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?
6 comments:
Is UD's class sooo interesting that u brought classroom work to ur blog itself?!
This is not work, I (and the rest of my classmates) finished understanding it in the class itself. I just wanted to see if I can make non-fin and non-eco people understand it since the funda seemed so simple and lucid to me...that is why the posts.
BTW, UD Sir's classes are interesting, no doubt :-)
baba re baba
Hmm.. I could figure out the risk taking behaviour of the masses by the last post, but could not associate any mathematical formula to it.
Mathematics and its applications never cease to amaze me! It was wonderful to realize that even the very suble aspects of life are all guided by mathematical principles.
Great.
Mathematics is amazing, no doubt but only for those who understand it, ask the people on the other side of the fence and you will know what they think of mathematics :-)
very true!
Post a Comment