The beta coefficient is a measure of the volatility of an individual stock in comparison to the volatility of the entire market. Beta coefficient calculates the expected return on an asset considering systematic risk of its volatility in comparison to the market’s return of investment and its volatility/risk.
The beta formula is used in the Capital Asset Pricing Model (CAPM) for calculating the rate of return of a stock or portfolio and calculate the Cost of Equity as shown below:
Cost of Equity = Risk Free Rate + Beta x Risk Premium
This can be calculated using below formula:
Re: the return on an individual stock
Rm: the return on the overall market
Covariance: how changes in a stock’s returns are related to changes in the market’s returns
Variance: how far the market’s data points spread out from their average value
As you see, the beta coefficient represents the slope of the regression equation of data related to the return of an asset or stock against the return on the total market (such as S&P 500 stock index representing the entire market) or another portfolio. For beta to be meaningful, the stock and the benchmark used in the calculation should be related. A stock with a higher beta has greater risk and also greater expected returns. The beta coefficient can be interpreted as follows:
β =1 exactly as volatile as the market
β >1 more volatile than the market
β <1>0 less volatile than the market
β =0 uncorrelated to the market
β <0 negatively correlated to the market
A beta greater than 1.0 could indicate an investment that moves with the market and/or is more volatile than the market. Adding an investment with a beta greater than 1.0 to a well-diversified portfolio should increase the portfolio’s risk. A beta of less than 1.0 indicates that only some of its returns are due to overall market movements. Adding an investment with a beta less than 1.0 to a well-diversified portfolio should reduce the portfolio’s risk. A beta of zero means that an investment’s returns are independent of market returns. A beta of -1.0 implies a 100% negative correlation between the investment and the market (e.g. a short position in a stock).