The capital asset pricing model (CAPM) can be written as E(Ri ) = R f + i

The capital asset pricing model (CAPM) can be written as E(Ri ) = R f + βi [E(Rm) − R f ] (2.62)

using the standard notation.

The first step in using the CAPM is to estimate the stock’s beta using the market model. The market model can be written as Rit = αi + βi Rmt + uit (2.63)

where Rit is the excess return for security i at time t, Rmt is the excess return on a proxy for the market portfolio at time t, and ut is an iid random disturbance term. The cofficient beta in this case is also the CAPM beta for security i .

Suppose that you had estimated (2.63) and found that the estimated value of beta for a stock, βˆ was 1.147. The standard error associated with this coefficient SE(βˆ) is estimated to be 0.0548.

A city analyst has told you that this security closely follows the market, but that it is no more risky, on average, than the market. This can be tested by the null hypotheses that the value of beta is one. The model is estimated over 62 daily observations. Test this hypothesis against a one-sided alternative that the security is more risky than the market, at the 5% level. Write down the null and alternative hypothesis.

What do you conclude? Are the analyst’s claims empirically verified?

AppendixLO1