One of the basic equations of financial markets is that risk is directly proportional to return. For taking a particular level of risk, an investor expects to get an appropriate return. But how can we know what our return should be, considering the level of risk undertaken? Theoretical answer to this common question is provided by what is known as the capital asset pricing model.

**Johnny:**If I remember correctly, last week while talking about beta you had mentioned about capital asset pricing model (CAPM). I was curious to know more. Can you explain what exactly CAPM is?

**Jinny:**CAPM (pronounced as cap-m) was developed by William Sharpe and some other financial economists—Jack Treynor, John Lintner and Jan Mossin—during the 1960s. All these economists worked independently; however, all of them shared the same curiosity—how is risk related to return for a particular security? Harry Markowitz, another financial economist, set the ball rolling by defining risk in his Modern Portfolio Theory (1952). Markowitz measured risk by calculating the number of times the actual returns varied from the mean. By creating linkages between risk and expected return, CAPM took our understanding of risk to a higher level.

This model is based on the idea that any investment in financial markets faces two kinds of risks—systemic risk and unsystemic risk.

Illustration: Jayachandran / Mint

Unsystemic risk is something that is more specific to individual stocks—for instance, the chances of a firm indulging in fraud. You can reduce the unsystemic risk in your investments by choosing a diversified portfolio. The more diversified your portfolio is, the lower would be unsystemic risk.

However, there is no way of reducing the systemic risk. As long as you are part of the financial market, you would face the systemic risk. CAPM devises a formula which tells us how much return an investor should get for taking the systemic risk.

**Johnny:**How does the CAPM formula calculate the expected return?

**Jinny:**CAPM uses the risk-free rate of return as the benchmark. A risk-free asset is something that does not carry a risk of default, for instance, government securities. If 10-year treasury bonds are earning a return of 6%, then investment in the stock of a firm ought to earn more. How much more? CAPM uses a formula in which the difference between the return generated by the overall market and the risk-free rate of return is multiplied with the beta of a particular stock to arrive at the extra return. This extra return is the risk premium any stock should earn for taking the systemic risk.

**Johnny:**Could you explain this formula by taking an example?

**Jinny:**Say, for instance, a stock has a beta of 1.5. How much return should it generate? For the sake of convenience, presume that the risk-free rate of return is 6%. Now the only thing we need to know is the return generated by the market as a whole. For this, we would take a market index as the representative of the whole market to which your security belongs. If your security is a stock listed on the Bombay Stock Exchange, then you can take the benchmark Sensex as the representative of the market. How much the Sensex has earned over a period of, say, one year would tell you how much your stock should have earned over the same period, according to CAPM. Let’s presume that the Sensex generated a return of 9% during the period under consideration. Now you can do the remaining calculation on your own. Subtract 6, the risk-free rate of return, from 9, the return generated by the market, and multiply it with 1.5, the beta of your stock. The result is 4.5. So your investment should earn 4.5 percentage points more than the risk-free rate of return of 6%.

The main variable in the CAPM formula is beta. The other two variables, the risk-free rate and the return generated by the market, would remain common for stocks belonging to the same market. However, two stocks belonging to the same market would have different expected return because of the difference in beta.

**Johnny:**This formula looks simple but simple formulas sometimes have complex drawbacks. I wish you would tell me about that, too, in the future.

**What:**The capital asset pricing model (CAPM) creates a linkage between risk and expected rate of return for different securities.

**How:**CAPM uses a formula that adds the risk-free rate of return with the risk premium of a particular security for arriving at the expected return.

**Who:**The theory was developed by William Sharpe and other financial economists—Jack Treynor, John Lintner and Jan Mossin—independently.

*Shailaja and Manoj K. Singh have important day jobs with an important bank. But Jinny and Johnny have plenty of time for your suggestions and ideas for their weekly chat. You can write to both of them at realsimple@livemint.com*