Deciphering...continued

Carrying on from where I left last time, I will try to give a logical conclusion to the discussion (for whatever it is worth) that I started in the last post. I was talking about the fair game that Prof. Uday Damodaran had introduced us to and about our willingness to play the game. However, as I had tried to show in the last post, the actual payoff from the game was an uncertain Re. 1 which was to be won by giving in a certain Re. 1, which we were to understand, was the job of a gambler and not that of an investor or even a speculator.

Going forward, if we consider the utility that the player of the fair game has for the amount that he/she is going to put in to the game and the utility that he/she has for what he/she is going to get out of the game, we might just have a better idea of the way things stand. Let us say that the utility is represented by the alphabet 'U'. Therefore, the utility of the 1 Re. spent in playing the game is U(1). Utility of the Rs. 2 won if a head turns up is U(2) and the utility of 0 that is the return from the game if tail turns up is U(0).

Therefore, for an intelligent and rational investor who prefers a certain Re. 1 over an uncertain Re. 1

U(1) > 1/2 * U(2) + 1/2 * U(0)
[1/2 because that is the probability of either of the two utilities to be obtained by the player]

Multiplying the above inequality by 2 on both sides,
2*U(1) > U(2) + U(0)
or, U(1) - U(0) > U(2) - U(1)

This, as Dr. Damodaran explained, is nothing but the principle of Diminishing Marginal Utility. As we can see, the utility of going up from 0 to 1 is higher than that of going up from 1 to 2. This is the reason why most of the investor behavior in the financial markets follows a utility function that has a negative slope (assuming that there is no negative utility of wealth, which might not be true in the case of goods in the microeconomic sense where for example, eating more of say, fruits will start giving negative utility after a certain number has already been consumed).

To put it into more practical terms, the investor's risk taking behavior or tendency goes on decreasing as the amount of money involved starts increasing which is what you would expect, won't you?

Can you decipher this?

One of the courses this term that I have been really enjoying is Prof. Uday Damodaran's Portfolio Management. A change from the somewhat theatrical to a definitely more structured course being one important parameter that has grabbed our attention, there are several other reasons why there is almost full attendance in his classes, even if they are held at 7 in the morning.

Anyways, talking about the teaching methodology of Dr. Damodaran was not the purpose of writing this post. Ever since the last class, when we played the game that is popularly called St. Petersburg Paradox and subsequently analyzed it, I have been wondering if the explanation was so simple that even a lay person with absolutely no idea about finance or economics can understand the same. I will try to enumerate what took place in the class room and leave it for the readers of this blog to decide if they can decipher what I am talking about.

The game went like this: the class was divided into groups of six with one person in each group acting as the gaming house and the other five enacting the roles of players. There were five rounds in total with each round starting with closed bids by the players being submitted to the gaming house. The gaming house, based on the received bids, chose the player it wants to play with. Ideally, the player chosen should be the one with the highest bid but in case of ties, it depends on the gaming house's discretion. Irrespective of whether a player's bid has been accepted or not, he/she has to forfeit the amount that he/she has bid on the round to the gaming house.

Once the player is chosen, the game begins. The game involves tossing a coin till a head comes up. The number of times that the coin has to be tossed before the head turns up decides the payoff for the player who gets 2 raised to the power n where n is the number of tosses before a head appears. So the minimum that a player will get out of this game is 1 and the maximum can be infinity. Similar methodology is followed for the other four rounds.

Once the game was over, an average was taken of the amount that the players had bid for (including successful and unsuccessful bids) and for our class, it turned out to be nearly 7. Next up, Dr. Damodaran presented another game which is popularly known as the fair game. In this game, the player gives 1 Re. to play and a coin is tossed. If the coin turns head, the player gets Rs.2 and he/she gets 0 if it turns tail. When asked about how many of us would play this game, the majority said they will.

This, Dr. Damodaran said, disproved the basic assumption of finance and economics that we had been trying to understand for the past sessions of the course. The probability that head occurs is 0.5 and that of tail appearing is also 0.5. The expected payoff from the game, therefore, would be 0.5*2 + 0.5*0 (that is, a summation of probability of event multiplied by payoff from the event) which turns out to be 1. Thus, a person playing this game would be foregoing a certain 1 Re. for an uncertain 1 Re. (return from the game is only an expected payoff, remember but the money that the player puts into the game is a certain Re. 1). This is certainly not rational investor behavior but something that most people would claim to have when asked about it, primarily because of the positive connotations associated with risk-takers.

However, a similar payoff vs. investment analysis exercise carried out with the St. Petersburg game shows that the reality is quite different. Here, probability of getting head in the first toss (with payoff of 1) is 1/2. Head in the second toss has the probability (1/2) squared and the payoff is 2 raised to the power 1. For the head to appear in third toss, probability is (1/2) to the power 3 and the payoff is 2 to the power 2. Going on in similar fashion, we find that for each event (where event means the number of times that the coin has to be tossed before a head comes up), the product of probability and payoff is 1/2 in each case. Thus, expected payoff from the game would be a summation of 1/2 infinite times, which comes to infinity.

For an infinitely paying game, therefore, the average amount that our class bid was only Rs. 7. And we said we are risk lovers when asked about the fair game...just goes on to show how there is much more to behavioral finance than just asking the basic questions and trusting the investors' answers blindly. If put in a guise, the real picture does come up. There was a further follow up to this discussion, explaining matters in much greater detail but perhaps, I will save that for some other post to avoid an overdose and of course that post will come up given this one makes at least some sense.

The benches in the back *sigh*

The last time they made me sit on the first bench in class, I almost passed out. I have always been one of those typical back benchers throughout school, college, corporate training rooms and now in IIMK. For the back benchers, there is no need of any blog to tell them the merits of making their home where they choose to, but for all those souls who are ignorant of the multifarious opportunities provided by the back benches and for those poor sods who intentionally avoid the back benches for whatever reasons, here is an attempt to unravel the mystery. Before proceeding any further, however, I would like to acknowledge the source of inspiration for this attempt...none other than the back benches in the new class rooms at IIMK, which are built purely for the back benchers with chairs squeezed in to increase the class capaciy.

Today is the day when all your questions are going to be answered...there are going to be answers to the quizzical glances you always gave to the guy running in at the last minute (a side effect of being a back bencher) and heading straight to the last bench in a class hardly filled up to the third or fourth bench...there are going to be answers to all those times when you got frustrated because the teacher picked you to answer a question and not the back bencher snoring away to glory...even answers to the times when the back bencher was able to answer the question you couldn't despite snoring away to glory a moment ago.

The obvious difference that the back benches make is that of visibility. The absolute lack of it can be further accentuated by a certain shift in posture that only the back benchers are capable of (do come to me sometime if you want to learn the trick...I will try to help you with the best of my experience). This shift makes it virtually impossible for even the keenest of teachers to spot you and even if they do get some indication of your presence, the posture can be modified slightly to appear that you are the only student engrossed in whatever the teacher is saying and in your efforts to retain it all, you have gone into a scientific aasana.

Actually, it is all about perspective. The "global" perspective that a back bencher can gain from the class discussion is unmatched. Sitting at the very top (in case of sloping lecture halls like ours) or at the very back, in line with anything else but teacher's sight (as in schools with level floored classrooms), the back bencher enjoys the sound wave reflection that is unimaginable for anyone else. All the crap that gets around in the class room has to come and strike the back benches on their way to the rear wall of the class (don't ask me what the sound waves are doing near the rear wall) and thus have to come to the back bencher. This, here, is the answer to your pseduo intelligent back bencher you wanted to throw your book at for stealing your point and giving a detailed answer, leaving you with nothing else to speak on when the teacher caught you.

The overall personality development that a back bencher is capable of is unmatched, too. With novels, magazines, newspapers, and the like making the back benches their home (there have been so many occasions where I didn't even have the need to get a book along...it was already there under the desk, left by the previous informed inhabitant of the back benches), the back benches act as information highways. The journey on this highway, aided by the sound wave reflection make sure that the back bencher achieves much more than the ear-cocked-head-tilted first bencher.

There are so many other things that I can count as the advantages of being a back bencher but if you have not decided to attain salvation by now, then perhaps the devil owns you :-). Speaking of the devil and his followers who sit on benches other than the ones in the back, let me assure them that God sees everything in this world and He has given us back benchers a special power to get back at all of you. Of course, since I have that special power, I am not going to be naive enough to share it with you non-believers but for all those who want to belong, let me tell you my sisters and brethren, as Morpheus told Neo...unfortunately, no body can be told what the back bench experience is, you have to experience it to understand it.

Left up the spot light

To know that Prof. Uday Damodaran knew my by name did not come as much of a surprise (given his much acknowledged interest in student blogs) but that I came to know of it for certain in this way, really took the cake. It was the first of a series of UD's quizzes on readings from The Economic Times and I was peacefully writing whatever precious little I knew of the answers. I have this habit of moving my head and craning it upwards and towards the left at an angle of nearly 45 degrees whenever I am thinking hard (am not sure but I believe that I have read it somewhere that it is natural for people to look Left Up if they are trying to make up something, Right Down if they are trying to recollect something and so on).

To say that I had no idea that UD might take it as an indication that I was cheating, would probably be an exaggeration. I admit that it may look to the 'suspecting' eye as something not really out of a book but then again, the truth of the matter is that there was hardly anything that I could have cheated for (even at the cost of hypothetically admitting of my intention to cheat). Nobody would have known more than what everybody (including me) knew and so, it was not worth it at all. Whatever it may have been, as Ravi rightly pointed out, I am now in the spotlight and I better take care of myself and my neck movements from now on if I don't want any more trouble from UD.

I might as well go for that band those people wear around their neck for some back/neck problems...