this investment.

  7. 1. Expected gain =((100-80)*0.8)+((50-80)*0.2)=10
    A positive expected gain, hence I should take this investment opportunity.
    2. Since my analysis was based on probability, I would rationally behave and would still feel justified about my decision to take the opportunity and would take the realized loss. (I am assuming there is no hedging involved otherwise I would like to go for hedging)
    3. I believe my friend is suffering from Framing bias.
    4. I would try to rationally justify the investment decision by drawing his attention towards the success probability and the success rates of similar risk arbitrage examples from the past deals.

  8. Answer 1: I basically have two options, one is to put my allocated capital in say a risk free govt bond and two, to participate in the risk arbitrage. In case of the latter there is a 0.8 probability of making a 25% profit and a 0.2 probability of making a 37.5% loss. Overall there is positive payoff of 12.5% in 90 days. I can also hedge my position by buying some puts (in case the option is available). Either way, assuming the risk free rate is not comparable (opportunity cost) to the positive payoff of 12.5% in 90 days i should participate in the risk arbitrage. Since all the probabilities are “estimates”, to ensure over confidence doesn’t make a big dent to my investible capital, i will not bet the house on this one – possibly a 10-15% allocation to this bet.

    Answer 2: I would sell the shares at an average price of 50 and get out without worrying about sunk costs. If i decide to hold the shares i would be subjecting myself to many biases like endowment, anchoring (to a “fair value” of 100), ignoring disconfirming evidence etc and would tie up my capital to an unoptimum bet there by paying a big opportunity cost and lollapalooza effect.

    Answer 3: Primarily loss aversion; also status quo and zero risk biases. Also possibly pessimism and outcome biases.

    Answer 4: A simple way to help my friend would be to point out to her that she is suffering from the said biases. By definition, most people are unconscious of the biases they suffer from, so take them through Answer 1 using in step by step manner and demonstrate the reasoning. Most people do get it when its laid out bare in front of them. If my friend still doesn’t buy the positive payoff/decision tree argument i would tell her the following:
    a) Bet a very small amount of your portfolio on this so even if you’re wrong you don’t lose a lot of money and it has a minimum impact on your net worth.
    b) Consider the fact that this is just one bet among the many risk arb bets you will/can take in the future. Just like this one, assuming all those are positive pay off bets statistically there is a very low probability that you’ll go wrong every time. If you take multiple such bets the odds are very high that you’ll come out with a positive return.

  9. A1 – This opportunity is arising out of market inefficiencies, provides chances of 20% profit with 80% probability otherwise 37.5% loss. The good thing is we know both the outcomes, especially in case of loss we are capped to 37.5%. By any means this is a speculative operation with no margin of safety. Given the probability of occurrence, I would like to profit from this speculative operation.

    A2 – Never mind, move on.

    A3 – This could be recency bias

    A4 – Looking at the historical data, this opportunity is not in correlation with market and both the side for profit and loss are know precisely, one can dive into this.

  10. 1)Because there is a 80% probability of making a profit of Rs.20 on an investment of Rs. 80. If the deal gets completed in a span of 150 days, we can get a return of 25%+ which is a fantastic deal and annualized return could fall between 50% to 60%.

    2) I would analyse the company whether it has got any Margin of Safety or Moat. If the company does not have any moat and is trading above intrinsic value, i would sell the shares at loss.

    3) Availability Bias – Friend must have had previous loss in Merger offer. Loss Aversion – Mergers sometimes take longer period to clear all the approvals ( Jindal Steel acquisition Ispat). So what we are looking as 50% annualized return may be negative if takes longer period.

    4) In availability bias – Show my friend other case studies who have made profit in Merger offer.

  11. 1. You can gain Rs 16 (80%*Rs20) with a risk of Rs 6(20%*Rs30). So it is a reasonable risk reward to invest in. Also if u look at it on an annualized basis, the returns are awesome. I only wish one gets 100 such bets a year.
    2. I would sell the shares at expected sellout point of Rs 50, since I knew I was taking that risk and would have positioned accordingly.
    3. Loss aversion bias.
    4. By walking him through risk reward analysis. And showing him that if you take enough such investment risks they should pay off well on the whole.

  12. Q1: since I will not be investing in such a stock, cannot think of a particular reason. Eventually I will skip the remaining 3 questions for the same reason… Omg am gonna flunk in this midterm.!!

  13. 1) One should go for this investment as expected value of this investment is (-45*.20)+(20*.80)=7.
    2) If deal is not granted then only thing i will do is to sell the shares. Psychologically it wont affect me.
    3)can not name the bias but he is thinking more of downside without considering deal in favor of investor.
    4)By explaining him the logic that i gave as answer of first question.

  14. 1.Despite the possibility of a loss, I will invest in this opportunity because it has a positive expected value (after taking care of transaction costs).

    2.I will immediately sell the share in the market. I will try and control my emotional response to the loss by thinking of this opportunity as a part of several opportunities that I will encounter during my lifetime: I win some, I lose some. Over my lifetime, letting go any opportunity with a positive expected value (and not correlated to the market movements) will highly likely make me financially worse off.

    I will also ensure that the possible loss from this opportunity does not make me worry about my total wealth.

    3.Loss aversion (losses are twice as powerful, psychologically, as gains) and narrow framing.

    As Mr. Bazerman wrote in ‘Judgement in Managerial Decision Making’: The typical decision maker evaluates outcome relative to a neutral reference point. Consequently, the location of the reference point is critical to whether the decision is positively or negatively framed and affects the resulting risk preference of the decision maker….when facing a risky decision, you should identify your reference point. Next consider what other reference point exist, and whether they are just as reasonable. If the answer is yes, think about your decision from multiple perspectives and examine any contradictions that emerge. At this point, you will be prepared to make your decision with a full awareness of the alternative frames in which the problem could have been presented.”

    4.I will ask my friend to think like a trader who seeks such opportunity every day. While one bet may not work in his favour, a portfolio of such bets (uncorrelated to the market) will highly likely ensure that he is better off financially.

    I will also urge my friend to read Mr. Buffett’s letter to shareholders where one can see similarities between an insurance business and risk arbitrage. Berkshire 2011 letter to shareholders: “A sound insurance operation needs to adhere to four disciplines. It must (1) understand all exposures that might cause a policy to incur losses; (2) conservatively evaluate the likelihood of any exposure actually causing a loss and the probable cost if it does; (3) set a premium that will deliver a profit, on average, after both prospective loss costs and operating expenses are covered; and (4) be willing to walk away if the appropriate premium can’t be obtained.”

    NB: 100% of the aforesaid has been learnt from Prof. Bakshi (either through his blog and/or books/articles, recommended by him).

  15. Answer 1

    The expected annualised return from the transaction is 50% (calculated below). If the expected return of 50% is higher than any other competing investment opportunity, then investment should be made.
    Annualised Return = [Gain * p – Loss * (1-p)] / { Time period * Price paid }
    Expected gain = 20*0.8 = 16
    Expected loss = 30*0.2 = 6
    Expected value = 10
    Annualised return = 10/ {(90/360) * 80} = 50%

    Further, I think in this case a positive expected value (10) alone cannot justify making an investment because it fails to incorporate 2 key elements of this investment operation :

    1) time period involved – a higher time period can change the annualised return thus making a competing opportunity more attractive
    2) the price that you enter the trade – if price is lower then return will be higher, if price is higher return will be lower
    Therefore, we must look at the annualised return which incorporates both the elements.

    Answer 2

    As CCI approval is not granted I am going to realise a loss . A 50% return is based on a probability estimate of 80%. If the probability were to fall by 20% I will only break even in this trade ie no loss and no gain. Failure to get approval will mean the offer will be withdrawn. Probability falls to zero and stock price will go back to pre announcement price Rs 35.

    I have just lost money. Deprival super reaction is kicking in and I am going to feel miserable. Do Munger and Buffet feel so miserable after they have incurred a loss ? Probably not.

    I need to make sure that because of this loss I do not stop entering favourable opportunities in the future. (overweighing vivid and personal experience).
    Awareness of DSRS alone will help somewhat to reduce its impact.

    I know research shows people feel more misery (upto 2.5 times more) than joy for equivalent losses and gains. Therefore, I will now try to re-frame the loss scenario into a gain scenario to de-bias myself . Will I feel the same amount of joy for an equivalent gain ? No.

    Although I may now look foolish, but with the available information I had, I did not act foolishly. Therefore, I will think like a trader – you win some, you lose some. This investment is just one of the many (independent) small favourable gambles that I will make – so even though this one has resulted in a loss (despite favourable odds), repeatedly entering into such gambles over time will result in a positive pay-off.

    Answer 3

    Loss Aversion/DSRS . My friend is rejecting an investment where the odds are attractive. He is, therefore, thinking in possibilities and not in probabilities. Yes, the loss can materialise, but because of the possibility effect the anxiety of loss is much more. Therefore, he is viewing and pricing risk emotionally and allocating a much higher decision weight to the loss than the probability justifies. He wants to minimize his regret.

    Answer 4

    Ben Graham said that an investors worst enemy is likely to be himself. This is true in the case of my friend who is trying to minimise his regret. While minimising regret and maximising wealth may not be at odds, in this case they are – as my friend is motivated by loss aversion and is rejecting favourable trades.

    I will appeal to his interest and warn him the consequences of being motivated by loss aversion are severe – ” Loss aversion will financially and psychologically ruin you. It will make you into a lousy decision maker. All your friends who do not suffer from loss aversion will become richer, own better cars and gadgets and go on expensive holidays. They might even get a more attractive girlfriend(s)!”

    1. Motivated by a desire to minimize losses will increase the likelihood that you will follow the crowd.

    The reasoning is- if you don’t follow the crowd and are wrong, then not only will you suffer financial loss but also you will have to bear the psychological, emotional and social loss of seeing “similar others” enjoying their new found wealth.

    If you follow the crowd and the crowd is wrong, then atleast you have the comfort of knowing others share your financial misery. Regret and pain is a lot of less.

    2. Paradoxically, it will make you into a risk taker or gambler.

    In order to be consistent with your behaviour of avoiding losses, when faced with an actual loss scenario (assuming you actually own one), you will take unreasonable risks to avoid losses. You will not sell a loser or the bad choice in the small hope of an increase in value. By holding on to a mistake, not only will you incur a financial loss but also will be forgoing reinvestment opportunities elsewhere.

    3. You will expose yourself to misinfluence from other psychological models such as consistency and commitments ( as you have preference for stability over change), Endowment effect, Confirmation bias, Anchoring (anchored to changes in wealth rather than total wealth), Dopamine (constantly checking stock prices whether they have gone up or down to avoid losses) etc

    Finally, I will paraphrase what Khaneman said – Is this the only bet you will ever make in your life ? Is this your last bet in life ? As long as you don’t bet your entire financial worth in a single investment, you will come out OK even if you incur a loss. If you come out of the narrow frame of a single decision taken at a point in time and look more broadly – a portfolio or a series of gambles played over a long period of time with a positive expected value, you will allow probability to work in your favour and you will be financially better off. Be risk averse not loss averse.

    Overcoming DSRS is going to be difficult and will take a lot of training as evolution has programmed the desire for avoiding losses. So here are a few final anti-dotes: Ignore costs when deciding to sell, Reframe loss scenario to de-bias yourself and think like a trader (see answer 2).

  16. Assume that you are looking for opportunities which are uncorrelated to the market, why should you invest in this one?

    Ans. First about the trade in question: In terms of probability, this trade offers a positive pay off. If one assumes that if the deal is called off, one can exit the posn at Rs.50 per share, the expected annual return on such trades done many times over comes to around Rs.10 per share [0.8×20 + 0.2x(-30) = 10] on an investment of Rs.80 per share over a three month period (annualized gain ~ 50%) or around Rs.7 per share [0.8×20 + 0.2x(-45) = 7] in case the exit price if Rs.35 per share, on an investment of Rs.80 per share for 3 months giving an annualized gain of 35%. So yes, one should be looking to do such trades.

    Another way of looking at it is that if the exit price in the event of the deal being called off is Rs.50 per share, to break even on such a deal we will we need the success ratio to be atleast 60%! In this case, since the probability of success is 80%, there is every reason to undertake such transactions over and over again. Even if the exit price turns out to be Rs.35 per share, the required success ratio will have to be 70%…which is still less than the success rate in this example (i.e. 80%).

    Now, why do it? – Situations such as these are time bound binary outcomes. They are independent of the overall market and are dependent on only the deal specifics like a). return on investment upon completion, b). completion of the deal, and c). time involved in the completion. If done successfully over a period of time, risk arb can provide healthy absolute returns that are uncorrelated to the broader market with significantly lower volatility.

    In the above example, the trade has a positive pay off (potential yield on investment is greater than hurdle rate), it is time bound (i.e. 3 months) and lastly the only risk that needs to be assessed is that of the deal getting cancelled. Given that there is no counter offer and that the financing is also done, the only risk is that of clearnce from the CCI. And, given that the chance of it going through is 80%, the overall risk return profile of the trade is positive.

    How would you act if CCI approval was not granted and you have bought the shares? How would you psychologically respond to that situation?

    Ans.Sell, since the arb situation is now off the table.

    If your friend refuses to make this bet because of the loss scenario, what bias is he suffering from?

    Ans. I think its the size of the potential loss per share in the event of the deal being called off (-30 or -45) that is greater than the size of the potential gain (Rs.20 per share). Instead of thinking in terms of probability, he is thinking in terms of absolute size of the gain or loss.

    How would you help him over-come this bias?

    Ans. By running him through the probabilistic outcome of such transactions. Actually do the computations on paper for lets say 10 transactions with the said probabilities to show what kind of returns can be generated.

  17. Dear Sir,
    Regulatory Procedure are part and parcel of deal making, What I have noticed is these are time consuming and often the price movement on stocks are inferred as acceptance or rejection of offers.

    In most of the cases, the acquisition process follows these procedures
    a) You have to take permission from CCI
    b) You have to take permission from FIPB
    c) You get permission from SEBI

    I infer 2/3 things over here, the bid is not an FDI, where it will have to take permission of FIPB also. The bidders have also agreed to take over original promoters (No counter bids) or original promoters do not have majority.

    1) I feel we should invest in such scenarios because:

    These are my thoughts on this scenario

    a) If I look at only probability of 80 % acceptance and 20% rejection, the price arrived based on probability is Rs 84 /- (Selling Price 35(in case of rejection) and also cost of carry).
    Whereas it seems the market is giving it a lower probability of acceptance.
    b) As you have mentioned the money is lying in highly reputed bank and Investment bankers are highly trustworthy, it gives me inference that they are also professional and they would have done their homework (They would have consulted lawyers and CA about the outcome of CCI and FIPB.) The Competitor stakes are much bigger than mine.

    c) CCI will block the takeover if only it is convinced that it may create monopoly or it will hurt the interest and welfare of consumers else it will give go ahead.

    d) Most of the time till date; SEBI has given permission for open offer only after the acquirer gets permission from CCI and FIPB, and so if they have got SEBI permission for open offer, the road is clear. But there are 2 recent examples of conditional acceptance of offer by SEBI for FIPB approval

    2) If CCI does not give its approval, I will start selling in the market up to the price of 45 – 50 not below that, because market has the information that, there are buyers at higher price. Along with that I will try looking at reason of denial by CCI.
    If at all, they have put in terms for acceptance, then I might as well look at the terms. (Eg: In deal of United Sprits by Diageo, It is perceived that they will have to sell W & M stake to evade Competition laws)
    I will be unhappy losing money, vowing to be more cautious next time, but I will trade in such scenarios
    3) Is my friend suffering from Prospect theory of loss aversion?
    4) I will show him the probability of losing money and making money. Also I would explain him the “What if scenario” of the deal and also “I will show him my Trades to give him courage”.

    I would also like to share my experience
    a) Most of the time till date, SEBI has given permission for open offer only after the acquirer gets permission from CCI and FIPB but SEBI gave permission to B Braun for Ahlcon Pharma and Dashtag for Fulford without FIPB approval
    b) In case of Ahlcon Pharma, FIPB gave permissions after 4 deferrals, where I lost my patient and sold it in market. Also at that time there was no clarity of FDI in Pharma sector. Worth seeing the price movements along with regulatory confirmations
    c) In case of Fulford, I did participate and also got to take white swan event at Fulford increased the offer price. I did participate in open offer as the approval of Ahlcon had come in and government was ready to allow FDI in pharma sector
    Apart from these, I have not come across any instance where SEBI permission is there and FIPB or CCI acceptance is deal is not there
    Pedigree of acquires matters, I am sure you would have looked at delisting offer of Trangene Bio

    Jigam Gandhi

  18. Answer of Q1 -Investment of 100shares =80*100=8000
    Scenario 1 deal through -80% probability – gain on basis of 100 shares =100*20=2000 *80%=1600
    Scenario 2 –deal not through 20% probability –loss of =100*30 ( sold at 50) -3000*20%=600
    Overall scenario -2000 * 80% + (-3000)*20%=1600-600=1000 at the investment of 8K =12.5% in 3 month yearly means -12.5*4=50% yearly return
    Without deal if invested same sum of 8K in saving acc-5% -8000*5%*3/12=100 ( risk free return as invested for only 3 months)
    So overall return is 900

    Answer q2-if the deal is through -psychologically it depends upon how much of % of net worth I have invested
    I would not invest of assuming 0.5% of more of my net worth on same –which if loss –will result in to 3000/8000=37.5% of 0.5 % =3/8*.5%=.3% of loss –not much impact –can take risk
    Answers Q3 -he is thinking in terms of gain /loss ratio of 2000/ vs 3000 not in terms of probability number of 1600/600 gain loss ratio

    Answer Q4-by going through the past records of similar events in which CCI has rejected the deal
    By explaining equation

    Looking forward to corrections


  19. Ans 1. I shalln’t invest in this situation as the data provided here is not giving me a clear picture about valuations. I mean the fact that the competitor has offered Rs. 100 doesn’t substantiate the rapid surge in share price or give us a clear picture about changes in business structure or environment. Since, the data here in this equation is incomplete, I’ll not get invested. I’ll never get invested by somebody’s calculations or assumptions, even though thats by a player of the same field.

    Ans 2. Since, I’m not going to get invested, I don’t care for CCI’s verdict.

    Ans 3. He’s suffering from the same bias as I’m.

    Ans 4. I’ll not help him overcome this bias rather I’ll appreciate him.

  20. Hi Prof,

    I went through this experience in Ahlcon Parentarels .. Got out after having initially made up my mind that probability of the FIPB not clearing the deal was low. But as the exit clause of the buyer (6months for deal completion) came nearer and 3-4 times the FIPB rejected this case.. I was assigning a higher prob to shit happening hence quit with a loss of 3% absolute while expected gain was 11% ..


  21. 1. This is a special situation with a defined out come and schedule. The current interest rates for a safe investment at the best is about 11 to 12% (Fixed Deposit or Govt bonds or corporate bonds). For the three months we are looking at making a much higher annualized returns and is risk adjusted.

    2. Sell the stock as soon as the news is confirmed at a loss. Well if i were to do this a 10 times iam sure to win. Based on the expected value this was a positive transaction and over a larger sample set, it would have been a winner. Look for other opportunities with a similar payoff.

    3. Loss aversion bias. Losses hurt much more than the excitement he would feel if he wins. Losses stick more in the mind than an equivalent amount gained.

    4. So the explanation will be based on expected value.

    Initial Price 50 (Sell Price if the deal does not go through)
    CMP 80
    Offer 100
    time 90 days

    success 80%*20 = 16
    failure 20%*-30 = -6
    Expected Value = 10

    Returns could be about 144% annualized. If we do this say five times and win 4 out of 5 and given the returns you are bound to make a lot of money. Yes there might be losses but it will be easily compensated with other positive transaction. If the expected value were negative, we would never get into the transaction as the odds are against you. Using the explanation, try to overcome the loss aversion bias.

  22. 1. 25% returns for 3 months wait with the question why is the competitor paying such huge premium?
    2. Wait- there is a reason why even CCI is rejecting this deal. So second reason to stay invested and do more research. Secondly, the stock may go down below 35 because mass exodus.
    3. Conversative bias or technical chart bias? Sorry little I know about the biases.
    4. If the deal goes through we 25% profit within 3 months on gross level keeping aside taxes and brokerages.
    If the deal fails, there are 2 organisations which know more than us which keeping the deal to fall apart.

  23. Q1: Assume that you are looking for opportunities which are uncorrelated to the market, why should you invest in this one?

    Ans: Putting the thinking cap of various role models:

    Warren Buffet: Should think interms of probabilities * outcomes rather than outcomes alone ….. 0.8 * 25% gain – 0.2 * 37.5% loss = 12.5% gain …odds are in our favour….Should invest, however the amount of investment as % of portfolio should be such that incase of catastrophic loss, the portfolio is not effected….

    Daniel Kahneman: Assuming the probabilities and average selling price are assessed based on base rates and after overcoming WYSIATI and overconfidence…should invest as the odds are in our favour… we would be seeing many such odds in our lifetime, if we lose in this one, we will gain in another bet…..

    Nassim Taleb: The bet is exposed to negative black swans….since the upside is limited (Rs 100) and downside is unlimited (i.e. zero)….Shoudnt invest…

    Graham: Return of our money is more important that return on our money…There is no margin of safety…Should not invest….

    Myself: Would not invest, because this isnt my area of core competency and I can live with missed opportunities….

    Q2: How would you act if CCI approval was not granted and you have bought the shares? How would you psychologically respond to that situation? (10 marks)

    Ans: Would sell the shares booking the loss….however, would not feel bad, because though the outcome is bad, the process followed is good….

    Q3: If your friend refuses to make this bet because of the loss scenario, what bias is he suffering from?

    Ans: Loss aversion (doubling the probability of loss scenario and calculating the odds)…..or WYSIATI / Silent evidence (not seeing the future similar bets)….

    Q4: How would you help him over-come this bias?

    Ans: Converting the loss scenario into either gain or nil gain scenario….by asking him to invest 95% in FDs and 5% in this investment…The gain in the FD will more than compensate for the possible loss in the bet….

  24. 1. Given the probabilities of the two outcomes, by buying the stock at Rs.80, we have an 80% chance of making a profit of Rs.20 and a 20% chance of making a loss of Rs.30. The expected value works out to a profit of Rs.10, so the odds are favorable. And since the outcome is dependent on the decision taken by CCI, it is uncorrelated to market movements.

    One might argue that the upside in case of approval by CCI is uncorrelated to the market, but the downward move in case of non approval may be affected by market conditions and the stock might go below the pre offer price of Rs.35. So, how bad will the down move have to be in order to make the trade unattractive? I thought of what the outcome has to be to make the expected value of the profit zero. It turns out that the expected value will be zero only if the stock price goes all the way down to zero in case of non approval (0.8*20 + 0.2*(-80) = 0 ). And since that is the maximum loss possible, my expected value of profit will be positive no matter how severe the adverse outcome.
    With these odds, it is quite favorable to invest, even if I am a little wrong in my estimate about the average selling price of Rs.50 per share.
    2. Before buying the shares, we must be sure that we are willing and able to bear the loss in case of an adverse outcome. If the approval is not granted, there is no point in holding on to the shares unless there is reason to believe the stock is undervalued. We must beware of anchoring to the cost of Rs.80 which may prevent us from selling the shares at a loss.

    3. Our friend seems to be suffering from a Loss Aversion bias and Availability bias. He is overweighing the loss scenario and ignoring the probabilities, possibly due to a past experience that he remembers vividly.

    4. One could appeal to reason by pointing out the favorable odds offered in this opportunity and the rationality of buying the shares.
    The other way would be to use other biases to counteract his existing bias. By framing the situation in a different way, one might point out what a great opportunity he stands to lose and trigger a Deprival Super Reaction and/or invoke Scarcity by pointing out how unlikely he is to get another such opportunity.

  25. answer 1 – if i have invested for 100 shares (8000 rs).

    optimistic scenario i will get 100*100 =10000Rs 20% profit in 90 days
    if deal gets cancelled – pessimistic scenario i will get 35*100=3500Rs (5
    if deal gets cancelled – optimistic scenario i will get 50*100=5000Rs

    80% probability of deal approval
    20% probability of deal cancellation

    so pessimistic scenario – 80*100+20*35=8700 (8.75 % in 90 days i.e. 35% pa)
    so optimistic scenario – 80*100+20*50=9000 (12.5% in 90 days i.e. 50% pa)

    so on average i will make 35% to 50% money if i bet on a lot of such deals. this is reason i should/will invest in this kind of deals

    answer 2 – i have realized from my past experiences that i suffer from endowment bias so i will hold on to my investment forever (until one day for no reason i sell it off for whatever price i am getting or because of luck i get some 50-60% profit)

    answer 3 – my friend is suffering from Loss Aversion bias

    answer 4 – i would help him by showing him calculation done in answer 1.

    for me i will not be able to invest in this opportunity as it will be very difficult for me to determine probability of success of deal approval. i may not invest in a such opportunity because of reason in my answer 2.

  26. 1. The present risk arbitrage provides a very high expected return of 50% on annualized basis.
    It shall be worthwhile to take loan @ 12% p.a., in case no idle funds are available and invest in the present arbitrage.
    Since, it is very difficult to find opportunities to invest at expected return of 50% p.a.,
    I shall surely go for the transaction.

    2. Before awaiting CCI’s decision, I shall calculate Intrinsic value of the company. Assumed calculated intrinsic value to be Rs 35/-.
    After CCI approval was not granted I shall sell all my Co. A’s share, irrespective of its quoted price upto Rs 35/-.
    Below Rs 35/-, I shall look for other available opportunities, and shall probably shift to some other better opportunities in the absence of margin-of -safety in Co A’s share.
    By taking this decision, I shall try to avoid psychological traps of loss aversion, consistency, deprival syndrome, anchoring to wrong numbers, stress confusion and social proof (in case share price does not fall).

    3. My friend seems to suffer from loss aversion, which may stress him to mental confusion leading him to maintain status-quo position.
    He also seems to suffer from probability decision weight mismatch, leading him to assign lower probability of expected gains instead of expected 80%.
    There may be a case in which he has suffered losses in the market, the vividness or recency of which might prevent him to invest further. The pavlovian association of the loss situation along with the consistency bias and deprival syndrome to loose further might prevent him to invest further.
    All the above factors either singly or jointly may lead to lollapalloza effect to disable him to invest in this expected high return arbitrage.

    4. I shall try to explain him how investing in bunch of these expected high return situations might help him to be beneficial in the long run.
    Explaining him of the detrimental effects to his financial conditions of the above mentioned biases will be a step further.
    Referring him to Prof Sanjay Bakshi’s blog and his reference books, especially books of Influence and Poor Charlie’s Almanack along with Warren Buffet’s letters to his shareholders will hope-fully and permanently solve his above biases to make him a better investor.


  27. 1.Assume that you are looking for opportunities which are uncorrelated to the market, why should you invest in this one? (10 marks)
    – You should invest in this opportunity because the outcomes based on probability are weighed towards reward vs. risk. If you were to invest in this, you will make 80% * (100-80) = 16 Rs, while the probability based risk is 20% *(80-50) = 6 Rs. Hence you stand to make 16 Rs. vs losing 6 Rs. and hence on a risk reward basis one should invest in this.

    2.How would you act if CCI approval was not granted and you have bought the shares? How would you psychologically respond to that situation? (10 marks)
    – If CCI approval does not come through, you would decide to immediately sell the shares. Psychologically, you would decide never to bet on event driven events

    3.If your friend refuses to make this bet because of the loss scenario, what bias is he suffering from? (10 marks)
    Don’t know the answer

    4.How would you help him over-come this bias? (10 marks)
    Don’t know the answer

  28. Sir, Just a thought that occurred to my mind, you have mentioned above that

    “learning value investing because it requires a mindset of an unbiased, unemotional, and rational decision maker”.

    Can an inference be drawn that the Judges of the courts, who, after years of service learn and practice rational and un emotional thinking, have value investing as an alternate or Post retirement career option??…..:) Just a thought

  29. 1. Investing in company A still gives me an upside of 25% (Rs. 20 over Rs. 80). Since there is 80% probability that the deal will go through I would not mind take the bet though this would be termed as impulsive or behavioral decision. As a rational investor, I will look at the probability. Rs. 20 upside with a probability of 80% and Rs. 30 downside with a probability of 20%. Combined probability is Rs. 10 (20*.8-30*.2). Hence I will go for the offer. If this stock is traded in F&O, I will definitely look at buying puts if cost equation looks fine.
    2. Psychologically I will little bad but eventually this is a part of game. I will accept the decision and look for next opportunity.
    3. Not sure the technical names of biases but this would be termed as too concerned about losing wealth and would likely to miss out many opportunities.
    4. I would take him through couple of deals similar in nature to see the historical performance. I will tell him upside as well as risks that he carries. In all I will give him numerical calculation if he buys that.

  30. With an 80% chance of making a profit of 20 bucks and a 20% chance of incurring a loss of 30 bucks, the expected pay off in the trade is plus 10 which is a gross expected return of 12.5% over a period of 90 days or 50% annualized. Looks good but one needs to compare it with the risk free rate before taking a call on the trade. If the risk free rate is 30% per annum or more, it might not be worthwhile to invest in the given trade. Why to take unnecessary risk of permanent loss of capital and also reinvestment risk (since the given trade is only for 90 days while the risk free return can continue for an year) when the risk free rate itself is good enough ?

    The risk free rate is not given in the problem. Let’s assume it to be the going rate of 10% per annum. Now, does the trade make sense ? The trade offers an expected gross return of 12.5%; a maximum upside of 25% and the maximum downside of 37.5%. Even though the expected return compares favorably with the risk free rate, the range of outcomes is very wide. In my view of arbitrage, the risk of permanent loss of capital should be extremely low. Isn’t that the primary reason one is looking for arbitrage opportunities and not investing in the equity market? Losing 37.5% in a trade even though the probability might be 20% is not an acceptable scenario.

    It will also depend on the number of opportunities available in arbitrage sphere. How well is the list populated ? If there was only 1 arbitrage situation with the given odds, I would stay away from that. However, if instead of only 1 opportunity, the list is populated with let’s say 10 arbitrage opportunities with somewhat similar expected payoffs, then I would invest equally in all of them knowing that the probability and the expected values work well when the number of events is large.

    Just rephrasing the problem, would you bet on a single flip of a coin turning head ? It’s given that the coin turns heads 80% of the time. My answer would be no if the coin is going to be flipped only once. My answer would change to yes if the number of flipping attempts is large. Probability will eventually catch up.

    Now to objectively answer the questions :

    1. If the risk free rate is high and/ or the number of such arbitrage opportunities is limited to this trade alone, I wouldn’t invest in the trade.
    2. If I were to still buy the shares and CCI approval were not to come, I would sell all my shares at 50 bucks. Sunk costs are irrelevant and one shouldn’t let the idea develop new legs.
    3. No comments as I myself will refuse to make the bet under the given circumstances.
    4. No help needed. The friend doesn’t have any bias.


  31. 1) 80% probability of deal going through. Expected profits are 20*80% – 30*20% = INR 10. Provides annualised return of 50% b) money is blocked only for 90 days c) Though chances of appearing something better is remote, but the fact that only uncertainty is CCI approval provides some comfort.

    2) If CCI approval is not granted, I will immediately sell the shares because the reason for which it was bought is no longer present. I will not get anchored to the price at which I bought.

    3) Because of loss aversion and being anchored to the price at which he purchased the shares, he is refusing to book losses.

    4) Will explain him of the points mentioned in (3) and try to explain that loss is incurred the day we have made the investment and its only got confirmed today. Once the reason for which we bought the stock no longer remains, we should sell the stock

  32. 1. Why should I invest in this Opportunity?: Expected value of this operation is positive (0.8*20(gain in Rs)-0.2*45 (max loss in Rs.)=+7. If I consider that I will be able to sell @Rs. 50, then the EV becomes +10. In case of gain of Rs. 20, it turns out to be 25% returns in 3 months, i.e. 100% returns (before tax) in 1 year. That’s attractive.

    2. In case CCI approval is not granted: I will immediately sell the shares without thinking. Psychologically, I will feel bad, but would know that this possibility existed.
    3. He is suffering from loss aversion and/or first conclusion bias. Loss gives more pain than gains can give pleasure.
    4.Will making him aware of behavioural anomalies help? In reality I have tried to provide incentives for betting on such operation and offered profit sharing and taking the loss as mine. (All the loss is mine, profit will be shared equally if he invests). It did work but he is yet to give me the share of the profit! 🙂

    Thanks professor! Looking forward to participating in more complex problems!

  33. 1. We can invest in such a situation because the returns are uncorrelated with the return from the broader market. If the deal goes through, we make a profit of Rs 20 and if the deal does not go through, then we make a loss of Rs 30. These returns or losses do not depend on what the market activity is. Since there is an 80% chance that CCI will approve the deal, the expected profit is Rs 16 and the expected loss is Rs 6. Also, since this is not a buyback situation, all the shares to be given to company B will have to be accepted and hence, there is no risk of only a part of the shares offered to company B being accepted.

    2. Even if the deal does not go through, I would still think about the fact that if a competitor company is willing to pay Rs 100 for the whole company, surely it must be worth more than Rs 35, even though not exactly Rs 100. I would also think that if the CCI did not approve the deal, it surely must be because the industry is controlled by a few companies and hence, there must be some pricing power with companies in this industry. Hence, it would require a much more in depth analysis of this industry and the valuations of the companies in particular. Only then would I decide to sell the shares or hold them. The above answer mostly shows my psychological reaction as well. Remain unperturbed by the gyrations of the market and think numbers and probabilities.

    3. If my friend refuses to invest in this situation, he suffers from loss aversion and the tendency to not act when there is a certain amount of uncertainty in the market (maintain the status quo). He is seeing a loss of Rs 30 versus a profit of Rs 20 without considering the probabilities for the outcome of each one. Its like I have read in the book Influence by Robert Cialdini, that loss is more painful than joy of a small profit.

    4. To overcome this bias of his, I would show him the probabilistic calculations of loss and profit in such situations make him understand what kind of biases he is suffering from by giving examples of past situations and how it was profitable for others to take advantage of these biases. Like in the book How to Make Friends and Influence People by Dale Carnegie, if you want to convince someone, try to tell them in terms of what they will gain and what they will lose rather than just trying to change their mind by making them understand your view of it.

  34. Hello Sir,

    Thanks for posting the questions. This reply is my attempt to answer those questions.

    1. Assuming i am able to buy at current price i.e. 80/- per share, so if share price goes to 100/- in case everything goes right, whose probability is 80%, and if everything falls apart, i would be able to sell @ 50/-, so my expected gain/loss is
    = 0.8 * (100-80) + 0.2 * (50-80) = 0.8*20 – 0.2*30 = 16 – 6 = 10/- per share.

    If i remember correctly, WEB says that to judge any risk arbitrage opportunity, one should pay attention to following:
    a) What is the expected return
    b) Duration for which funds will be tied up
    c) What happens if the deal fails
    d) i m forgetting the last point 😦

    so my expected return is 10*100/80 = 12.5% for 90 days, i.e. 50% annualized. If there are no such opportunities in the market, i would like to invest in this situation.

    2. Since i would have made his investment operation based on the premise of successful acquisition, and that premise doesn’t hold true now, i would sell my holdings in case acquisition falls. As per Bob Rubin, one has to invest in many such kind of situations and out of 7, 1 to 1.5 situation don’t turn up as expected, i would think this is one of those 1-1.5 situations.

    3. My friend is looking at the loss of 30/- from 80/- to 50/- per share, magnitude of loss is what he is looking at, not the expected loss.

    Regarding type pf bias, i think availability bias, as loss of 30/- per share comes easily to mind, calculation of expected gain of 10/- per share takes effort.

    4. Ben Franklin said: “I you would persuade, appeal to interest, not to reason”, so i would show him first that in case deals goes through, result is 50% annualized gain, and then if he inquires, would show him how i got that figure.


    PS: Sir, please keep on posting such questions.

  35. Q1. Assume that you are looking for opportunities which are uncorrelated to the market, why should you invest in this one? (10 marks)

    A.1. I would assess the company as if there was no arbitrage opportunity to begin with. I would be interested to see where the bidder is seeing the value. I would ask myself the following questions:
    Is there inherent & solid real value in company-A or is the bidding competitor acting based on an enormous credit line and an ego to match?

    Would I buy the company in its entirety on a Rs 80 per share value?

    If it makes sense to buy at Rs.80, does it make sense to sell at just Rs.100, what if real value is many times the open-offer price?

    If it is rubbish at 80 and the only attraction is the Rs.20 upside, should I enter this trade and lose sleep for 2-3 months fearing an adverse development?

    (By the way… If it is gambling that I am after should I instead get 2 tickets booked for Macau, for me and my friend which would be more exciting? )

    If company A is a good value buy at Rs 80 based on the answers to my above questions, I would happily invest up-to 70% of my investable cash, otherwise I’m not touching it.

    Q.2. How would you act if CCI approval was not granted and you have bought the shares? How would you psychologically respond to that situation? (10 marks)

    A.2. If I decide on buying Company A at Rs. 80 (based on reasons in Ans.1) then the adverse outcome of the CCI approval not coming through, or any other unknown-known’s like a court case, political involvements, etc. which may delay or stop the take-over, would not be of any concern to me. I would then wait for the price to revert back to Rs.35 where I would slowly start deploying my remaining 30% invest-able cash, which would bring my buying to Rs 66 – 67 per share.

    Q.3. If your friend refuses to make this bet because of the loss scenario, what bias is he suffering from? (10 marks)

    A.3. By looking at the situation his mind immediately thinks:
    Okay competitor is willing to buy share @ Rs100
    Share is available @ Rs80
    But Wait,
    CCI approval is not there??? WARNING (in RED)
    Money is there in Escrow but what if approval is not given?
    Share started moving from Rs.35, what if it starts falling again if approval is not granted? RISK hai boss… Maybe low proabability, but there is RISK??
    Who can predict the government departments?? FORGET IT??

    Bias No:1 He would be suffering from bias due to “Loss Aversion”. In his mind the fear of a possible loss is twice as powerful as a similar gain. In this case the Loss scenario is 38% with a 20% probability and a chance for profit is 25% with a 80% probability. He is not able to divert his mind from the 2 out of 10 chance of making that 38% loss. Assuming he is a normal irrational creature of emotion, to him this 80:20 chance of making a profit feels more like a 60:40 type chance.
    In non-numeric terms the small profit appears even smaller when compared with an equal amount of loss.

    Bias No:2 He is suffering from “Availability Heuristic” as he is basing his assessment of the situation and its consequences on the most easily available facts i.e. without making any efforts to dig deeper. Not just basing, rather his mind has assumed that whatever information is available on the face of it is the most important thing to know which causes his thoughts to just focused only on what is supplied to him. (This is how the magician does the “taking the watch off your wrist” trick.)

    Q.4. How would you help him over-come this bias? (10 marks)

    A.4. I would tell him that “Risk comes from not knowing what you are Doing”.
    Assuming that I am convinced of buying company A at Rs.80 myself, I would first of all tell him to forget all about there being any open offer to start with so that he can make an UN-BIASED study of the company. Then I would share my reasoning and my assessment of the intrinsic value of Co.A. I will tell him that he should invest in the Company A hoping not FOR but rather AGAINST the CCI approval going through, in which case we would be getting the company at an ever better price.

    Then I would go with him on a non-gambling vacation to Macau 😉

  36. Dear Prof. I don’t have detailed answer for your questions. I would though purchase the share at Rs. 55 Max. Is there any way to follow the posts for future comments (without commenting on the post)?

  37. Sir,

    . A.) I ‘d be investing in this particular special situation. As it is given that only CCI controls the approval of the deal.

    Estimated probability that CCI will approve the deal is 80%. It gives Rs.16 (80% of 20 the profit) in 90 days. So, ROI is 20% for 90 days.

    And the probability that CCI will not approve is 20%. And We can average out in selling around Rs 50. Loss is 30. Applying the probability of 20% we get the expected value of that event is (-Rs 6) giving negative ROI of 7.5%.

    This is the first thought occurred to me, may be this is called first conclusion bias. And I think, Vividness bias can be the reason for my friend’s backing off from investing in it.

    This is Syed Raeez. I am a big fan of yours, and you are one of my role models

  38. Here are the responses:

    1. This is like a special situations or “work-outs” opportunity to use the terminology of Buffett. Here the financial results depend on the corporate action rather than demand and supply factors created by buyers and sellers of securities. Thus, if I am looking for opportunities which are uncorrelated to the market, this would fit the bill.

    2. I would keep my cost of acquisition out of the picture while evaluating in such a scenario. I would try to work out the intrinsic value of the share as per my estimate considering reasonable margin of safety. If the current market price is below that value, I would probably decide to hold on to the share for some time. However, if the price is over my value estimate, I would sell.

    3. Loss aversion bias or Deprival Super Reaction Syndrome.

    4. Give him the facts…probability, downside, upside, intrinsic value of the shares etc. Tell him to limit his downside by having a stop loss order (to take away his fear that he might lose everything)…else I can even underwrite his investment for an appropriate premium.

  39. 1. Assume that you are looking for opportunities which are uncorrelated to the market, why should you invest in this one?

    The probability weighted price comes to Rs.90 (i.e. 100 * 0.8 + 50 * 0.2). Thus this comes to an annualized return of 50% (Rs.10 on 80 for three months, thus 10 / 80 * 12 /3). A 50% percent return is a very good return and thus this is a very good opportunity which must be invested in.

    2. How would you act if CCI approval was not granted and you have bought the shares? How would you psychologically respond to that situation?

    I would sell off the shares. The investment in this situation was made only for the reason of risk arbitrage. Since the investment was not made on the underlying financials or other considerations, and the situation didn’t work as expected, thus the shares should be sold off.

    Also, the probability of price reaching back to Rs.35 (its original price) will play its role too, and thus it would be better to sell off the shares at 50.

    3. If your friend refuses to make this bet because of the loss scenario, what bias is he suffering from?

    “A Fear of losing a dollar hurts more than the joy of gaining 80 cents.”

    The friend is suffering from the bias of ignoring the probabilities. Though on absolute terms, the downside risk is of 150% (annualized) while the upside opportunity is 100% (annualized); the probabilities of the downside are only 0.2.

    4. How would you help him over-come this bias?

    Showing the calculations from the answer to the first question might help him over-come the bias. The risk-probability weighted price comes to Rs.90, while the current price is of Rs.80.

    Thank you sir for sharing this wonderful example of risk-arbitrage. Looking forward to more such questions.


  40. Q1. Assume that you are looking for opportunities which are uncorrelated to the market, why should you invest in this one?
    A1. Given that there is a 80% probability of CCI approving the deal, the probablistic price comes out as 90 (0.80*100 + 0.20*50) and assuming that the cost is 80 with minimal transaction costs, yes I would invest in this one.

    Q2. How would you act if CCI approval was not granted and you have bought the shares? How would you psychologically respond to that situation?
    A2. Easier to answer to difficult to realise until in the exact real situation !
    I might look backwards for signs that were signalling that CCI approval may not actually come in. (opp. to hindsight bias I suppose) and would attempt to get out of the position asap.

    Q3. If your friend refuses to make this bet because of the loss scenario, what bias is he suffering from?
    A3. Regret avoidance bias or the loss aversion bias

    Q4. How would you help him over-come this bias?
    A4. not sure…may be give some examples of such deals which were successful in the past

  41. Hi Prof,

    1. The payoff on this trade works out to 12.5% absolute returns. 80% probability of making 25% returns + 20% probability of losing 37.5% = (80%*25%)+(20%*-37.5%)= 12.5%. This translates to returns of 50% annualized over the 90 day period. The trade is attractive under the given assumptions.
    2. Would sell immd if CCI approval does not come through. Would not confuse a special situation with a long term investment. Book losses and get out.
    3. He is suffering from loss aversion. The chance of a 7.5% loss (20%*-37.5%) weighs more on him than the chance of a gain of 20% (80%*25%)
    4. Assuming that there is consensus between us on the probability as assumed, he can be told that the stock would need to fall to 0 to lose arithmetically on the trade. The 20% gain as computed above can only be wiped out if there is a 20% probability of running up losses of 100%. For those looking at opportunity cost, if the stock falls to 8Rs, you still make 8% annualized return. At the same time would remind him of the anchor of stock price of Rs 35/- at the time of announcement and the low chance of the stock falling below that price. In reality however, this is akin to saying that a person with a height of 5ft cannot drown in a pool with an average depth of 4 ft. One ignores that you need to look at the maximum depth.

    The same situation had arisen recently in a stock called Ahlcon Parenteral, wherein the acquirers (B Braun) went ahead with the open offer inspite of the lack of FIPB approvals. They held the payment in abeyance after accepting the tendered shares till they received the approvals and had the right to return the shares in case of FIPB rejection. While the probabilities were probably as high as assumed in this example, the returns on the table were not as attractive.Also the downside seemed higher. Thus gave it a miss. The other question i struggled with at the time is even if you accept the odds what % of the portfolio should you allocate towards this idea. A meaningful weight could result in drowning in the pool if things go wrong. A small weight would only give an emotional high but no meaningful gains. Was reminded of Warren Buffets quote of picking pennies before the steamroller. Any thoughts on the subject??

  42. 1. Assume that you are looking for opportunities which are uncorrelated to the market, why should you invest in this one?

    If we assume that the risk arbitrage findings are correct, this is a situation that can be evaluated unbiased and unemotionally by pure mathematics.
    Our upside is Rs 20 which materializes 80% of the time. Our down side has a probability of 20% and results in Rs -30. Therefore our expected value is:
    (Rs 20 * 80%) + (Rs -30 * 20%) = 16 – 6 = Rs 10 per share. This is a return of 12,5% in just 3 months or 50% annualized, which obviously is very good. This is why we would want to invest in this risk arbitrage situation. As long as the expected value of the risk arbitrage is greater than our expected value from our other investment alternatives, the risk arbitrage situation is going to be attractive.

    Answering this question is quite straight forward when we rely on math only and rely 100% on certain assumptions. Additional thoughts and questions arising and answering before we go ahead and place our buy-orders would be in order.

    How much should we invest? Well, this would be a product of the expected value – the higher the EV, the higher the investment. We would also have to take a closer look at how much we stand to loose when the deal falls through. Clearly it wouldn’t be wise investing 100% of our funds knowing we would loose it all 20% of the time.

    Another important issue is how certain we really can be that the deal will materialize 80% of the time. If it only materializes 60% of the time our expected value would be zero. Also, we expect to sell for an average price of Rs 50 if the deal falls through. What if this is too optimistic…?
    These concerns show why it is really important to be humble and acknowledge that you could be wrong [beware of overconfidence bias] and thus always insist on a margin of safety when investing.

    2. How would you act if CCI approval was not granted and you have bought the shares? How would you psychologically respond to that situation?

    If the approval was not granted we should follow our plan which was based upon our findings, i.e. we should sell our (overpriced and risky) shares as soon as possible as they are expected to plummet to Rs 35.

    Loosing a coin-flip is to be expected, but loosing a 80/20 is harder to take – that feels unlucky (…and truth be told is a little bit unlucky). So we’re feeling sorry for ourselves, because we might have felt entitled to win on this investment even though we were bound to loose 1 out of 5 times or 200 out of a 1000 times!
    Our misery might even lead us to regret having invested and swear never to invest in risk arbitrage again, even though our analysis proved that the investment had very attractive expected value. So we – human beings – are heavily influenced by the results we get. This is of course the wrong way to go about things. Instead we should focus on our processes. If we do that and get unlucky, so be it. Long term we are going to be a lot better off concentrating on process rather than results, since results are derived by our process.

    3-4. If your friend refuses to make this bet because of the loss scenario, what bias is he suffering from? How would you help him over-come this bias?
    Our friend would be suffering from loss aversion – the fear of loosing for example Rs 100 is greater than the joy of winning that amount. He could also be suffering from risk aversion, which is a preference towards investments that are more certain but have lower expected payoff rather than the uncertainty of the bargain investment. He could also suffer from regret aversion which is the fear of experiencing the pain of regret.

    I would try to educate him. With the help of math I would explain and show him the expected value of the investment. I would also talk to him about the different biases and how they are hurting his long-term results.


  43. Hi Mr. Sanjay,

    Please consider my answers as from an individual small investor (neither a management student nor a professional) with an open-book.
    1. Yes. In my understanding, this merger risk arbitrage opportunity should be generally considered uncorrelated to the market as the deal is mostly dependent on CCI approval (this approval action is uncorrelated to market as they are probably done based on CCI’s internal guidelines on market concentration). Alternately, M&A activity is usually high only during market booms and hence this opportunity is uncorrelated only if there are not many such opportunities (even then, it can be safely assumed all these opportunities put together is still much smaller than overall market activity). The investment return probability of [12.5% – 3 month interest] (using the findings) is satisfactory returns for this opportunity that will mature in 3 months.
    2. As a Risk Arbitrager who understood the risks and the probability of loss before investing, I would first try to sell all the shares which can expected be completed at the original estimate leading to a loss of 37.5% of principal over the invested period. Alternatively, I can perform fundamental analysis of the company to understand the intrinsic value of the business which might be higher than the pre-deal price considering that one competitor was willing to pay a premium of 185%. I can also analyze other parties (foreign companies/investors) who might be willing to acquire the company at the offer price. Psychologically, I might exhibit ‘regret’ of loss (even though I calculated the loss probability before investing), exhibit ‘commitment tendency’ and ‘Anchor’ at 100 and not sell after CCI disapproval (even if analysis shows that the price will not reach 80 anytime soon).
    3. After agreeing to the findings and return estimate, if one is refusing to invest in the opportunity even when they do not have other opportunities for higher return on their capital, then they can be considered as exhibiting ‘Loss Aversion’ bias since they are confusing calculated probability of losing some part of capital with the ‘chance of losing invested money’.
    4. To help the friend overcome ‘Loss Aversion’ bias, I would first help the friend understand the findings until he is agree with the probability or able to come up with his own probability of deal closure using which he can calculate return estimate. If the return estimate is above this threshold, he should invest in this opportunity. I could also highlight historical data on CCI approvals on similar merger deal to reinforce 80% probability finding.

    Thanks for the opportunity.


  44. Respected Professor,

    Here is my submission on the Case study :

    Ans 1 : Considering the Graham’s formula on Risk Arbitage(as mentioned in Security Analysis), the indicated annual return on the deal is coming out to be 50 %. Taking the cue from Kelly’s Criterion, I will bet 50% of my bank roll on this event.

    Ans 2 : In case the CCI doesn’t approves, I would have to square off the transaction as this being a All cash deal.

    In this deal, I am betting for Rs. 20 profit ( Rs. 100 – Rs. 80) against the probable loss of Rs.30 (Rs. 80 – Rs. 50), so in order to break even, the probability of success should be 60 % (viz Rs.30 / (Rs. 30 + Rs. 50)). With the success chances of 80%, I consider this opportunity.

    Ans 3 : Sorry Professor, being a novice value investor, I have not graduated upto mental model level. I dont know the exact terminology for the mental model, but in layman terms, here one will the face the bias of overfearing the apparent numerical loss, despite of the fact that in probabilistic terms, the deal is more profitable.

    Ans 4 : Will let him wait and see me making profit in this deal. He will automatically be free from all biases then. Jokes apart, I dont know the answer to the question.

    Awaiting your guidance !

    Abhishek Chaturvedi
    +91 9909984595

  45. Dear Prof,

    Since I have the luxury of not bothering about the marks, I simply went through a thought stream and tried to capture the questions within that. It also led me to some extensions that were probably not meant to be there. Hopefully, you won’t mind.

    So here’s how I thought about it:

    First, what is the payout matrix 90 days hence, as per data provided:
    – 80% chance to earn Rs 100 per share if CCI approves
    – 20% chance to earn Rs 50 per share if CCI does not approve

    What is the fair value 90 days hence? It is Rs 90 per share (80% x 100 + 20% x 50).

    [Q1] So what is the expected return if I buy today at 80? It is 12.5% (Rs 10 gain on Rs 80 invested) in 90 days which is a very attractive return.

    Is it right to assume that the bet is uncorrelated to the market? What in the payout matrix can be impacted by market movements? It would be fair to assume that market movements have little bearing on CCI approving or not. The factor that may be impacted by the market movements is our selling price in case CCI does not approve as market movements may impact the price we get while getting out of the transaction.

    So how to think about that – What’s the absolute worst case scenario in case CCI does not approve? It is that we get back nothing (big market crash, company goes bankrupt). In that case we loose Rs 80 per share. But we are interested in the expected value, and the expected value of transaction in that scenario is Rs 80 per share, so we still do not have a loss on expected value basis.

    If we have a hurdle rate of 20% per annum, what price do we need to realize while selling (in case CCI does not approve) to beat our hurdle rate on an expected value basis? This means a 5% expected return in 90 days. So need to realize an average selling price of Rs 20. (100 * 80% + 20 * 20% = 84 which gives positive return of 4, or 5% in 90 days). Based on data provided, we should easily beat this.

    [Q3] Why are we focusing on expected value and not on absolute gains and losses? Well, the answer to that is that this is going to be a part of multiple bets we are going to make. We are not going to bet the house on a single bet. So the right way to think about the bet is as part of a collection of bets. This also helps avoid loss aversion given that the psychological impact of losses is twice that of the gains which prevents us from making some bets that make sense when thought of as a collection. In a collection of independent bets, the outcome of a single bet does not matter as much as how we think it would when we consider them individually.

    Why does the outcome of a single bet not matter? Well, as per the law of large numbers, in a set of large number of independent trials, the outcome will be close to the expected value and will come closer to it as the number of trials increase. So if we are going to make many such bets, then the right way is to think about expected value. And as the number of trials increase, the probability of deviating from expected value will reduce.

    To make this clearer, think about what are the chances of loosing money in a diversified pool of such bets, assuming the payout matrix as above (80% chance of Rs 20 gain and 20% chance of Rs 30 loss). In a single bet, we know that there is a 20% probability of loosing money. What about 3 such bets investing 33% in each? To loose money in this scenario, at the min 2 bets need to go bad (if only 1 bet goes bad, we make 40 and loose 30 for a net positive). So what are the odds of that? The chance of all 3 bets going bad is 0.2 x 0.2 x 0.2, and the chance of 2 bets going bad is 3 x 0.2 x 0.2 x 0.8, so the chance that 2 or more go bad is .008 + .096 = .104, or 10%. Thus for a pool of 3 independent transactions, the chance of having a loss is down to 10%. We can reduce the odds of actual loss to minimal by further increasing the number of bets. Similarly, the odds of outperforming the expected value will reduce too and the result of such operations will come close to the expected value.

    What else are we missing? Well, we haven’t really thought about the intrinsic value of the business. The business was selling at Rs 35 per share, but there is a private buyer who is assigning a value of Rs 100 per share to the whole business. He may be crazy to provide this value, but it makes sense to investigate the true value given the large disparity between market assessment and buyer assessment.

    So maybe the intrinsic value of the business is between 35 and 100. How does this impact our assessment? There are 2 broad impacts –
    1. It changes the expected value computation. But given that we already find the bet attractive, and it will simply improve the outcome matrix, so we need not think about that further.
    2. It can impact behavior in case CCI does not approve the transaction. To better understand this, let us assume that we study the business and arrive at an intrinsic value of 80 and see a reasonable chance of a catalyst acting within next 3-4 years (this price of 80 may not be very off in a realistic scenario given that private buyers tend to pay a premium for cash flow control, plus various behavioral biases edge them on to pay a little higher than value). Now let us assume we typically buy businesses at 50% discount to intrinsic value and sell at about 80% or above to intrinsic value. So in this case, if CCI does not approve, we will quickly start selling as much as we can, but if the price keeps falling, at some point we may stop selling, and around Rs 40 per share, may become a buyer again. Of course, this depends on the other long term opportunities on hand.

    [Q2] What if we are unable to value the business? In that case, we should simply sell as quickly as possible.

    What are the biases that may impact our selling in case CCI does not approve and I am unable to value the business? Psychologically speaking, one would need to overcome biases that may prevent acting quickly and decisively. The typical biases and how they act can be enumerated as:
    – Anchoring plus Endowment effect: the moment we’d own the shares, we’d start valuing them higher and tend to forget about the reasons we bought them for. This may make it difficult to part with them below the price we bought them at.
    – Loss aversion plus Denial: It is difficult to take losses since they hurt more than the gain, and the typical response is denial. In case CCI does not approve, instead of simply accepting a bet gone wrong, we’ll try to imagine scenarios to justify an intrinsic value in our head that is higher than the price we bought at. Thus we’ll be inclined to hold on to the shares till we at least are able to recover our invested amount.

    How to think around these? The right way to think is to focus on the payout matrix and expected value of the transaction. Once we update the new information of CCI not approving, the payout matrix changes as:
    – 0% chance to earn Rs 100,
    – 100% chance to earn Rs 50 (and this Rs 50 keeps falling as the price falls, we can keep it somewhere between current price and 35)
    The expected value will thus continuously remain below the current price. Keeping this payout matrix in mind will help have the right perspective to sell quickly.

    What are the other assumptions in the payout matrix? The one other assumptions in the payout matrix are 80% chances of success and on timeliness of CCI approval (within 90 days). If we suitably base them on past data, we can go by them.

  46. My answers –

    1. Considering the findings arrived at, this would indeed be an opportunity worth investing in as one of many such bets. That’s because it is a situation in which thorough analysis indicates the odds to be in favour of the investor. By virtue of this, investing in multiple such similar opportunities promises safety of capital and a satisfactory return.

    The numbers show that having an 80% chance of a 25% gain (from Rs 80 to Rs 100) along with a 20% chance of a 37.5% loss (from Rs 80 to Rs 50) yields an expected overall return of 12.5%, over 90 days. Which is an effective return of about 60% when compounded over a year. Even if one may not have 4 consecutive such situations to invest in over a year, it does indicate that this opportunity is a good home for one’s money for those 90 days. What’s more, at an effective annual yield of 40% if the shares were to fall back to their pre-offer price of Rs 35 instead of Rs 50, it would still be a good opportunity, all the more making it a favourable situation.

    Of course, the assumption that one is looking for opportunities which are uncorrelated to the market is important as deciding to invest in it would also be dependent on the returns offered in other opportunities existing at the time. If stocks are selling low enough (and thus promise better returns), then one may be better off choosing them instead.

    2. If CCI approval is not granted, I would sell the shares immediately. Even if they happen to fall to a level lower than the Rs 50 that I had estimated I would be able to sell my shares at.

    To make it psychologically easier to sell at a loss, I would remind myself that the original thesis for buying the shares did not include speculating on short-term price fluctuations of the stock, and holding on to the shares any longer would in fact amount to that. The negative outcome was just a natural statistical outcome, and it by itself does not indicate that the decision to invest was a bad one. One might be tempted to look back and speculate on whether one made a mistake in estimating the odds of an approval by the CCI as 80%. But after the fact, one’s thought process is quite likely to be suffering from hindsight bias while doing so.

    3. If my friend refuses to make this bet because of the loss scenario, he would be suffering from loss aversion bias. He is psychologically overemphasizing the negative value of the loss scenario, and under-emphasizing the positive value of profit scenario. Despite the fact that rational calculations show that the profit scenario, if weighted for the indicated probabilities, will more than compensate for the loss scenario when many such similar bets are made.

    4. I would attempt to help him overcome this bias by showing him how a loss in an investment is not necessarily a bad thing if such an investment is also accompanied by the prospect of a profit whose probability and quantum more than compensate for the loss scenario. I would tell him that in such situations, a loss in any individual case is a necessary evil. One cannot reap the benefits of the overall odds which may be favourable if solely focused on avoiding any and all losses. There are no absolute certainties, and in the absence of absolute certainties, all decisions are about probabilities. The search for absolute certainties is an unrealistic one.

  47. Dear Prof.
    i do not think that i have enough tools/devices/knowledge to answer your questions in a more technical manner which would have befitted the kind of your writings…but i am trying to apply some of my common (sic) sense….which i think/know i have a little bit….
    so here are the answers…
    1) Assume that you are looking for opportunities which are uncorrelated to the market, why should you invest in this one? (10 marks)
    Ans) if i am looking for uncorrelated market opportunities then this is the one as the bid is binding and is deposited in a trustworthy escrow a/c. These two things make the price target independent of the news flows and completely in the realm of logical thinking.
    So if the bid goes through (80% chances) then then i will be able to make a profit of 25% in 90 days or an annualised return of 100%. suppose if were to invest Rs. 8000 to buy 100 shares of the target then i will make Rs. 2000 straight. If i deposited the same in a bank FD for the same period then depending on the prevalent interest rates i would get peanuts (Rs 157.8 for 8%pa; 197 fro 10%; 236 fro 125 and 295 fro 15%). Now taking in the probability and quantum of loss along with that of profit:
    80% chances of profit of Rs. 2000 makes it Rs. 1600 (2000*80/100)
    20% chances of loss of Rs. 3000 (100 shares sold at 50 or loss of 30 per share) makes it Rs. 600 (3000*20/100)
    Therefore, i stand to gain a net profit of Rs. 1400 with 80% probability again a return of 17.5% in 90 days or 70& annualised. So i will take this bet, but will mark only 10% of the investible surplus in this GAMBLE.

    2) How would you act if CCI approval was not granted and you have bought the shares? How would you psychologically respond to that situation? (10 marks)
    Ans) Before giving the answer to this question i would like to confess that my first thought was this (which is not my answer) — If have bought the shares of A, after that much logical thought process then, the day the CCI verdict is pending, I will start my day with a strict stop loss at different levels starting with 70 and going up to 50…..
    Now the answer: If company B, which being competitor of A deems it fit for a hostile bid at Rs. 100 (at almost thrice the price) and also knows very well (at least more than me) about the sector they operate in, then I would also put a premium on the book value of A. Let us assume that the earlier price of Rs. 35 was close enough to the book value of A, then also there is a very strong fundamental reason to stick with the shares of this company. The CCI will reject this offer most likely because the proposed merged entity would become too big in the market to control it dominantly, it means A and B are among themselves very big already. I would now assume that the value of A must be between 1.5x (close to Rs. 50 or cut off in answer) and 2.5x ( Rs. 87.5). This is assumption as i do not know about financials of A. With this i would research the sector, the company and the policies in the sector a bit more (which probably i should be doing in the 90 days cool off period to save later pains). If on my research i find the stock interesting m then i may keep it for a longer term and if not then would sell it at Rs. 50 per and book my losses.

    3) If your friend refuses to make this bet because of the loss scenario, what bias is he suffering from? (10 marks)
    Ans) I cannot think (remember) a name for the bias but would try to explain it by symptoms – being from a family of teachers and lawyers of middle class i know it as the fear of loosing the capital. this fear makes one sit tight on cash even if it looses value due to inflation and more so the fear of uncertainties due to lack of knowledge and metal aptitude to think within the box.

    4) How would you help him over-come this bias? (10 marks)
    Ans) I would have two options (i) to sell him the risk-reward calculation done above in answer to #2; and (ii) if the sum involved (final loss) is not a very big sum then i can promise him that i can make his losses good up to an extent (say 50%) to give him confidence in me.


    thanks prof. for writing such thought provoking posts that are helpful in not only money matters but otherwise as well.
    regards 😀

  48. 1. At a price of INR 80, there is a 80% chance of gain of INR 20 and 20% chance of loss of INR 30. Therefore, probabilistically there is a gain of INR 10 on INR 80. This equals a gain of 12.5% in 90 days. This is higher than the gain I can expect from the market in a 90-day period. Thus, I will invest in this opportunity.

    2. Psychologically, I will cut my losses and sell the shares as soon as possible.

    That said, it may make more sense to work out intrinsic value of the company’s stock as well when analysing this opportunity. If there is a margin of safety at a price of INR 80, or lower, I can hold or buy more shares while people are selling.

    3. Loss aversion bias. A possible loss of INR 30 which is greater than a gain of INR 20 may result in my friend passing on this opportunity.

    4. We can explain the loss aversion bias to my friend. We can also share the probability-based analysis to show that it is a favorable bet to take.

  49. Socratic Mind at Work

    1. The stock was trading at Rs. 35. Was Mr. Market correct in valuing the business?

    2. If yes, why is the Competitor bidding a premium of 185% and willing to pay Rs. 100 for such a business?

    3. Well, I think I know the answer to this one. Looking at the base rates, most of the acquisitions, are a result of an over-confident management, enhanced projections of the future and over-optimist expectations.

    4. If I buy the shares and the above hypothesis is true and the Deal doesn’t go through, I will be left with shares of a company whose business is sloppy. In this case I would be looking at a potential loss of Rs. 30 (or more, if I decide not to sell). Ok.

    5. Back to Point 1. But what if Mr. Market has incorrectly valued the business at Rs. 35/share. In this case, the Competitor is really smart. And if he’s valuing the business at Rs. 100/share, then there must be really something in it. What am I missing? (A possible gain of Rs. 20. Wow!!)

    6. But wait a minute. If there is a real value in the business, why aren’t there any other bidders who are willing to pay a higher price?

    7. Maybe all of them are dumb (highly unlikely) or maybe there aren’t any other bidders/competitors around. If there isn’t anybody else, and only these are the 2 companies around, wouldn’t this lead CCI to reject the offer?

    8. Coming back to Point no. 5 & 6. Assuming there are a few competitors around and that no one is willing to pay a higher price than 100, meaning that the intrinsic value (as assumed by them) seems to be under 100. Say Rs. 80.

    9. If that’s the case, could it be that the Competitor is really smart. He’s put up an offer of Rs. 100 which he is pretty that he won’t have to pay up because there is no way that CCI would allow the deal to go through (for whatever reasons)? If that’s the case, the stock price will plummet back to the levels of Rs. 50.(A loss of Rs. 30). But why would a competitor do that and force the prices up of his rival by more than 100%. Guess he really sees some value in the business after all.

    10. Will someone else have a look at the company then, and provide an offer again? If such a scenario does happen, what would be the price offered then? How long will it take for the entire deal to happen? Maybe another 6-8 months? Would it be prudent to buy at current levels of Rs. 80 and wait for such a scenario (huge uncertainty) with a long holding period? (Huge uncertainty + Long Holding Period + No returns)

    11. Back to point no. 8. If the deal doesn’t go through, and the intrinsic value is Rs. 80. Would there be some other means by which the management will be forced to unlock the value? Would there be some activists/realization on part of the company/buyback program?

    Generally, low down side risk combined with high uncertainties result in huge “possibilities” of profits. But in this case the down side risk isn’t low. Rather if you focus on magnitudes it is +20 v/s -30.

    Combining this with the frequencies, the expected value comes out to be +10.(if I buy the stock)

    Does it make any sense for me to short the stock? Should I take a Short position?

    Suppose I short the stock…Lets say the CCI rejects the Deal (20% probability) , my upside is +30 atleast, if CCI doesn’t and the deal goes through, I would have to cover up my position at around 85-90 levels. So a 80% probability of say Rs. 10 loss.

    Expected Value with a Short Position = Loss of Rs. 2.

    I Guess on paper and thinking about this virtually, I’d be ready to short the stock!!

    Answer to the questions which were asked:

    Q1) It makes sense to invest (either a buy/short) in such an opportunity since it provides the investor an opportunity to earn a reasonable percentage return over a very short holding period, thus increasing the holding period return.

    Additionally, the chance of deal going through is 80% and thereafter presence of no major roadblocks makes the entire operation dependent on success/failure of just one event.

    Thus, the only decision which an investor has to make is between an expected gain of Rs. 20/share (80%) v/s an expected loss of Rs. 30/share(20%). (provided he has bought the shares)

    Or a choice between Rs. +30/share (20% prob) v/s Rs. -15/share (80%) (provided he has taken a short position)

    Q2) Assuming I have bought the shares, a few mental models come into play here. This would have been the way I would have thought a few months ago:

    Psychological Denial: It doesn’t matter CCI has rejected the Deal. The Competitor has rightly valued the business at Rs. 100/share and the stock sooner rather than later will definitely trade at that value. I will not sell my shares at a loss no matter what. I have made a sound investment.

    Near Miss: I was real close to get a profit of Rs. 20 this time. I am hopeful that someone else will come and give an offer of Rs. 80 atleast. CCI will not reject it, and I shall be able to sell off the stock at a latter stage.

    But today, I would think differently and based on the assumption that I have analysed the business and assuming that I have bought the shares only for an arbitrage opportunity, I would sell off the shares and book a loss rather than holding onto the stock and suffering a further wealth erosion. (assuming that Rs. 35.share was right and business is crappy)

    Q3) Loss aversion Bias

    Since losses have more impact than equivalent gain, I believe he could be suffering from loss aversion bias. He’s being over sensitive to the losses and not thinking about the possible gains. (Maybe he’s right :P)


  50. 1. The movement of A’s stock price is now contingent on any developments that impact the success of the competitor’s bid and is independent of the movement of overall market. Any developments that increase the chances of success will move A’s price closer to 100 while developments that reduce the likelihood of success will move the price away from 100 on the downside. Thus movement’s in A’s price are uncorrelated with the market.

    2. In the event that the approval was not granted, I would sell the shares. The sooner I sell them, it is likely that lower would be my losses. Psychologically, I would suffer from an anchoring bias (the anchor being Rs. 100) which would cause me to delay my sale. With the anchor fixed at 100, I would be loath to offload my shares at a price considerably below the level.

    3. My friend is probably suffering from negativity or pessimism bias whereby he assigns a greater weight to the occurrence of a negative outcome to the event than is warranted in the given situation. It could be due to a recency bias as a result of a recent bid being disapproved by the CCI. He could also be focusing on the absolute outcome (loss of 30 versus gain of 20) rather than expected outcome (gain of 10).

    4. The recency / negativity / pessimism bias can be overcome by providing statistical data over a longer period of time which shows the percentage of deals approved by CCI. This would probably lead him to reassess his weights and change his expected outcome. I could also make him aware of the distinction between what is possible (absolute outcome) and what is probable (expected outcome) which he may be confusing. Another way out could be to ‘frame’ the situation in terms of an opportunity loss (loss of expected gain) and bank on his loss aversion tendency to take the bet.

  51. 1. Assume that you are looking for opportunities which are uncorrelated to the market, why should you invest in this one? (10 marks)

    You should invest in this opportunity because it has no correlation with the markets and even if the stock market does go down, this deal can give you good risk adjusted returns if it goes through, because it is an off-market private transaction. This deal will give you a probability adjusted return of 51% p.a. in the 90 days period and is likely to beat almost every other investment opportunity with a similar risk profile.

    2. How would you act if CCI approval was not granted and you have bought the shares? How would you psychologically respond to that situation? (10 marks)

    If I had judged the odds of the deal going through correctly and then based on those odds I had invested in this opportunity, I would try and act rationally and take the loss and get out of the stock at the best possible price.

    I will tell myself that even though the possibility of the deal not going through was only 20%, it was still possible and that if I keep investing consistently in such opportunities over the long term, I am more likely to make money rather than lose money. I would also limit the amount of investment in any such single opportunity depending on my risk profile, and will try and make sure that I do not become greedy and put a disproportionate amount of my money in this single risk arb. situation.

    3. If your friend refuses to make this bet because of the loss scenario, what bias is he suffering from? (10 marks)

    Loss Aversion

    4. How would you help him over-come this bias? (10 marks)

    I would make him realise that there is a possibility of suffering a loss in the best of the value buying opportunities, and this is an opportunity where there is only 1 known unknown and we can also predict the worst case outcome with a fair degree of certainty, thus limiting the downside risk.

    I will also try to make him understand that if we keep investing in such opportunities consistently over time, we should make good risk adjusted returns on an overall basis.

  52. 1. Expected Outcome = 80% * 100 + 20% * 50 = 90 (worst case 87 @ 35 per share). At the cost of 80, the return is 12.5% (8.75%) = annualized 60% (40%). So, the bet is a favourable one.
    2. Sell the share if I do not estimate the fair value of the stock to be substantially more than 80 (something in the range of 120-160 or higher).
    3. Extreme loss aversion – might not be the correct technical term. In general, I would say he is not looking at the complete picture.
    4. No idea about it. Some reasoning about the overall picture could help maybe.

  53. 1. Assume that you are looking for opportunities which are uncorrelated to the market, why should you invest in this one?
    (I haven’t read much about Socratic questioning method but I will try to structure it in the way its given on the Wiki page)
    a. I will start thinking with why should I not invest in this one , following points come to mind :
    • The deal may not get approved by CCI , as certain times govt. wants to have increased competition for benefit of consumers . But by diligent evaluation we figure out that there is 80% probability that the deal will get finalized.
    • But there’s also a low probability (20%) of deal not going through which will make the stock dwindle to its earlier levels .we expect to sell our stock at an avg price of 50 in this case..
    • The Indian regulatory authorities are notorious for the delays in approval ,which may severely affect the IRR of the operation . Going by the empirical data here , we figure out a timeframe of 90 days.
    Next, I would like to construct different scenarios

    Case I : deal goes through
    Gain (g) = 20 probability P(g)= 0.8
    Case II : deal doesn’t go through
    Loss (l) =-30 probability P(l)= 0.2

    Expected value = 20(0.8)- 30(0.2) = 10
    Annualised return = 50%
    Since, the operation has a positive value and crosses my hurdle rate of 20% p.a. , I will invest in this arbitrage operation.

    P.S. this can be done in much detailed manner by assigning conditional probabilities to different types of risk(deal, price and time) in different scenarios , but, at the risk of being too mathematical.

    b. Why do you think that this assumption holds here?
    The assumptions hold here as they have their basis in empirical data and a structured reasoning process.
    c. Evidence as a basis for argument
    The evidence is the past data that risk arbitrage operations evaluated using a right analytical & psychological framework provide positive returns.
    d. Alternative viewpoints and perspective
    Counter argument to participate in the arbitrage operation is , that we have to be constantly updated with facts and review our decisions ,any delay or wrong judgement can cause huge losses. A few percentage points can make or break the game.
    e. Implications and consequences
    We make a profit/loss in this particular bet and now face the reinvestment risk.
    And also , with the benefit of hindsight ,after the event has occurred we can tweak our process for new learnings/shortcomings.
    f. ‘Why do you think that I asked that question?
    The question was asked as a part of an experiment . This experiment may provide useful insights to participants about the loopholes/missing angles in their process.

    2. How would you act if CCI approval was not granted and you have bought the shares? How would you psychologically respond to that situation?
    I would like to avoid the panic and fear situation, weigh the facts and if it’s apparent that the deal has fallen through; offload my stake at the best possible price.
    Since I was giving a low probability to the deal not getting completed . two biases which I think I would be like to be aware of : commitment bias and denial .
    The alternative could be to wait for the market to realize value of the company which the buyer could see, but that’s not the reason I bought this stock at first place.
    Consequently, I should not view the results of one bet in isolation and become loss-averse.
    3. If your friend refuses to make this bet because of the loss scenario, what bias is he suffering from?

    The friend may be suffering from various biases in his thinking :
    • He may draw the first logical conclusion without forming probabilistic scenarios that if the deal doesn’t go through, he will have a huge loss. Availability bias .
    • He may look at the percentage of loss vs percentage of gain whereas he should be calculating expected values of different possible scenarios . Contrast effect & Loss-aversion bias
    • Consistency bias to not participate in probabilistic gain scenarios.
    • Social proof bias to be loss averse.
    The implication could be my friend becomes rational and starts taking such bets and over a long term compounds his money .

    4. How would you help him over-come this bias?
    I would lay down the possible scenarios of the arbitrage operation infront of him .
    And ask him to give right weightage in his decision to probability of different events and not overweigh the loss scenario.
    Also, I would like to mathematically show him , how if one takes many such positive expected value bets , the aggregate result turns out to be in our favor (assuming we have assigned the right probabilities).
    An alternate way could be to explain to him if he isn’t taking these positive expected value bets , he will have to settle for negative real returns with very safe instruments like treasury bills and that will significantly erode his purchasing power over a longer term.

  54. Hi Prof.

    Here are my answers:

    1) Though the opportunity is uncorrelated to the market but if someone (in this case the competitor) is offering Rs.100 against the market tag of Rs. 35, obviously she has seen some kind of strategic advantage attached to the company. I can think of the glass industry as an example. The gestation period of setting up a glass manufacturing plant is 2 years. Transporting glass products (take bottles in this case) for more than 700 KMs is not profitably viable. With this base in mind lets take HSIL. HSIL commands 80% of the South Indian glass market. It’s a vendor for all big soft/hard/ultra-hard drink producers. Economically it’s rational for these players to have only vendor for all the bottling requirements (rate fixation, supply agreements and all). Now if these drink producing companies have one manufacturing unit in the North India, they would like to have HSIL as a supplier. If HSIL thinks that it can command the same kind of market in the North Indian market, it’d like to go for having a plant there as well. Now having a green field capex wouldn’t make sense. So HSIL can look out for a player in the North India and can think of acquiring it by giving some premium. Perfectly Strategic…! Right? 🙂

    2) I got into the share because there was a value being created by the strategic alliance of two competitors. I’ll directly sell the stock and will try to minimize my losses until or unless I find something really worth in the stock.

    3) Stereotype bias. He may have some past bitter experience and this may be the reason for this resistance.

    4) ?? 😦


  55. 1) The situation is company specific and the offer has been made. As such the happenings in the market would not affect the deal. Hence , i would be interested if looking for opportunities un correlated with the market.
    2)I would still hold the shares @80. The valuation by the competitor has given me an anchor to hold on to, and the company could reach its potential ahead. Psychologically i would be bit disappointed but would probably rationalize the fear of loss.
    3)Loss Aversion Bias
    4) I can reframe the situation highlighting the higher probability of potential gains. We can debate on the merits of the fear of loss argument. We can open up the discussion further and speak to the subtle but powerful emotions that harbor the fear.

  56. Hello Sir,

    Please find my responses below :

    1) Yes. I would invest in this kind of a scenario as the net value of this transaction would be Rs 10 / share ((80% * 20) – (20% * 30)) (This is assuming my average selling price per share is Rs. 50). The transaction would be profitable till the probability of deal getting approved is 60%.

    2) If the deal doesn’t go through, the price of the share is assumed to fall to Rs. 35.
    Considering the following scenarios :
    a) Company A is under-valued
    b) Company A if fairly-valued
    c) Company A is over-valued – This case is unlikely as the bidder wouldn’t have quoted a 3 times the current price.

    However, I would hold on to the shares of Company A in case a) and sell it out in cases b) and c).

    Psychologically, due to the higher displeasure from a loss as compared to a pleasure a person feels when in gain, I would be tempted to sell the stock as soon as the result is out, ignoring the fair value of the stock.

    3) My friend would be suffering from Deprival Syndrome (Loss Aversion) if he decides not to invest in the stock.

    4) Persuasion principle of “Appealing to interest and not to reason” would be one of tactics that would help me to persuade my friend in this scenario. Also, creating some kind of scarcity in the scenario by mentioning a limited review offer and so on would help me further.

    Awaiting your response for the answers!

    Thanks & Regards,
    Akshat Gupta

  57. Dear Prof. Sanjay Bakshi,

    Many thanks for this post – indeed a very interesting experiment.

    May I attempt to submit responses? The responses are supported by rationale (including several assumptions) and questions (to enable and facilitate further discussion and insights). I hope you find this useful.


    1. You should invest in this opportunity. Rationale:
    a. The underlying value of Company A is likely to be in the vicinity of 100 (i.e. as indicated by its share price of 100). The assumptions and related questions are:
    i. The acquiring company is likely to have undertaken adequate due diligence and therefore, it is likely to have better information about its acquisition target – company A.
    1. Questions:
    a. How likely is that the acquiring company makes a bid without adequate due diligence?
    b. Is it not likely that the acquirer has a better ‘understanding’ (than any buyer of stock of company A) of the business and forces that shape business environment?
    c. Isn’t the due diligence exercise likely to be more rigorous and likely to generate better insights than that made by a stock investor?
    ii. There has been no competitive bidding for company A. Therefore, the offer price is less likely to be driven by ‘ego’-nomics of the acquiring company. Hopefully, the acquisition decision is driven more by fundamental economics.
    1. Questions:
    a. Are other players in the industry interested in company A? Are private equity (PE) players and strategic investors interested in company A?
    b. What is the likelihood of competitive bidding?
    c. If there has been competitive bidding, then, is the underlying value of the company more than 80?
    iii. The acquiring company is better equipped to shape the outcomes of company A. (…the acquiring company could be better on several parameters – better management, better understanding of business, better relations with stakeholders in the industry, better grasp of consumer preferences, better financial capability, better strategy and execution record, etc.)…
    1. Questions:
    a. Is the industry facing and is it likely to face consolidation forces? Is there underlying growth in this industry?
    b. Is it possible to analyze the acquiring company?
    i. What has been its track record in making investment decisions, more so acquisition decisions?
    ii. Has the company displayed ‘value adding growth’?
    b. Company A, at a share price of 35, is trading at a discount to its underlying value.
    1. Questions:
    a. Has the market has not ‘recognized’ the underlying value of company A? What are possible reasons?
    b. Is this company playing in a stale-mate industry?
    c. What has been the share-ownership pattern?
    d. Are there any questions on governance of company A? Are there related party transactions with privately held companies? Are promoters trading in and out of stock, etc..?
    e. Has this company (and other players in the industry) experienced any ‘momentum’ in stock markets? (such momentum could be both positive and negative)
    c. If the acquisition goes through, you have better chances of reaping superior long term returns on your investment. (…it is likely to be a better managed company; it could reap benefits of consolidation; it could be discovered and re-rated by markets, etc.…)
    1. Questions
    a. Will consolidation benefits be reaped by the investor? Or are these benefits likely to go to other stakeholders?
    b. What is the industry structure?
    c. What about management and governance quality of company-A and that of the acquiring company
    d. What are regulatory constraints/opportunities in this industry
    e. What are typical capital costs, operating leverage and margins in the industry
    d. The overall expected value of this decision is likely to be a gain of about 10% (…with an assumption that gain outcome is 25% with probability of 80%; loss outcome is about 50% with probability of 20%)

    2. If CCI approval is not granted, I would prefer to evaluate the situation at that instant of time – i.e. take a fresh view with the benefit of better information. If my assumptions of making an investment are valid, then it is likely that I may continue to hold the stock. Or for that matter consider buying at lower prices. Here the assumptions and possibilities are:
    a. Company A appears to be a good acquisition target. It trades at a discount to its underlying value. There is sufficient scope to tap this ‘undiscovered’ value. It is likely to attract attention of PE players, of other players in this industry, etc…
    b. In due course of time, the markets may ‘discover the true potential’ of company A
    c. Company A could refine itself
    i. It may work towards realizing its full potential over time (…the acquisition process may trigger new ideas; this could be a ‘wake up’ call for business managers, etc…). This may result in improving its fundamental performance
    ii. Company A may work towards improving its communications with markets towards re-rating of its stock.
    iii. It may attempt to consolidate its ownership to avoid another acquisition bid
    iv. It may seek PE investment
    v. It may voluntarily seek a friendly strategic investor
    1. Questions:
    a. Is it worth waiting for markets to ‘discover’ the full potential? Is this likely to be a value trap?
    b. Is this bid a potential ‘wake-up call’ for company A? Is it likely to refine/change/improve its performance?
    i. Will it attempt to learn from its peers?
    ii. Will it be open to ideas from investors – like PE players or strategic investors?
    If the assumptions are fully negated, then a decision to exit be dependent on the investment horizon and other available investment opportunities.

    3. If a friend is refusing to take this opportunity, his/her decision may be influenced by the apparent loss – i.e. share price dropping below 80. He/she may be avoiding loss and the potential uncertainty. If he/she is unable to grapple with this uncertainty, which is solely dependent on CCI approval, he/she is quite right in his/her judgment.

    4. With the above backdrop, if the friend is unwilling to make an investment, it is fine to respect his/her decision. However, if there is a conceptual fallacy in the appreciation of this opportunity, then the above discussion may help to change his/her decision. Specifically, probability of loss is low and the overall expected value of the decision is a gain of about 10%…

  58. Reply for template #2:

    Q1). What’s the expected return of this operation?

    Ans. Assuming taxes are considered:

    The theoretical expected return of this operation is 4.3% over 90 days and annualized about 17%. Now, this assumes one buys shares at Rs.60 and tenders it in the open offer. Theoretically, the acceptance ratio will be 53% (26%/49%, i.e. offer size / non-promoter float). So 53% of the shares will get accepted at Rs.100, which net of tax (which in this case will be at the marginal rate of 30% plus cess since there is no STT being paid) would be around Rs.87.6 per share. The remaining 47% of the shares will get sold at Rs.35…yielding a net realization per share of Rs.2.6 per share.

    No taxes:

    In a country with no tax or if we are doing this in a mutual fund scheme (which is highly tax efficient), this deal would have been incredibly positive with a theoretical expected return of 15.8% for 90 days and around 63.9% annualized.

    Q2). Should you look at fundamentals of the target company? Why or why not?

    Ans. Yes, I can think of one situation wherein one can look at the fundamentals of the target company. This will be in case where one already owns the stock & intends to own it in future as well or has no exposure under new management, but intends to own the stock in future since the change of management has taken place (a la Sabero Organics or Shanthi Gears, etc.). The idea will be to reduce cost of holding shares. So one buys more than the required quantity, tenders a large part of the same and holding onto the shares that come back, with a significantly reduced cost!

    From purely a risk arb point of view, fundamentals may not be important since it is already assumed that one can exit the stock @ Rs.35 per share post the open offer.

    Q3). What is the likely acceptance ratio i.e. how many of your shares are likely to get accepted under the offer (theoretical vs. practical) and what key factors will govern that ratio.

    Ans. While the theoretical acceptance ratio in this case would be around 53%, in reality more often than not this is significantly higher. This will most likely happen in cases where there is fragmented shareholding, i.e. the company has a lot of small shareholders (many of whom might own 5-10-50 shares)…some may still hold them in physical format, some might belong to shareholders who do not even exist any more, etc. In my experience, around 5-7% of the shares outstanding of any company will fall in this category. If one adjusts for that, it will be fair to assume that the acceptance ratio could be closer to 60%.

    Q4). How can you use the inversion trick to estimate market’s assessment of acceptance ratio?

    Ans. Assuming taxes:

    the way to use the inversion trick is to assume the the current price is the optimum price and doing any trade at the price will at best generate the markets cost of capital. So, if we work backwards in this example, with a net yield of Rs.87 per share in the tender offer and a post offer exit price of Rs.35 per share, the markets expectation of the acceptance ratio is around the theoretical acceptance ratio, i.e. 53%.

    But, if we believe the acceptance ratio is going to be around 60%, there is every reason to doing the trade as the expected payoff would then be 10.3% for 90 days or around 41.9% annualized. This comes from the following:

    Buy 1000 shares @ Rs. 60 = 60000
    Tender 600 shares @ net yield of Rs.87 (net of tax) = 52200
    Sell the remaining at Rs.35 = 14000

    Total sale proceeds generated: Rs.66200 or around Rs.66.2 per share
    Net gain ~ Rs.6.2 per share or 10.3% for 90 days or 41.9% annualized.

    Q5). Should you borrow money to do this operation? Should you have done it in Template 1? Why?

    Ans. Yes one can borrow to do this operation, given an expected yield of around 41.9% (my assumption here is that the acceptance ratio is going to be 60% and not 53%). Cost of borrowing is most likely going to be around 15-18% that leaves ample room for one to leverage up! More importantly, unlike in case of template 1, one does not need too many such transactions to take place for one to earn the expected returns.

    One would not have taken leverage in Template 1, even though the expected annualized gain in case of Template 1 would be around 51%. This is because, in case of template 2, the chance of making a loss on capital is fairly low…it would take the price to go down to as low as 20 or below for some one to make a loss, chances of which would be very low realistically speaking whereas in template 1, for the risk arb to be successful, it needs to be done many times over with small bets each time. Adding leverage to this will increase the downside further from 37.5% to 42%. And, if one has two consecutive wrong bets, he loses almost the entire capital. This is assuming that one uses leverage to increase the size of the bets rather than invest small amounts. For the template 1 to succeed over the period of time: it a). needs a lot of such transactions and b). its done over small amounts with no leverage.

  59. Template 2

    1. What’s the expected return of this operation?
    As the MNC has offered to buy 26% out of the 49% free float shares, the acceptance ratio will be a minimum of 53%. Buying at Rs.60 per share, if I buy 100 shares, I can tender back 53 shares at Rs.100 and sell the remaining 47 at Rs.35. The overall return will be 15.75% for 90 days or around 63% annualized.

    2. Should you look at fundamentals of the target company? Why or why not?
    Yes, we should look at the fundamentals of the target company because this might be an opportunity to acquire some cheap shares in a good company. If I buy a 100 shares at Rs.60 (total cost of Rs.6000), and tender 53 shares at Rs.100 for an amount of Rs.5300, then I am left with 47 shares at a net cost of Rs.700, i.e. a little under Rs.15 per share. If the company’s fundamentals are good and intrinsic value of the shares is well above Rs.15 per share, then it means I can acquire shares in a good company at a very attractive price.

    3. What is the likely acceptance ratio i.e. how many of your shares are likely to get accepted under the offer (theoretical vs. practical) and what key factors will govern that ratio?
    The theoretical acceptance ratio is 53% assuming all the minority shareholders tender their shares. However, many might not do so. I think most institutional shareholders will closely follow developments of this kind, but retail participants may not keep a close eye on the company developments. I cannot offer any specific number but one might look at acceptance ratios of similar tender offers in the past to get an idea of the base rate, and make adjustments for the level of fragmentation in the shareholding structure of this company.

    4. How can you use the “inversion” (invert, always invert) trick to estimate market’s assessment of the acceptance ratio?
    The market’s assessment of the acceptance ratio would one that makes the expected return of the operation equal to the market’s estimate of the opportunity cost of capital. If we assume that cost to be around say 10%, then it would seem the market is assuming an acceptance ratio of around 41%.

    5. Should you borrow money to do this operation? Should you have done it in Template 1? Why or why not?
    In Template 1, we should definitely not borrow money for the operation as there is a 20% chance of making a large loss and leveraging will make it much more risky and can wipe us out. The positive expected value will deliver returns when diversified over a large number of small operations. One should not make the mistake of crossing a stream that was on average 4 feet deep.
    In Template 2, the possibility of loss is remote. As long as the share price stays above Rs. 20 per share we can cover our borrowing costs. So, in this case it might make sense to borrow money for the operation.
    We must also keep in mind the temperament of the investor. If borrowing money makes you uncomfortable and you have trouble sleeping at night, it might be better to avoid it.

  60. Answer 1:

    With an acceptance ratio of 53% we have 53*100 and 47*35 which gives the overall payoff equal to 945 on a 6000 ruppee investment.

    This is an absolute return of about 15.75% in 90 days or 64% annualized which is comfortably above the annual risk free rate right now.

    I am unaware of the detailed tax treatments to these operations. In of the posts i see, Ravi R Purohit has considered taxes which is great but i was wondering since Ravi has deducted tax for the profit part can’t he also write off some tax for the loss part. Ravi, can you explain? TIA.

    Assuming a 33% tax (or is it 15% short term capital gains since we’re buying and tendering within 90 days?) is paid on the net profit on 9.45 per share the overall profit comes up to about 6.33 per share post tax which is about 10.55 % for 90 days or 43% annualised.

    Side Note 1: Since MNC owns 51%, there is no threat of a competing bid coming in.

    Side Note 2 :Since post this offer the overall shareholding will go above 75% to 77%, there is a high probability of an open offer for the remaining 23% to delist the stock before the SEBI deadline – assuming this is happening in India.

    Overall makes sense to play this just on the return calculation merit.

    Answer 2:

    If you’re a special situations fund who is only concerned with this arb opportunity: Since our expected return calculations plan to sell the excess stock post offer at
    a price of 35 which is far away from the tender price fundamental evaluation would not be necessary.Fundamentals valuation would have been required if the tender price was close to the market price. For example if the tender price was 40 when the market price was 35, it would have been important for us to calculate the
    fundamental/fair value at which we would be able to sell the excess shares post the offer for our return calculations.In the present case tender price is almost 3
    times the market price so there is little chance of price going below 35 – which is the value we used in our calculation.So from a downside perspective fundamental
    evaluation is not key in this case.

    If you’re an individual investor: You should run the fundamental tests to value this company and you could use this opportunity to buy and retain the shares at a lower average price like Ravi above has pointed out,assuming your average price post tendering is much lower than your estimated fair value price.

    Answer 3:

    There are two ratios here:

    a) Theoritical: This would be 26/49 = 53%. This is assuming ofcourse that all the remaining share holders will tender their shares.

    b) Practical: In reality everyone might not tender their shares and the acceptance ratio might end up higher than 53% which will obviously increase our returns.The key things to look out for would be:

    1. Fund/FII/large holding – Typically large shareholders will skew the acceptance ratio by deciding to participate or not participate in the offer. If they
    don’t it’s immensely benefecial since most of our shares will be accepted at 100. But given that the offer price is almost three times the market price before the
    offer most of them would tender in the offer.
    2. Public shareholding – If the general public is the largest shareholder of the remaining 49% a number of who might not participate in the offer due to various reasons, then again the benefit will flow to the participants of the risk arbitrage.

    Assuming that the remaining largest shareholders might tender 75% of their shares and retain the remaining 25% in case there is an open offer where they can tender at

    a higher price, the acceptance ratio could be 26/(0.75*0.49) = 70%. Ofcourse this is just a guesstimate and there isn’t much value in predicting how a varied group of investors will behave. In our calculations we assume the lower minimum figure of 53%.

    Answer 4:

    The market price post the announcement is the key determinant of market’s anticipation of the acceptance ratio. That price is at 60.

    A price of 60 means the market has left a 43% p.a. post tax return (with an expected acceptance of 53%) on the table when the risk free rate is say 10% pa. This clearly means that the market is pricing in a much lower acceptance, which when used should give me a return of 10% p.a.

    10% pa is about 2.5% for 90 days.

    This means post offer my capital should be 6150 (assuming i bought 100 shares at 60) and profit is 150.

    6150 = a*100 + (100-a)*35

    This gives us the a = 40 or acceptance as 40% which is being expected by the market.

    Answer 5:

    Before answering this it would be wise to reiterate a quote from buffett – If you gave me a gun with a thousand chambers with just one bullet in it, no matter what the payoffs i wouldn’t take the bet.

    In template 1 – Its hard to argue for a case where we should leverage given that there is a clear chance of a substantial loss of capital although the overall payoff is positive. Don’t jump into a river with a an average depth of 4 ft…

    In temlpate 2 – It makes sense to leverage given that the probability of a permanent loss of capital is small but again like the first quote suggests don’t bet the family silver on it. Black Swans do happen. Leverage but understand that if things don’t go as planned you have enough backup to live to fight another day and another bet. This is pretty much common sense.

  61. Risk Arbitrage II

    I think we can look at this in the following ways :

    1. Buy shares but don’t tender them. Exit before closing date at a gain.

    Assuming a hurdle rate of 18% and a cost price of Rs 60 – the price needs to increase by only Rs 2.7 to Rs 62.7 to achieve my hurdle return. Therefore, if the spread between the market price and the offer price converges, as the closing date approaches, I can exit at any price higher than Rs 62.7. Annualised return would depend on the sale price and number of days I held the security

    2. Buy shares and tender them

    % Eligible for tendering = 49%. Therefore, acceptance ratio = 26/49 = 53%
    However, there will be some shareholders (perhaps non-institutional) who will not tender their shares perhaps because of stock market illiteracy (probably bought the share from someone else’s recommendation and now don’t know what to do) or suffering from status quo bias (requires effort, default option is not to opt-in).

    Assuming there are 4% such shareholders, the acceptance ratio = 26/ (49-4) =58%

    So for every 100 shares that I purchase @ Rs 60 ( Total = Rs 6000) and tender, I expect to receive Rs 5800 in cash (=0.58*100 shares*100 price) and the remaining 42 shares. These 42 shares could be sold in the market for Rs 35 ( =Rs 1470). Therefore, total profit is Rs 1270 over a 90 period at a cost of Rs 6000. This gives an annualised return of approx 85%.

    The annualised return can also be derived using Graham’s formula

    Annualised Return = [Gain * p – Loss * (1-p)] / { Time period * Price paid }

    Expected gain = 40*0.58 = 23.1
    Expected loss = 25*0.42 = 10.6
    Expected value = 12.5
    Annualised return =12.5/ {(90/360) * 60} = 85%

    What is the markets assessment of the acceptance ratio ?

    I am not really sure about this. My first thought here is why has the price not gone up to say Rs 80 ? Why is the price at Rs 60? What would a price of Rs 80 mean for my return. It will give me a return a -38% with a 58% acceptance rate. To achieve my target return of 18% at this price I need the acceptance rate to be 75%, which is not likely. Therefore, the price needs to be lower.

    Using the same reasoning, target return of 18% at the current price of Rs 60 implies an acceptance ratio is around 43%. If the market corrects for this, then the stock price can increase to Rs 69 and still give a return of 18%.

    If I have invested at Rs 60 and the price goes up to Rs 69, then I will exit the trade without tendering.

    What about the fundamentals of the company ?

    In template 2, irrespective of whether the deal is completed or not, you will still hold some Company A’s shares. So it makes sense to look at the fundamentals.

    Further, template 2 can be viewed as a means to acquire cheap shares in Company A i.e. the profit from the accepted tender shares can be used to offset the cost of the returned shares.

    Using the same figures, the “cost” of the returned 42 shares is now Rs 4.8 [= (6000-5800)/42 ]. Since, “price changes everything” spending time to look at the fundamentals to identify any price-value gap will be worthwhile. You are getting the same earnings at Rs 4.8 as you earlier getting at Rs 35.

    Should leverage be used ?

    I think in Template 2 leverage can be used. I don’t know how much leverage would be sensible, but risk of permanent loss of capital is low. If we could hedge the price decline using futures or options then we could increase leverage further.

    In Template 1, I will stay away from leverage. There is a 20% chance of permanent loss of capital.

  62. Hi Sir,

    Please find my responses to questions posed in Template 2:

    1) On my net investment, I would earn around Rs 21.22 while lose Rs 11.73 per share (Profit : (100 – 60) * (26 / 49) and Loss : (60 – 35) * (23 / 49))

    So on an investment of Rs. 60, I would make a net gain of Rs. 9.5 per share, translating into a return of 15.8% in a quarter and around 63% annually.

    Answering question 3 here, this can be considered to be the minimum profit one can make from this situation as there would be a few market participants who wouldn’t tender their shares in the open offer. So, in a theoretical situation, the acceptance ratio would be 51%, the actual ratio would be still higher.

    2) I shouldn’t be looking at the fundamentals of the company in such a situation as I would be selling the shares in the market at the end of 90 days (no matter whatever the case). As mentioned by you, this security should be considered as a bond where-in a part of the principle (& interest) is paid by the acquirer and the rest by the market!

    4) Sir, I am not completely sure of how to approach this. But considering a forward looking scenario where-in the security would be worth Rs 35 in 90 days that is worth Rs 60 today, it wouldn’t make sense for any investor not to tender his / her shares to the acquirer. So the acceptance ratio should be some-where around the theoretical acceptance ratio of 51%.

    5) Though the transaction seems profitable, however, one cannot be completely sure of the future outcomes. Assuming this stock price would be be correlated to the market, one would make a net loss in this transaction if the stock price falls below Rs 15 per share at the end of the offer period. Assuming surety on the prices mentioned, only then one should take borrow money for this operation. However, even then in a real life situation, the stock price wouldn’t have remained at Rs. 60. It would have been somewhere around Rs 70 where-in the net gain / loss would be NIL.

    Looking forward for your feedback sir.

    Also, had a question regarding a similar real life situation we had recently on IGL.

    –> How could one even remotely assign probabilities of the deal going in IGL’s favor in the High Court? And a similar probability on the Supreme court judgement due in future.

    Thanks & Regards
    Akshat Gupta

  63. Answers to Template 2 –

    1. Minimum acceptance ratio on this offer would be = 26% of balance 49% (26/49) = 53.06% = 53%

    So if I buy 100 shares @ 60, my initial investment is Rs. 6000. 53 shares would be sold at Rs. 100 giving me Rs. 5300 back. While balance 47 shares would be sold at Rs. 35 each giving me Rs. 1645. So total payoff = Rs. (5300+1645) = Rs. 6945 giving me a return of Rs. 945 on investment of Rs. 6000 which works out to 15.75% absolute and 63.87% per annum.

    2. A 63.87% p.a. return is good enough to merit investment in this offer without looking at the fundamentals. Still, it wouldn’t hurt to know the actual details of the offer made by the MNC. Why are they buying out the promoters in the first place? Are the promoters in some sort of financial trouble? Were the promoter shares pledged? Was the concerned MNC one of the existing investors in the company (as a public holder with more than 1% stake)? Is the MNC in the same line of business? (eg. AP Paper – International Paper) If yes, then do they have existing subsidiary or operations in the country or is this going to be their first foray into the country? How big is their global operation and what is their outlook on India (presuming the deal pertains to a company listed in India)? etc

    My reason for asking the above questions is to ascertain whether this is an opportunistic buy (at a depressed valuation) or a more strategic foray into the business. If it is the latter, then it begs to note that post the offer, the MNC will hold (51+26) = 77% in the company which would make the target a prime delisting candidate (eg. Patni Computers). If analysis of the above questions suggest future positive intent of the acquirer for the company, then it begs to consider further accumulation of the stock at the residual price of 35.

    3. Theoretical Acceptance Ratio is 53.06%.

    However, the likely ratio would be higher than that. This would depend on some or all of the following factors –

    a) No. of minority shareholders, especially individuals who are holding shares in physical form. Experience shows that majority of them tend to be dormant (or maybe simply unaware) of offers like this. If there are large no. individual shareholders with small holdings then chances are that the merchant banker handling the issue will not be able to get in touch with them and consequently they may not be aware or properly informed about the issue / opportunity. Some or large percentage of this population can be expected not to participate in the issue.

    b) If there is a large strategic shareholder (individual, company etc), then it merits to study the purpose of their holding. For example, ITC is a strategic shareholder in EIH, so it can be logically assumed that they would not participate in any activity which would dilute their holding in the company.

    4. I am not sure if I understand the “inversion trick” completely so I would refrain from making guesses on this question. I would appreciate if you could point me to where I can study about this.

    5. Logically thinking, borrowing money for Template 2 does make sense as their is no CCI (or any other) risk in the deal not going through. However, this again would depend on the rate of borrowing prevailing in the market and leverage should be taken for strictly the deal period with clear intent of liquidating everything at 35 and locking in the gains.

    However, in Template 1, borrowing could prove to be disastrous if the deal doesn’t go through due to CCI not approving. There is an actual loss possibility in Template 1 and leveraging will only make it worse, with chances of wiping out the whole of initial capital.

  64. Dear Sir,
    I am using my discretion about some data of the company, like Share holding pattern, Fundamentals of the company. Names of Big Share holders other than Promoters, Also total no of Share holders

    1) The Expected Return from the transaction is at least 134 % Annualized (Excluding Transaction Cost, Statutory Costs and Taxes). Further I will explain you the rationale of using the word “at least” in later part.
    2) Yes, I will look at the fundamentals of the company, because there will be residual shares lying with me and I should know the value of that stock. Also I may take another bet to buy stock at 35 to 15 Where Rs 15 is value of Residual Shares and maybe for some reason price would fall up to that level , Provided I feel that the process of price discovery has not done justice to stock and It needs to be re – Rated after this development
    3) The Minimum acceptance Ratio is 53.06 % which is also theoretical. But Practically the acceptance ratio will be minimum 53.06 % and maximum 100 % because
    a) There may be some big long only shareholder, who would not want to sell it because they may have bought expecting such outcome or they may want to ride the wave of stock after open offer. Because all the less committed player would have exited in open offer. ( Eg :Open offer of Sabero Organics by Coromandal Fert)
    b) There are some people who would bet on delisting which may follow after open offer and some years. As MNC holding would become 77 %, which is more that 75 % threshold. (Many E.g. Thomas cook, OFSS, Fulford etc)
    c) There are shareholdings stakes held by govt corporation, They may not sell it for strategic purpose (E.g. If an offer is launched by BAT for ITC, LIC won’t sell no matter about price)
    d) There are some retail shareholders, who are fragmented, who may be holding the shares but they may not be aware of offer properly, Shares certificate and folio may be misplaced as they may be holding it for decades or Qty do not tally or Shares are held in abeyance because of family disputes.
    e) Depository Receipts holders cannot tender the shares unless they are converted into Equities.
    f) Pledge shares or partly paid shares cannot be offered in open offer unless they are unencumbered and fully paid up.
    Evaluation of above scenarios is only possible after looking at shareholding pattern.
    4) We believe market discount everything in “long run”. We can calculate the expectation of acceptance ration of market by inversely calculating inversely. The acceptance ration expected by market 39 % which is less than minimum acceptance ration, hence we can infer that market is giving very less value of Rs 15 to 18 for residual shares or THERE is an Arbitrage opportunity.
    5) I may leverage a bit in this situation, but Call can be taken only after looking at the fundamentals of the company. I feel If fundamentals evaluation point at Rs 35 /- after Open offer, I will leverage expecting people to take bets on this company and price will move up in level of 66 to 69.5/-. The mentioned price of 69.50 is the price at which the cost of residual value of shares is Rs 35/- and at this point I will liquidate all my leveraged positions and take bet on my own money only.

    Jigam Gandhi

  65. 1) Suppose i buy 100 shares @ 60 each, so total outgo = 6000/-
    Since offer is to accept 26% of the non-promoter shares, i.e. out of 49%, and assuming 3-4% brain dead investors, 45% of shares would be put up for tender offer, so ratio of acceptance is 26/45 = 58%,

    so out of 100 shares i bought and put up for tender offer, 58 would be accepted @ 100, and rest of 42 would be sold @ 35, so total inflow in this case would be

    = 58*100 + 42*35 = 5800+1470 = 7250/- approx.

    on 6000/- it would be around 21% return in 90 days, or 85% annualized, in case prevailing interest rates do not change and inflation doesn’t increase too much, i would like to invest.

    2) In case we decide NOT to sell the unaccepted shares, on investment of 6000, we would have got 5800 back, so for rest of 42 shares, cost would be 6000-5800 = 200/-, i.e. close to 5/-per share, so downside is kind of limited but if we come to conclude that share is worth much more than 35/- based in fundamentals of the company, we should not sell it. So yes, we should worry about fundamentals of the company.

    3) As i mentioned earlier, out of 49%, only 26% are on the offer so theoretically, acceptance ratio is 26/49 = 53%,
    But because of some brain dead investors, it would be around 26/45 = 58%

    Key factors can be:

    %age of Brain Dead investors,
    turbulence in markets
    change in interest rates/inflation
    any subsequent BETTER offer

    4) Suppose prevailing interest rates are 10% annually, so for 90 days, i should get 2.5%

    Lets say acceptance ratio is “x” out of every 100 shares,

    so, in ideal situation, following equation should hold good:

    6000*1.025 = 6150 = 100*x + (100-x)*35
    => 6150 = 100x + 3500 – 35x
    => 6150-3500 = 65x => 2650 = 65 x => “x” = 2650/65 = 40.7%

    5) One can borrow money for this situation, provided it costs lesser than 85% annually and repayment period is greater than 90 days.

    In template 1, i wont have done it as there was a huge downside risk also.

  66. Assumption: I am buying 100 shares at Rs.60/-.

    a) What’s the expected return of this operation?

    Given that the theoretical acceptance ratio is 53% (26/49), and assuming I need to pay up the marginal rate of tax of 30% (exclude cess) on the gains on 53 shares (because I tender and hence no STT) and add back the tax saved due to losses (netting off against my short term gains at 15%) on the remaining 47 shares, my gain would be 8.08% for a period of 90 days and 37.04% on an annualized basis.

    b) Should you look at fundamentals of the target company? Why or why not?

    Apart from multiple angles on change in management, change in strategy, strong tailwinds etc., even on a pure numbers perspective, it makes great sense to evaluate the fundamentals of this company – the major reason being getting to hold shares at a very cheap cost (a.k.a your trade in Eicher motors/BOC India etc in the past). From this perspective, after 53% tendering at Rs. 100/-, the cost of holding the remaining 47 shares would be Rs.15/-. Since the market price before the open offer itself was around Rs.35/-, unless the management coming in has a reputation of destroying value, this would be a very good bet to evaluate fundamentals and hold on to the stock, unlike the first case where there was a possibility of severe commitment bias (there is a case right now in the markets where I see this commitment bias kicking in even after the special situation has not worked out) inspite of a clear loss scenario.

    c) What is the likely acceptance ratio i.e. how many of your shares are likely to get accepted under the offer (theoretical vs. practical) and what key factors will govern that ratio?

    Theoretical acceptance ratio as discussed above is 53%. This is a base case and the worst case scenario if everyone else in the remaining 49% tenders their shares.

    Practical acceptance ratio however can vary widely. And it can be only above 53% and not below it. The reasons might be multiple –
    a) Some retail investors may not know about this tendering information or process.
    b) Some retail investors are overseas and may not have a way to tender.
    c) Some retail investors might be stuck with physical shares yet.
    d) A large strategic investor may not want to tender their shares.
    e) Certain institutions/mutual funds might have a mandate not to tender shares/churn portfolios as part of tendering.

    On a historical basis, after looking at the shareholding pattern, it seems like a 5-7% brain dead investors assumption works pretty well. Corporates/Institutions/MFs not tendering would be a bonus for the retail investor who tenders. But in general, any optimistic assumption above 10% not tendering and investing on this assumption would be pretty foolish. Therefore, if we assume 7% of investors are brain-dead, the practical acceptance ratio would be 62%.

    d) How can you use the “inversion” (invert, always invert) trick to estimate market’s assessment of the acceptance ratio?

    I always feel that this is the most difficult part of any investment. How and what to invert? But, I’ll give it a try.

    We are assuming the market has already priced in the cost of capital (or interest cost, if you will, along with all other tax implications) and hence the share is still quoting at Rs.60/- and not Rs.80/-. Let’s say interest cost and tax implications would be around 16% p.a, which roughly equates to 4% in 90 days.

    That is, an investment of Rs. 6000 (Rs.60 * 100 shares) in this investment scenario at which the market is pricing the stock would at the end of 90 days give me Rs. 6240. Now, the math is elementary.

    Rs. 6240 = Offer price * Accepted shares + Remaining shares * Resultant share price after open offer.

    Rs. 6240 = 100 * x + (100-x) * 35 (assumption: I bought 100 shares)

    Solving for x, we get an acceptance ratio of 42%. However, as we already stated above, the acceptance ratio can not be below 53%. Therefore, in this particular case, the market is clearly underpricing the situation and we need to exploit it to the hilt.

    (However, in most cases, like Shanthi Gears/Tata Sponge Iron/Tinplate etc., I did not see any such chance of mispricing/underpricing. After the open offer became public, Tata Sponge Iron quoted at Rs.340/- while its offer price was Rs.375/-, while the price expected immediately post open offer was Rs.300/-. The theoretical acceptance ratio was 23%. Work the math – no mispricing).

    I hope my invert logic was right. I find it very difficult to invert situations (the why and how of it. If the Prof. could enlighten, that’d be great!).

    e) Should you borrow money to do this operation? Should you have done it in Template 1? Why or why not?

    As long as we are not talking of betting the bank here, borrowing in template #2 should be perfectly ok. The reason being, the chances of loss are close to zero.

    Let’s work the math. I have invested Rs. 6000/- (Rs. 60*100 shares). Minimum tendering would be 53 shares at Rs.100/- per share, resulting in Rs.5300/-. In what case would my investment result in a loss? That will happen only if the remaining shares quote below Rs. 15/-. Given that the market price before the open offer was Rs.35/-, the chances are remote (but non-zero). Hence, borrowing at a reasonable cost (say around 15-20%, if the hurdle rate is 18%) should be absolutely fine. Don’t bet the bank because you don’t know what can go wrong.

    In Template #1, we have a clear loss scenario. That is, there is a 20% chance that I’ll lose Rs. 30/- if not more on an investment of Rs. 80/-, atleast a 37.5% loss. 2-3 such losses would wipe out the entire capital, not to speak of the stress involved in borrowing. What you really want, if you want to borrow, is an extremely small (if not zero) chance of a loss and a large upside along with a reasonable cost of borrowing. In Template #1, the chance of loss is not small and unless I am on my death bed, I wouldn’t borrow to invest in the deal.

  67. Answers:
    1) Expected return is 16% (assuming 0% brain dead investors and no taxes/other costs. The transaction costs will reduce the expected return by a few percentage points). That translates to 64% annualized returns pre tax.
    Shares bought: 100. Cost Rs. 6000
    Theoretical acceptance ratio: 53% ( 26%/49%) (assuming no brain dead investors)
    Hence shares accepted: 53. Proceeds @ Rs 100 = Rs. 5300
    Remaining shares: 47. Proceeds @Rs. 35 = Rs 1643
    Hence profit = 5300 + 1643 – 6000 = Rs. 949. i.e. 16% and 64% annualized (before taxes and transaction costs)
    The profitability on this transaction can be increased if there are some brain dead investors.
    If we assume brain dead investors to be 4% we get a return of 21% from the transaction i.e. 84% annualized

    2) In this case, I would not look at the fundamentals because they do not matter in this case. The fundamentals of the company would not impact the transaction. The offer is more about credibility of the MNC which has come out with an open offer.

    3) Theoretical Acceptance ratio is 53% (26%/49%) while the practical acceptance ratio may increase based on the number of brain dead investors. Liquidity is an important factor based on which the number of brain dead investors would depend. If the stock is highly liquid the brain dead investors may be less (2-4%) and more in case of less liquid stock. As I do not have any experience of such cases, I would assume brain dead investors to be 3% just to me a bit more conservative. Hence likely acceptance ratio would be about 57% ( 26%/46%).

    4) By inverting we can arrive at the acceptance ratio as per the market price.
    i.e. 40x -25(1-x) = 0 , where x = acceptance ratio.
    Solving for x, we get acceptance ratio as 38.4% which is much less than what actually should be. Assuming no taxes and transaction costs to simplify. With taxes and other costs the acceptance ratio would increase by a couple of percentage points.

    5) Yes, I would borrow money in this case as there is minimal or no chance of permanent loss of capital while in earlier case there was a 20% chance of loss of capital. Also with annualized return of ~60% or upwards, if we can borrow at 15-18% the transaction can be still be highly profitable.

    Manan Patel

  68. Template #3:

    CMP: Rs. 65/-
    Offer Price: Rs. 100/-
    Post-offer price: Rs. 35/-

    Acceptance ratio: 67% (in the absence of competitive bid)

    CCI Approval probability: 80%
    CCI Rejection probability: 20%

    CCI approval: 6 months
    SEBI approval: 3 months
    Offer completion: 1 month
    Total time taken to completion: 10 months

    Cost of carry: 12% p.a

    Competitive bid: 25 days from now

    a) Will you buy now and hedge your net long exposure using futures? Why or why not?

    Ans. Let’s look at the returns first (excluding taxes, cess etc.) on a simplistic basis, assuming no competitive bid, CCI and SEBI approvals come through and the offer gets completed in 10 months.

    I buy 100 shares. 67 get tendered at Rs.100/- and 33 get sold at Rs.35/-

    Return = ((67*100+33*35)-(65*100))/(65*100) = 20.85%

    That is, if everything goes through smoothly, we will have a 20.85% return over a period of 10 months and 25.9% on an annualized basis.

    On a simplistic basis, since the cost of carry is 12% p.a and the expected return is close to 25.9%, excluding transaction costs, F&O can be used in a profitable manner.

    If there is a competitive bid, then the price will only rise and the returns will take care of themselves. However, we need to definitely hedge the risk of share prices falling down. The share price can fall because of a) market risk, but more importantly b) CCI rejects the deal.

    Given that the stock trades fairly liquid in the F&O segment, I can hedge the risk of prices falling down due to market risk. This involves buying the stock in cash market and shorting the futures of the current month, near month and the far month and repeat the same for about 6 months (that is the far month will be the 9th month) (or till SEBI approval comes in, whichever is earlier). If the CCI rejects the deal, our shorting of futures should have ideally made up the loss that we make on the cash market and we would have incurred only the transaction charges for 12 legs across 6 F&O sessions.

    For the 10th month, something interesting can be done. There are two legs to this trade. The first leg involves buying the stock in cash and simultaneously selling the 33 shares expected to be received back (due to non-acceptance of 100% shares) in the futures market (in fact, if a lot of capital chases this deal, the futures can quote at a discount to spot). The second leg of the trade would involve selling the surplus 33 shares as and when received in the spot market and simultaneously squaring up the short futures position.

    b) How will your estimate of acceptance ratio change over time?

    Ans. Acceptance ratios will change over time depending on

    i) If the retail holding is moving into more sophisticated investors’ hands like fund houses/large investors (in this case, acceptance ratio will fall)
    ii) If the competitive bidder is going to acquire more shares from retail and fund houses alike (in this case, if the bidder realises he can’t compete, it’ll lead to a fall in the acceptance ratio)
    iii) If large investors don’t want to get into this open offer rigmarole, the acceptance ratio may increase.
    iv) People nowadays have shorter memories and this open offer might fade away from public memory since it is 9 months away. That may lead to increase in acceptance ratio.

    c) What’s the worst case scenario, if you buy now and also hedge using futures?

    Ans. The stock price goes down and the futures goes up. This can happen, especially the futures hedge may go wrong. Case in point: Mylan-Matrix labs deal. In this case, the November futures deal was quoting at a discount to spot. Suddenly, the news of a delay came in and investors scrambled to buy back November futures and sell December futures.

    d) How will you deal with the possibility of a competitive bid?

    Ans. I am not really sure how to deal with this. My simple thought process is, if the competitive bid comes in, it’ll be icing on the cake, since you will be getting more bang for the buck. If it doesn’t, then you have already evaluated your returns at an offer price of Rs.100/-. A successful competitive bid can do three things –

    i) Get into a bidding war, the result being that the shareholders win big time.
    ii) Get more parties interested in the deal which, if it interests large investors, may drive down the acceptance ratio
    iii) It will take longer than 10 months to complete the deal. So, the returns need to be re-calculated both for the cash position and F&O position, if any.

    e) How will you deal with the CCI risk and the SEBI risk in terms of a probability chain? (Hint: How many things have to go right for you to make money?)


    Consider the CCI approval case (80%)

    I buy 100 shares. 67 shares tendered at 100, remaining 33 shares sold at 35.

    Return = (67*100+33*35)-(100*65) = Rs. 1355/-

    Consider the CCI rejection case (20%)

    I buy 100 shares at Rs. 65/-. I need to sell all 100 at Rs.35/-, i.e., all 100 shares will be sold at a loss of Rs.30/-

    Loss = 35*100-65*100 = – Rs.3000.

    Expected value = 80%*1355 + 20% * -3000 = Rs. 484/-

    Rs.484/- on an investment of Rs.6500/- over a period of 10 months translates to a return of 7.45% on a gross basis, and 9.2% on an annualized basis.(I understand that there is a time gap between an approval and the offer going through (which takes 10 months) vs rejection (which can take less than 6 months. But I didn’t want to get into time value of money calculations for 4 months).

    With the CCI risk taken into consideration, as we calculated above, the returns are 9.2% p.a. If we consider SEBI’s risk too in the same proportion of 80:20, then the returns dwindle even further, maybe even giving returns lesser than a risk free bond.

    f) What kind of deal-related (not market related) volatility can you expect in this transaction? How will you deal with that volatility?

    Ans. Since the money is already deposited in the escrow account, and the bidder cannot back away and the investment banker is reputed, the risk of deal falling through due to non-regulatory reasons is minimal. However, the deal may get delayed due to various reasons – CCI, SEBI, open offer completion – essentially timeline risk is paramount in this case. I would deal with this volatility by having a smaller position (and not using leverage) so that it doesn’t affect my overall portfolio returns.

    P.S: I am a novice at F&O nuances. So please do explain the angles I may have missed.

  69. Sir,
    In Template 3, we have not been given a probability for SEBI approval. Does this mean we are expecting SEBI to definitely approve the deal if CCI approves it, or we still have to estimate/assume some probability of rejection by SEBI?

    1. Lokesh, SEBI is very unlikely to reject the offer. If CCI approves it, SEBI too will. SEBI might ask the acquirer to make more disclosures in the offer letter and may take longer to approve, however. But I see nothing wrong in your factoring in a small probability of SEBI approval not coming in your model.

  70. Risk Arbitrage III

    I am not really sure of my answers. I have never done any risk arb and I don’t know how the futures market/contracts work. This will show in my reasoning and analysis. Nevertheless, here are my thoughts.

    Answer 1

    Without hedging the expected return from this deal is around 9% pa. This is calculated as follows

    Cost of 100 shares = 6500.

    = 0.8* [ gain from 67 accepted tendered shares – loss from 33 returned shares ] + 0.2 * [ loss on 100 shares ]
    = 0.8 * [67*35 – 33*30 ] + 0.2 * [ 100* 30 ]
    = 0.8 [2345 – 990] + 0.2 * [3000]
    = 484

    If the acceptance ratio falls to 58%. I break even at this price.
    With hedging the expected return jumps to 31%. This is calculated as follows

    I will trade buy 100 shares @ 65, Sell 33 futures to cover the returned shares ( Assuming strike of Rs 67)

    = 0.8 * [ gain from 67 tendered shares + gain on 33 futures – loss from 33 return shares ] + 0.2 * [ gain on 33 futures – loss on 100 shares ]
    = 0.8* [ 2345 + 1220 – 990 ] + 0.2 * [1220 – 3000 ]
    = 1704

    If the gain on futures perfectly offsets the loss on 33 shares then return is 27%. So to get a return I think you would need to hedge.

    I am not really sure what will I do in this situation. A lot of things can happen here – a competing bid, acceptance ratio can change, delays in the deal etc.

    If I buy 100 shares at Rs 65 and hedge 33 shares, I cover myself against some losses and my net long position can still benefit from the higher tender bid. But I know the competing bid has to be made in the next 25 days. If it comes through then the stock price is likely to increase. Suppose it increases to Rs 68. So I can earn a return Rs 3 in 25 days ie return of 67%.

    So maybe I will buy the stock, but not hedge my position (immediately) and I will postpone the decision to sell futures by 25 days. Post 25 days, if I still want to be a part of this trade (considering possible delays, opportunity cost) I will hedge my position before the CCI date.

    Answer 2

    I think at least one factor that will contribute to a change in the acceptance ratio is the interest of the risk arbitrage community in the deal. To measure this we can :

    1. estimate the change in the shareholding pattern post announcement. We can assume that most of the activity post the announcement is by the risk arbitrageurs.

    2. look at prices of futures contract to give us some clue. The futures at present is trading at a premium to the spot. If a lot of risk arbitrageurs throw money in this deal, they too will hedge their position. This is likely to depress the prices of the futures. So we should monitor the prices.

    The present acceptance ratio is 67%. So this implies at present only 39% outstanding shares will be tendered. Acceptance ratio will decline if risk arbitrageurs holdings increased further ( as they will all tender their shares).

    I am not sure what are the other factors that will impact the acceptance ratio.

    Answer 3

    The worst case scenario with hedging could involve
    1. Delays in the completion of the deal
    2. Need to constantly keep rolling and/or adjusting for the relevant futures contract date
    3. Continuously changing acceptance ratio so you need to keep readjusting your futures position
    4. Finally the deal not working out.

    If I have borrowed then the outcome will be worse.

    Answer 4

    A competitive bid will imply a higher tender price. This is good for my returns. It could also mean delays. This will lower my returns. So I think we need to constantly monitor opportunity cost of this deal and the changes in the expected value of the deal. We should not neither get too committed to the deal nor too averse to it. Also see Answer 1 and Answer 6.

    Answer 5

    The expected value can be calculated using a binomial decision tree diagram. The final payoff is based on chain linking probabilities – CCI Approval * SEBI approval * % tender. A chain link results in a lower probability than the lowest probability in the chain = 80%*98%*67% = 51%.

    Further, a failure at any stage would mean the probability falls to zero, and the deal is off.

    Answer 6

    The situation in Template III is more dynamic – here things can change – because of a competing bid and CII/SEBI approval or possible delays. We have imperfect information and the whole thing can change with one announcement. We can think of the expected value calculation from this deal as a binomial tree diagram. As events unfold, both expected and unexpected, the probabilities and payoffs at each node of the tree will change.

    The situation is analogous, I think, to a binomial tree used to price options. Higher volatility in option pricing implies a higher value. I think higher deal volatility here too can imply better result, provided we are able to wait and filter new information correctly. By waiting and delaying the trade, the better result can take the form of not entering the trade at all, existing the trade early or taking advantage of uncertainty when other don’t want to.


    1. Why can’t we simply sell futures and not buy the stock ? In all scenarios the stock price falls, so provided the timing works out I will be in the money.

    2. I think selling the futures is equivalent to buying insurance here ? If a lot of risk arbitrageurs buy insurance wouldn’t the cost of buying become too expensive ?

    3. There must be someone at the other side of the trade ie who is buying the futures. Why is he buying when in all scenarios the stock price is falling ?

  71. Dear Sir,

    There is positive cost of carry on the stock, giving me perception that people are expecting counter offer but I fail to understand, why would somebody make a counter offer? The promoters have agreed to sell 51 % to the acquirer.
    Does that mean there is some more equity dilution to take place? FCCB, ESOP etc else competitive bid is futile (INOX – Fame India – Reliance Saga) as it would not give control.

    I feel if there are counter bids in such scenario, they will not wait till offer; they will accumulate from market and then make an open offer.

    Ans 1) I will buy shares as competitive bid may come in, if such thing happens the price of stock will only zoom up as there may be bidding war. But I will give very less probability to that as promoters hold 51 % of shares.
    I will not hedge my position because hedging position for 10 months is very long and I am sure as the date of offer comes nearer, there will be backwardation in futures price taking away all my gains. In fact it makes more sense to be long on futures for first 6 months
    Since the stock is in Derivatives segment, many weeds and speculators will enter this stock on both long and short side.
    I can assure there will be steep discounting on futures price, for the month where there is an X date of Open offer (After 10 day of Refund of shares). If the discounting is not there, I will make more money shorting the stock futures. (Please see price of Ranbaxy Futures, when it made an open offer also Bombay Rayon Fashions)
    I will not hedge my position in futures as I have seen backwardation taking away all the returns.
    As Such at acceptance level of 67 % my cost will be recovered from offer money itself, I will get a profit of Rs 2/- per share (I am not considering cost of carry)
    Ans 2) Acceptance ratio may change and it will go on becoming lesser and lesser as new hand would buy stock only after considering open offer, unless there is a competitive bid. In case of competitive bidding the acceptance ratio is immaterial as the bidders will start buying from market.
    Ans 3) If I don’t hedge, I will have to sell the stock at 35 /- which will be the worst case, but hedging may reduce loss but it will add more uncertainty of Dividend declaration and Backwardation.
    Ans 4) I have discussed the probability of competitive bid as very low, but if that comes in I will increase my position as the competitive bidder to succeed will also have to buy stock from market.
    Ans 5) if competitive bids come in, CCI will miss its timeline as there will be more players in the loop to judge. SEBI is the last authority to give permission and they will give permission if all other permissions are there and the application is in order. Yes if I add probability to SEBI acceptance to offer, my overall probability will fall from 80 % by some more percentage points.
    Ans 6) There will be many rumors about counter offer, there will be news about the acceptance of deal by CCI and offer by SEBI. Since the stock is also in Derivatives segment, we will also see volatility in Basis of Stock from positive cost of carry to Backwardation and maybe vice versa.
    If I don’t hedge with derivative, I will live with volatility but will not venture to time the market. I will only sell if there is rejection to offer or Stock price moves above acceptance probability of more than 85% to 90 % which is Rs 85.
    I feel Cmp of 65 /- is cheap compared to offer price and residual price, the price will correct upwards before the offer itself.

    Jigam Gandhi

  72. Reply to template #3:

    The Trade:
    Step 1: Take a long position in the cash market.
    Explanation: The expected pay off on the deal is 24% annualized. This is based on the following assumption: 67% acceptance ratio @ Rs.100 and selling the remaining shares at Rs.35 in the cash market post the open offer.

    Step II: Hedge the long position to nullify the CCI deal risk.
    Explanation: The expected pay off in the above holds true only if there if the deal goes through. But, for that to happen we need the CCI to clear this. Probability of that happening is around 80%, which also exposes me to a downside risk of 46%, thereby reducing my overall expected payoff dramatically (from 24% to 10% making the deal not worth doing). Thankfully, we have the F&O market to hedge this risk. Had that not been the case, the deal might not have worth doing. So we sell the stock in the F&O market till the CCI verdict is out and hedge our position.

    Step III: Hedge the long position to nullify the CCI deal, but do it after 25 days!
    Explanation: Now we want to hedge our position against the possibility of the CCI cancelling the deal, at the same time there is also a small possibility of a competitive bid. Why let that upside go! Which is why, I will hedge my cash market position by the futures position, but only after 25 days. We will still have another 5 months to go for the CCI to come out with its verdict, and if no competitive bids come in our trade continues the way it has been envisaged above.

    If there is no competitive bid over the next 25 days, the deal would still make sense and might become a little more attractive (small chance, but maybe), if Rs.65 included some speculative component in it, which then goes away in the absence of a competitive bid and the price drops below Rs.65 in the absence of any announcement and one gets to up the ante a bit more.

    Step IV: Remove the F&O hedge post the CCI clearance and the now just wait for the deal to go through since by and large SEBI clears most of the deals, it at best may put in some lag of a few weeks for some clarifications, etc., but that’s about it.

    Now, the questions:
    • Will you buy now and hedge your net long exposure using futures? Why or why not?
    Ans. Yes. But will put in the hedge only after 25 days and hold them till the CCI announcement (as explained above).

    • How will your estimate of acceptance ratio change over time?
    Ans. The original estimate was 67% but given all the excitement around the stock due to the takeover and a subsequent possibility of competitive bid, maybe more people might become aware of it so if about 8-10% people don’t usually tender, in this case that might drop to 5-6%. The thing about this deal is the time to completion which makes the possibility of more and more people becoming aware and taking some action towards tendering by getting their physical shares converted to demat, change of name, etc. These are small changes, but since the time availability is large, it might make sense to assume that the usual %age of people who do not tender could be slightly lower in this case. This is of course, assuming there is no competitive bid. But, if there is a competitive bid, then the entire trade changes.

    • What’s the worst case scenario, if you buy now and also hedge using futures?
    Ans. Like I mentioned in my Trade above, it does not make sense to hedge right away simply because we will take away any potential upside from a competitive bid. The hedge needs to be done after 25 days and upto the announcement of the deal by the CCI. However, in the interim there will be a small chance of the stock getting suspended from the F&O market, thereby exposing us to the downside of the CCI cancellation of the deal. But, the chance of that is quite small. Why would SEBI just arbitrarily remove the stock from the F&O list?

    • How will you deal with the possibility of a competitive bid?
    Ans. There is very little chance of a competitive bid. Why would a competitor enter into a bidding war when the erstwhile promoters of the Company in question have already sold out to another competing company and that too a majority stake 51%. Not only will this competitive bidding be expensive for the competitor it will also not help him get any material value out of the same under normal circumstances. A la Reliance vs Inox case is very rare! But, anyways by not hedging our position we keep ourselves open to benefiting from a competing bid.

    • How will you deal with the CCI risk and the SEBI risk in terms of a probability chain? (Hint: How many things have to go right for you to make money?)
    Ans. Factoring in CCI risk in terms of probability will make the trade unattractive in terms of expected pay off, i.e. 80% * 24% + 20% * (-46%) = 10%. This is an unacceptable outcome. The trade is meaningful only if we have the option to hedge away the risk of the deal not going through, i.e. by selling in the futures market.

    • What kind of deal-related (not market related) volatility can you expect in this transaction? How will you deal with that volatility?
    Ans. The deal related volatility will be very high during day 1 and the day when CCI announces its verdict. Keeping our cash position open during day1-day25 allows us to take benefits from any competing bid. If there is no bid, and if there was some speculative build up already there in the price, in the absence of a bid the stock might drop a bit, though not very significantly given that the original premise of tender offer by the acquirer still holds. But if the price does drop below Rs.65, it might make sense to up the ante and then on the entire position take a futures posn to hedge against the risk from CCI decision.

  73. Good evening Sir,
    First time I’m attempting an answer. I’m no management student, just a 2 bit software engineer.

    Template 3:
    Let’s say I buy 1000 Shares
    Invested amount = 1000 * 65 = Rs. 65,000/-

    Expected return with no competitive bid
    67% at Rs. 100/- & 33% at Rs. 35/- (my exit price) => 67000 + 11500 = 78,550/-
    Rate of return => (78,550 – 65,000)/65,000 => 13,550/65,000 =>20.85%
    Annualized, it comes to (this is over 10 months) => 20.85 * 12/10 = 25%
    Considering probability of 80%, the positive deal value = 20%

    If deal is not approved by CCI, the liquidate all at Rs 35, giving Rs. 35,000
    Hence, loss in this case => 35,000 – 65,000
    Annualized it comes to = (30,000/65,000)*(12/10) = 55.4%
    Considering probability of 20%, the negative deal value = 11.1%

    Since positive deal value is almost double the negative deal value,
    I’ll go with the deal even without shorting the futures.

    Now let’s consider that I short an equal number of shares in the F&O segment.
    Considering zero margin (!) and no transaction costs, AND positive cost of carry only(!)
    I’ll keep rolling my short position for all 10 months (or till the offer is closed)
    with closure in 10 months, my cost of carry = 65,000 * 12% * 10/12 = 6500

    (i) case when CCI approves the deal, my payoff:
    Tendering 67% shares @100/-: 67,000
    Selling 33% of remaining shares @35/- = 11550
    Gain on 1000 shares in F&O (assuming it falls to 30/-) = 35,000
    Absolute gain = 67,000 + 11,550 + 35,000 – 65,000 – 6500 = 42,050
    In % terms, it is 42,050 / (65,000 + 6,500) = 58.81%
    Annualized, it comes to 70.57% (NOT BAD!!!)
    Considering probability of 80%, it is 56.45%
    (ii) case when CCI does not approve the deal, my returns:
    Selling 100% of the shares @35?: 35,000
    Gain on 1000 shares in F&O (again assuming it falls to 30/-) = 35,000
    So my net gain/loss = 35,000 + 35,000 – 65,000 – 6,500 = -1500 (ONLY??)
    In % terms, it is 1500/(65,000 + 6,500) ~= 2%
    annualized, it is 2.5%
    considering probability of 20%, it is 0.5%

    Now, let me start answering:
    Answer 1: Absolutely necessary to hedge, since payoff ratio changes dramatically in my favor
    Answer 2: If there is a competitor bid, then price will go up, but acceptance ratio will fall (since more will tender).
    But that should generally not affect me since I’m guessing that product of price * acceptance ratio will be generally maintained.
    Also, my temporary loss in the futures (due to the price rise) should be recovered when the price falls post the offer.
    Answer 3: Worst case scenario if I hedge in the futures (with no competitor bid) is loss of 2.5%
    Answer 4: Competitor bid will cause me to lose in my shorted futures, (but only temporarily), so I must keep rolling over my position
    till the offer is fully completed and the price falls after that.
    Answer 5: CCI Risk and SEBI risk have to be handled by holding the shorted futures for the entire
    period and not just the CCI approval.
    Answer 6: Deal related volatility will be price rises at every competitor bid (over the next 25 days).
    Actually, over the next 25 days, I should not short the futures, but only after it is certain what is the highest bid
    (and price rises to corresponding that price) I should short.

    Humbly yours,

  74. Template #3
    SEBI’s probability of accepting the deal – 95%

    Ans. 1)
    Yes, it makes sense to hedge using the futures.
    Without hedging:
    Expected profit is Rs 310 on investment of Rs 6500. The returns come out to be 5% that is 6% annualized.
    This considers the SEBI’s probability of accepting the deal along with CCI’s probability which comes to 76% (80%*95%)
    With hedging: That is buying futures contract to sell the shares at current market price for next three months and rolling over at expiry.
    The expected value in this case increases to Rs. 1782 which is 27% or 33% annualized. With cost of carry of 10% for 10 months (simplistic assumption as I am not very familiar with the intricacies of futures market) the returns are still 23% annualized which are decent enough for me to enter the trade.

    Ans. 2)
    The acceptance ratio may change decrease over time if the other risk arbs start entering the trade. In the worst case scenario it may turn out that all brain dead investors exit the stock and the acceptance ratio is equal to the theoretical ratio.

    Ans. 3)
    Worst case scenario would be when the any one of CCI and SEBI reject the deal. There would be a cost of carry and an opportunity cost of capital which would result in a loss.

    Ans. 4)
    Competitive bid may result in a new opportunity. It would be expected that once a competitive bid comes in the price of stock may rise. For example, if the stock price rises to Rs. 85 after the competitive bid, the investor would get a chance to lock in the returns on the trade and exit very early. This would result in a very high annualized return. The pains and costs of rolling over futures contracts will be removed and also the probabilities of rejection of the will go out of the equation.

    Ans. 5)
    For the investor to make money the i) CCI should accept the deal (80%) ii) SEBI should accept the deal (95%)
    The probability of all these happening is 76% (80% * 95%)
    Unexpected delays can also be factored in by assigning a probability which would further reduce the probability of making expected returns.

    Ans. 6)
    Volatility can be cause due to following reasons:
    i) Competitive bid – which may turn out to be beneficial and investor can think of locking in the returns earlier than expected
    ii) Unexpected delays – which an investor should remain very active to. It may increase the cost and decrease the expected return but also provide an opportunity window as mentioned in Matrix-Mylan case


  75. A quick caveat, I have no experience in risk arb and futures markets, so my assessment is purely theoretical. I simply hope this exercise will help me at least understand some theory 🙂

    Answer 1:

    Will you buy now without the futures?

    No. The payout matrix based on what we know is as follows:

    – 80% chance of receiving Rs 78.6 in 10 months
    – 20% chance of receiving Rs 35 in 6 months

    So net expected value today, assuming a 12% expected return per annum (simplifying to 1% per month) is
    = .8 x 78.6 / 1.10 + .2 x 35 / 1.06
    = 63.8

    Current spot price at 65 is higher than this, so will not even give a return of 12%, something I can possibly earn simply by buying today and selling in futures market.

    Would availability of forward contracts make a difference?

    The forwards currently are available for 3 months. As I understand it, the open position in the future contract will necessarily have to be squared off within next 3 months (I guess even roll over amounts to square off plus new position at a different price).

    This buying spot and selling future should not impact expected returns from the transaction. For example, if I buy 100 shares and sell 30 in futures, the transaction can be considered 2 independent transactions – 70 shares bought to be tendered in open offer, and 30 shares that have a locked return of 12% from futures sale. The return earned on 70 shares will be independent of the 30 shares used to cover the short sale. So selling in future should not make a difference.

    The case where this buy spot sell futures can impact return is if the future expiry date is post the date of receiving back the tendered shares not accepted. In that case, the shares tendered in open offer are not independent of the shares sold in futures. This is because the shares bought today and sold in future can be tendered to increase the acceptance rate of the remaining 70 shares from 67% to nearly 100%. This scenario is almost equivalent to borrowing 30 shares, tendering 100 and then returning 30 shares received back post tendering, and paying a negative interest rate of 12% for the same.

    So selling in futures should help when the date of tendering is close and more or less concrete. But in that case the futures price would shift to reflect this logic, and hence will need to be evaluated based on prices at that time.

    Answer 2:

    How will estimate of acceptance ratio change over time?

    Not sure of this, but my guess would be that as time passes, more of the informed buyers would be holding the shares and hence the percentage of people tendering will increase, thus decreasing the accceptance ratio. In worst case, it will be 53%.

    Answer 3:

    Worst case scenario if you buy now and also hedge?

    If one buys now and hedges using futures, this will basically lock the returns at 12%. The worst case scenario will be in case the CCI approves the proposal and thus the spot price will increase to reflect the new reality. In this case, the opportunity loss will be the expected loss.

    For example, if CCI approves within 3 months (and assuming 100% chance of SEBI approval), the expected payout at the end of 4 more months (3 more months for SEBI and 1 for transaction) will be:
    = 67% x 100 + 33% x 35 = 78.6
    Thus the spot price 3 months hence will be
    = 78.6 / 1.04 = 75.6

    But since we have already sold at 67, our opportunity loss will be Rs 8.6 per share.

    Answer 4:

    Dealing with possibility of competitive bid?

    Since this is an unknown and it seems difficult to assign probability to it, and given that its expected impact is to increase the spot price, I will ignore it in my current computations.

    Answer 5:

    How to deal with CCI risk and SEBI risk together?

    If we assume that SEBI has 10% chance of rejecting the offer, this will reduce the odds of eventual acceptance of transaction and hence the payout matrix will be impacted as below:

    – 72% chance of receiving 78.6 in 10 months
    – 8% chance of receiving 35 in 9 months (SEBI rejects)
    – 20% chance of receiving 35 in 6 months (CCI rejects)

    This will change the expected value

    Answer 6:

    What kind of deal related volatility to expect and how to deal with it?

    There are basically 3 major events that should impact the volatility – competitive bid, CCI judgement, SEBI judgement.

    First, look at the competitive bid. In case there is a competitive bid, one can expect the price to shoot up to reflect the expectation of a bidding war. In that case, there is a chance for the price to go way beyond that can be derived based on fundamentals of the deal. At that point it may make sense to exit the transaction by selling the position (if you have built it) instead of waiting for the open offer. Similarly if there is no competitive bid, the price may fall and go below what can be derived based on logic and hence it may make sense to increase (or enter into) the position.

    Similarly, the events of CCI approving or not and SEBI accepting or not would likely trigger moves that are higher than warranted by fundamentals providing option to enter or exit the positions.

  76. Template 3:

    The current share price is Rs 65

    If the deal is not through because of numerous reasons like CCI not approving or SEBI not approving and some other unkown unkown reason, etc….then the end result will be that the share price will plummet to Rs 35 or even lower.

    If on the other hand, the deal is through, then for the remaining shares which are not accepted, the share price will still plummet to Rs 35….

    So one thing is certain….the share price will plummet to Rs 35 some time in the future whether the deal is through or not (may be 9 months down the line, which is contingent to competitive bid, in which case it will take even longer)….

    So the question is why bother going long in the deal…..why not just short by selling futures without taking any long exposure?……I would be net short in the deal, rolling over the futures every 3 months…… The cost of carry is only 12 % p.a……The profit earned in futures if the share price plummets to Rs 35 (which is for sure) is 61% p.a….. Net profit by just shorting is 49.5% p.a. with 100% certainty i.e. risk free….

    Or am I missing something?

    1. The futures contracts are trading at a premium reflecting cost of carry of 12%, but they are available for 3 months and do not cover the CCI / SEBI event.
      When futures contracts expiring after those events become available, the relation between spot and futures price will not remain the same as today. Futures might be trading at a discount reflecting the expected value of share prices. so, you can’t simply roll over

      1. In addition, there are other risks in naked shorting. When the time to square up the position comes, the stock could be very illiquid. Recall that there may be a competing bid of 26% or more, and if you add that to existing bid of 26% and then also consider that 51% of the shares are with promoters, then virtually all the liquidity from the stock would have disappeared just when you’d have to square up your position. While you are merrily thinking about the huge supply to come when returned shares hit the market and bring the price down making you tons of money on your short position, what if those shares come back too late i.e. well after you have to square up? What if the liquidity is totally dried up and there are no shares in the market because all the shares are with the custodians to the offer? In that situation you will be exposed to the possibility of a short squeeze which with ruinous outcome. Do you want to take that risk?

        Read this:

        and this:

        Do you want to end up like Adolf Merkel?

        I think not.

        SEBI should stop allowing F&O trading in stock which become illiquid due to tender offers but that hasn’t happened yet.

        I am VERY averse to the idea of naked short selling because I don’t enjoy the prospect of jumping in front of a train one day.

  77. Template 3

    Not sure if I’m thinking about this template the right way, as I am not familiar with futures markets and there might be many factors I am missing here. But here goes:

    1. Will you buy now and hedge your net long exposure using futures? Why or why not?
    By buying shares now and hedging using futures, I will lock in a return of 12%p.a (less any transaction costs) for a maximum of 3 months. After that, I have to roll over my futures contract but the cost of carry might change by then so I have to review the situation then. If I am looking for returns in excess of 15-20%, then this trade won’t be attractive. If I’m just looking to park my funds for a few months and am satisfied with a 12% return, then I might consider this.

    2. How will your estimate of acceptance ratio change over time?
    Acceptance ratio of 67% is based on present shareholding. However, there is a possibility of counter bid in the next 25 days and a potential bidder has already expressed interest. The shareholding pattern could change over the next 25 days if rumours of a counter bid gather steam and more risk arbs move in. So I think I should reduce my expectations of the acceptance ratio. If there is indeed a counter bid and a long drawn battle in the media spotlight, some of the brain dead investors might wake up and acceptance ratio might fall further.

    3. What’s the worst case scenario, if you buy now and also hedge using futures?
    Worst case scenario: At the end of 3 months, I make a return of 12% annualized as my selling price is fixed.

    4. How will you deal with the possibility of a competitive bid?
    A competitive bid will result in increase in offer price but could also mean further delays, lower acceptance ratio, greater volatility in share price. The unknowns are many: Probability of competitive bid, How long and how high the bidding war may go on, the probability of CCI approval for competing bid. I was unable to figure out if there’s any way we could make a good trade with favorable odds.

    5. How will you deal with the CCI risk and the SEBI risk in terms of a probability chain? (Hint: How many things have to go right for you to make money?)
    I am assuming a small probability of rejection by SEBI of 5%. In the absence of a competing bid, the current offer must be approved by CCI (P=0.80) and by SEBI (P=0.95) for a total probability of 0.76 (0.80*0.95), in which case I make a return of 20.85% in ten months (or 25.02% annualized).
    The probability of rejection by CCI is 0.20, in which case I make a return of -46.15% in six months (or -92.31% annualized).
    The probability of SEBI rejecting the deal after CCI approval will be 0.8*.05 = 0.04, in which case I make a return of -46.15% in 9 months (or -61.54% annualized).
    The odds don’t seem favorable in this scenario.
    In case there is a competitive bid, there are too many unknowns to calculate expected values.

    6. What kind of deal-related (not market related) volatility can you expect in this transaction? How will you deal with that volatility?
    Volatility can be due to competitive bids, CCI approval and SEBI approval. During the first 25 days, there may be some volatility as potential bidders make statements or rumours start floating in the market. In case there is a competitive bid, there may be high volatility in anticipation of a bidding war or disappointment on early end to bidding war. CCI decision and SEBI approval will also have a major impact on the share prices. Not sure if there is any way we can take advantage of the volatility…

    Looking forward to your insights to throw some light on how to approach this kind of situation.

  78. Additional Questions

    Answer 1

    Filter the deals further down to deals that have the highest likelihood of completion and where the likelihood of delays is lowest. These deals may have the following characteristics – announced deals with definite agreements in place, strong financial strength of the company or deals where funds for the event have been made available, low regulatory risk, if it’s a merger situation then the acquirer should be bigger.

    After screening opportunities, my default position will be to invest more in deals (irrespective if returns are above AAA or below AAA) with low downside, have the potential for positive surprise and/ or where a contingent claim can be bought for free.

    Answer 2

    If I only do event driven or special situations and I manage substantial amount of capital, then I need to practice very wide diversification. So maybe I would invest 90% -95% my portfolio in 25-30 deals and have 5% -10% portfolio in cash for unexpected developments or opportunities.

    Assuming, I have the same conviction in all my deals, on average I will risk 3% of my capital in all deals. However, because of various factors such as return potential, limited downside, how the expected value changes over time, contingent claim, past experience etc, my actual position will vary from the 3% benchmark. I think, there should be a cap for risk management reasons – may be at 5% of portfolio. However, if there is particular deal which offers very high return potential with little downside, then an exception should be made and you may want to bet upto 8% – 10% capital.

    If my asset base was smaller, I would run a more concentrated position – probably make 10 bets of 10% each.

    If I am Buffer style investor – finding great companies at good prices – then I don’t think risk arbitrage has that much of a role in my portfolio. Ideally, I want to be fully invested, with cash available during a downturn to take advantage of mispricing than for Risk arb. Risk arbitrage will only play a role, I think, if :

    1) You are using the special situation as means to acquire cheap shares for a long-term investment – so position size in risk arb will be driven by long-term position size than the risk arb opportunity.

    2) There is a bull market and you can’t find long-term opportunities. In this case you can run the cash portfolio as a special situations fund – I would pro-rate the allocations mentioned above for my cash holdings.

    Sir – thank you for this experiment. It certainly has helped me know more about risk arb. I hope you carry out more experiments in the future.

  79. So now we have live example to discuss about, Bakshi Sir, why not initiate a thread on USL deal, might be its bit late but i am sure, you and our whole avid team of followers, will have lots to discuss about.

  80. i can see the utility of teaching these techniques. however, i would probably not invest using these techniques. i will probably do it only if i was privy to information that i think most people arent.

    there is also an issue with biases creeping in when estimating the probabilites. sometimes the aggregates of probabilites(the market price) tend to make better estimates because they tend to average the biases to zero(unless there are systemic biases that everyone has). i think “thinking fast and slow” qoutes “the wisdom of the crowds” on the same topic.

    depending on how crowded the trade gets(and seeing the same sort of reply by everyone), it might actually be more profitable to bet on the betters (game theory v/s decision tree) given that the betters have a predictable pattern.

    and then again decision trees are based on arithmetic-mean of the good and the bad case. and we all know of the statistician who tried to cross a river which on average was 3 ft deep and drowned(flaw of averages). i guess you counter that by saying, invest a small percent of your net worth(or a lot of other peoples money). and then “on average” you will do as good as your probability estimates. i wouldnt know how to come up probability estimates for merger deals happening across the spectrum(unless i spend considerable amount of time). therefore this one goes in my “too hard” box.

Comments are closed.