Question

The capital asset pricing model (CAPM) can be written as E(Ri) = Rf+ βi[E(Rm) − Rf] 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+ βiRmt+ uit where Rit is the excess return for security i at time t, Rmtis the excess return on a proxy for the market portfolio at time t, and utis an iid random disturbance term. The cofficient beta in this case is also the CAPM beta for security i. Suppose that you had estimated (3.45) and found that the estimated value of beta for a stock, β ˆ was 1.147. The standard error associated with this coefficient SE(β ˆ) 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 sixty-two 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? The t-critical (60degrees of freedom and at 5% level)= 1.6706. Use (a)test of significance approach, as well as (b) confidence interval approach. Questions forms: (a) Test of significance approach: conclusion: (b) confidence interval approach: conclusion

Answer 1

The null and alternate hypothesis will be

The above hypothesis is derived from the given CAPM equation and estimation equation between excess returns on security and returns on market portfolio.

implies that there are excess returns on security more than the retuns on market portfolio which makes it a risky asset but the estimates are that security market closely follows the market.

using test of significance to find if the hypothesis is sugnificant or not

Now the critical value of t at 60 degrees of freedom and at 5% level is 1.6706 which is given and calculated value is greater than critical value of t implies that the null will be rejected and the hypothesis is statistically significant at 5% level.

(b) confidence interval approach

hence, null hypothesis doesnot belong to the confidence interval above .

Reject null hupothesis

Therefore, the result implies that returns from security is risky.