Capital asset pricing model is a widely used technique to calculate the expected rate of return for equity investment. It considers the beta or systematic risk, expected market return and risk free rate to calculate the expected rate of return on equity investment.
E(R) = RFR + β [E(Rm) –RFR]
E(R) = Expected rate of return on equity investment
RFR = Risk-free rate of return
E(Rm) = Expected rate of return of the market index
β = Beta or systematic risk of the particular security
Risk free rate is calculated from the yield rate on domestic treasury securities which are considered to be free of any default risk. Sometimes, also the yield on a long-term Treasury bond can be used as a risk-free rate.
Expected rate of return on market index can be easily calculated from the historical data of market index returns over a period of time.
To calculate beta, we can rewrite the capital market equation as E(R) = (1-β) *RFR + β*E(Rm). The calculation of the beta coefficient can be done by using simple linear regression analysis with E(Rm) as the independent variable and the E(R) as the dependent variable. These data can be collected from the historical date of market returns and one particular stock returns.
Another equation to calculate beta is,
Β = Cov (Re,Rm) / Var(Rm) = σe2 / σm2
Where, Cov (Re,Rm) = Co-variance between market portfolio and equity
Var(Rm) = Variance of Market return
σe2 = standard deviation of equity return
σm2 = standard deviation of market return
Beta can be calculated by using all these variable whose values can be easily obtained from historical data.