Finding Beta of a stock

Beta is a measure of the systematic risk pertaining to a security. It is an estimate of the returns on a stock when the market changes by a unit percentage. A beta of 1 means that the stock is in perfect correlation with the market, if the market moves up by 1% the particular stock will also move up by 1% and vice-versa. There are many ways to estimate beta the most common one being using the historical data. Since beta estimates the returns using historical beta may not always yield the exact future returns, but most of the times they explain the trend.

Historical beta is calculated by regression of the stock return and market return for a particular time period unit. This may be daily, weekly, fortnightly, monthly, or quarterly depending upon the available data, accuracy required and relevance. The market returns are measured by taking the returns of some index which takes the representation of almost all the sectors of the market.

Lets find beta for State Bank of India (SBI). We have taken the returns on weekly basis and market as CNX-500. The data for the last five years up to December 15, 2007 have been plotted below.

Regression analysis yields the slope of the line as 1.156 which is beta.

The historical price movement of SBI and CNX till December 2007 is shown below.