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
riskfree rate of interest plus the stock’s beta coefficient multiplied
by the amount by which the market return exceeds the riskfree
interest rate.
Required rate of return = riskfree rate + β(market rate of return
 riskfree rate)
Using this equation, an investor seeks a return from a stock
that exceeds the riskfree 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
riskfree rate).
For example, if the riskfree 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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