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# Probability and Finance

June 10, 2010

Probability is one of the most useful topics whose application in finance and investment domain is pretty important. Let’s consider a practical example of one of the very interesting applications of probability.

You are a research analyst in an investment bank. Lets consider a hypothetical case, there are two firms in the power industry, Reliance ADAG, and Essar group. Government has decided to cut down the tax on the power sector. As a result of this information you believe the equity of Reliance reflects a 0.89 probability of such decision. The Essar group is equally benefited by the decision. But your analysis show that the equity reflects only 0.45 probability of such decision.

Here two cases arise

Case 1 The probability 0.89 is the correct probability reflected on Reliance equity, hence the probability 0.45 on Essar equity is not correctly valued, its stocks are undervalued.

Case 2 The probability 0.45 is the correct and shows the shares are fairly evaluated on Essar, the probability on Reliance is overvalued.

The cases show that Essar shares are a better value than Reliance, even if the probability 0.89 is accurate. Thus Reliance shares are overvalued relative to Essar shares.

As an investor what should be your investment strategy?

As an investor your strategy depends on the accuracy of your analysis and on any investment constraints that you face such as if you can short sell.

We can formulate 2 investment strategies here

First is a conservative strategy, as you know the Essaar shares are a better option, you buy Essar shares and eliminate or reduce any position in Reliance.

Second is the most aggressive strategy to short Reliance stock (relatively overvalued) and simultaneously buy the stock of Essar, which is also called pairs arbitrage trade.

This is one of the most simplest cases of application of probability in finance. A lot of competitive exams for MBA, CFA, FRM, PRM give high importance to probability sections. A logical approach to probability problems can make your preparation easy.

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