There was this problem which was debated for centuries. It is known as ‘Problem of Points’. It is described as two players playing a game of chance, while putting up equal stakes, and the one who wins the certain number of rounds wins the entire stake. But the game is interrupted before completion. How do the players divide the stakes fairly?

Blaise Pascal, a French writer and mathematician, came up with an idea that the share of stake received by the player should be proportional to their chances of winning if the game were continued. This led to the Expected Value Theory.

According to Wikipedia, “Expected Value is the arithmetic mean of the possible values of random variables can take, weighted by the probability of those outcomes."

This theory can be applied to anything that deals with the future, including investment operation.

An investor tries to determine their expected rate of return on an investment by analyzing the estimates of all possible returns. This is done by the defining the mathematical expectation, i.e., the range of all possible outcomes of future returns, including the negative ones, adjusted for their respective probabilities.

The investor then builds a portfolio of such carefully selected opportunities where their expectation of each is greater than his desired rate of return. The weightage of each stock is dependent on a) the degree of expectation and; b) the range of expectation. The first criterion is that one opportunity shall weigh more to the portfolio if it has higher expectation than the other. The second criterion is that when two opportunities have same expectation, the one with narrower range of expectation shall weigh more than the one with the wider range of expectation.

This is not as easy as it seems. It requires great knowledge and experience to perform the above operation. Ultimately, the performance of the portfolio depends on the skill of the investor. To be ‘skilled’, an investor must be able to identify which stocks are more undervalued than others, and construct a portfolio containing only the most undervalued stocks.

Let us conclude this discussion by jotting down the few simple and big ideas that we have learned.
1. Think about the probabilities and their consequences to define expectations.
2. Use opportunity cost concept.