Application of the Beta Coefficient

The purpose of the beta coefficient is to explain the relationship between a stock’s risk and return and that of the market. The formula illustrates that the required rate of return on a stock equals the risk-free rate of interest plus the stock’s beta coefficient multiplied by the amount by which the market return exceeds the risk-free interest rate.

Required rate of return = risk-free rate + β(market rate of return - risk-free rate)

Using this equation, an investor seeks a return from a stock that exceeds the risk-free rate of interest (the rate of return on a Treasury bill) and the risk premium of the stock (beta coefficient of the stock multiplied by the market rate of return minus the risk-free rate).

For example, if the risk-free rate is 3.5 percent and the market is expected to rise by 8 percent, the returns for two stocks with beta coefficients of 1.2 and 2, respectively are Stock with a beta of 1.2:

Required rate of return = 3.5% + 1.2(8% - 3.5%) = 8.9%

Stock with a beta of 2:
Required rate of return = 3.5% + 2(8% - 3.5%) = 12.5%

Because the stock with a beta of 2 is riskier than the stock with a beta of 1.2, the required or expected rate of return is greater (12.5 versus 8.9 percent). The returns of both stocks are greater than those of the market (8 percent) because their betas are greater than 1, indicating greater risk (volatility) than that of the market.

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