Category: CAPM and Beta

The CAPM states the following:

E(R) = R_f + β(E(R_m) – R_f)

where R is the return on the asset of interest, R_f is the risk-free rate of return, R_m is the rate of return for the entire market (the market portfolio) and β is a parameter that describes the sensitivity of the asset’s return to the market’s return.

To estimate a stock’s β, you therefore need historical data on a stock’s returns, the market’s returns, and the risk-free interest rate. You can calculate returns from an asset’s prices as follows:

R_t = (P_t + D_t – P_t-1) / (P_t-1)

Where R_t is the asset’s return in period t, P_t is the asset’s price in period t, and D_t is the dividend on the stock in period t (usually 0). It is customary to use a broad-based market index (such as the S&P 500 or the Wilshire 5000) to estimate the returns on the market portfolio and to use the returns on short term US Treasury bills to estimate the risk-free rate of return.

The following regression model can then be used to estimate a stock’s β:

R_t – R_ft = α + β(R_mt – R_ft) + u_t

If the CAPM holds, α = 0, and the regression output allows you to test this hypothesis (as well as other hypotheses related to α and β.