Lesson Corporate Finance: Beta

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This Lesson (Corporate Finance: Beta) was created by by Shruti_Mishra(0)

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About Shruti_Mishra: I am a maths graduate from India and am currently persuing masters in Operations Research.

<A HREF="beta_coefficient.wikipedia">Beta</A> is the measure of <A HREF="volatility.wikipedia">volatility</A> of a security relative to the market volatility. Fundamentally, <A HREF="beta_coefficient.wikipedia">beta</A> is that part of the volatility of the security which cannot be mitigated through <A HREF="diversification_finance.wikipedia">diversification</A> (by creating a portfolio). In general, the <A HREF="volatility.wikipedia">volatility</A> of individual security is more than that of a <A HREF="portfolio_(finance).wikipedia">portfolio</A> 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.

<b><A HREF="capital_asset_pricing_model.wikipedia">Capital Asset Pricing Model</A> (CAPM)</b> uses <A HREF="beta_coefficient.wikipedia">beta</A> as one of the main coefficients and measures the expected return on any <A HREF="portfolio_(finance).wikipedia"> of security. The <A HREF="beta_coefficient.wikipedia">beta</A> of a security can be found relative to the market return in the following way:

where {{{r[m]}}} is the market return and {{{r[s]}}} is the return on security. This means that a stock with <A HREF="beta_coefficient.wikipedia">beta</A> 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. <A HREF="beta_coefficient.wikipedia">Beta</A> is used only as a correlation to market movement and does not give indication on performance of the security. A stock with <A HREF="beta_coefficient.wikipedia">beta</A> 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 <A HREF="beta_coefficient.wikipedia">beta</A> of 2 does not indicate independently the performance of a stock.

The return on a stock can be estimated through <A HREF="beta_coefficient.wikipedia">beta</A> in combination with the market return. The equation (called CAPM) for the same is:

where {{{r[f]}}} is the risk free rate in the market. Thus if the <A HREF="beta_coefficient.wikipedia">beta</A> of a security is known, it estimated return can be calculated based on the historical market returns. The <A HREF="beta_coefficient.wikipedia">beta</A> is generally estimated by <A HREF="linear_regression.wikipedia">linear regression</A> 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: <A HREF="calculate_ROA.solver">Calculate return on security, given Risk Free Rate, Beta and Market Return</A>, <A HREF="calculate_beta.solver">Calculate Beta of a security or portfolio</A>