Lesson Corporate Finance: Beta

Beta is the measure of volatility of a security relative to the market volatility. Fundamentally, beta is that part of the volatility of the security which cannot be mitigated through diversification (by creating a portfolio). In general, the volatility of individual security is more than that of a portfolio created with that security. Since the prices of any most securities are correlated most of the times, the volatilities of do not cancel out completely on combining a large number of securities. If they were totally uncorrelated, the volatilities would have canceled out leading to risk free returns on the portfolio.

Capital Asset Pricing Model (CAPM) uses beta as one of the main coefficients and measures the expected return on any of security. The beta of a security can be found relative to the market return in the following way:



where is the market return and is the return on security. This means that a stock with beta of 2 would have double the volatility than the market. If the markets go up 5%, then the stock would go up by 10%.

However, there is a word of caution here. Beta is used only as a correlation to market movement and does not give indication on performance of the security. A stock with beta of 2 gives twice the return compared to market when market goes up, but it also leads to twice the losses than market when the market goes down. Thus a beta of 2 does not indicate independently the performance of a stock.

The return on a stock can be estimated through beta in combination with the market return. The equation (called CAPM) for the same is:



where is the risk free rate in the market. Thus if the beta of a security is known, it estimated return can be calculated based on the historical market returns. The beta is generally estimated by linear regression on security return and market return.

Example: Calculate the beta of a stock which gives an average return of 15%. The average market return is 10% and the risk free rate is 5%.

Solution: Beta can be calculated as - Beta = (Rs-Rf)/(Rm-Rf) = (15-5)/(10-5) = 2
To calculate the beta or the return on a security, refer to the following solvers: Calculate return on security, given Risk Free Rate, Beta and Market Return, Calculate Beta of a security or portfolio