By : Harish Srigiriraju
MBA Capital Markets ,NMIMS 2011-2013
Now
think about how much would you be willing to play for this game? As per the
probability theory since there is a payoff which is unlimited, it would suggest
that a player should ideally be willing to put any amount of money to play
this. However, people would not be willing to pay a high price for this. In a
survey conducted in 2004 on an average, people were ready to play it by paying
up around 25 Rs. Now what is the reason behind people paying up so less despite
the possibility of unlimited payoff? Few
theories can be used to explain this phenomenon. The “Expected Utility Theory”
explains this on the basis of diminishing marginal utility of money but this
might not be true in most of cases. The “Probability Weighting theory” gives
less weight to unlikely events but contrary to this it was observed that people
give more weight to unlikely events. Can it be explained based on the fact that
the casino cannot have infinite resources? How much ever finite the resource
are, this does not explain the low amount the players are willing to pay.
MBA Capital Markets ,NMIMS 2011-2013
“Price is what you pay and value is what you get” –Warren Buffet
Everything
in this world has a price and not paying the right price will always create
problems. Warren Buffet waited for about 30 years before he bought Coca-Cola.
He waited for that long only to get the right price which will then give him
the necessary returns. Many of the M&A deals have failed only because of
paying more than what was necessary. It is essential not only to select good
assets for investments, but also to pay the right price to acquire them, and
this brings us to the concept of St. Peterburg Paradox.
Petersburg
Paradox is a paradox related to probability and decision theory. It is an
essential theory to understand the behaviour of an investor and pricing
decision. The problem and its solution were first presented by Daniel Bernoulli
in 1738. Assume that a casino offers a play where there is an unbiased coin
which is tossed at each stage. The prize money starts with one rupee and
doubles every time a tail appears. At any point of time if the head appears,
the game ends and the player can take away the money earned so far.
Now
think about how much would you be willing to play for this game? As per the
probability theory since there is a payoff which is unlimited, it would suggest
that a player should ideally be willing to put any amount of money to play
this. However, people would not be willing to pay a high price for this. In a
survey conducted in 2004 on an average, people were ready to play it by paying
up around 25 Rs. Now what is the reason behind people paying up so less despite
the possibility of unlimited payoff? Few
theories can be used to explain this phenomenon. The “Expected Utility Theory”
explains this on the basis of diminishing marginal utility of money but this
might not be true in most of cases. The “Probability Weighting theory” gives
less weight to unlikely events but contrary to this it was observed that people
give more weight to unlikely events. Can it be explained based on the fact that
the casino cannot have infinite resources? How much ever finite the resource
are, this does not explain the low amount the players are willing to pay.
This
paradox can be explained in two ways. One with the help of the “von
Neumann and Morganstern axioms” where
it can be explained that the investor does not take decisions only based on the
expected payoff but always on the basis of the risk taking ability and the
payoffs are thus risk adjusted. As per the “Erodig Theory” the
time averages maybe different from space averages and the probability theory
should only be used when the systems are erodig in nature. To make things
simple, it implies that the expected gains increase with the increase in number
of games. So if only one game is played, the probability theory will not hold
true. These two theories explain that there is a rationale behind the paradox
which is based on risk aversion.
Similar
to this paradox are real life situations which investors face in order to
decide the price for a particular stock. For high growth companies, it is often
assumed that the payoffs are unlimited and any price paid can be justified.
However this is absurd as the payoffs even if unlimited, has to be risk
adjusted and hence there is always a right price for everything. In my recent
encounter with Ashwath Damodaran, someone asked him if he was willing to invest
in a company with very good growth prospects but corporate governance issues.
His answer was a bit surprising but logical when he said he would definitely
invest but only at the right price.
