The capital asset pricing model (CAPM) can be written as E(R_i) = R_f + beta_i[E

Question

The capital asset pricing model (CAPM) can be written as E(R_i) = R_f + beta_i[E(R_m) - R_f] 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 R_it = alpha_i + beta_i R_mt + u_it where R_it is the excess return for security i at time t, R_mt is the excess return on a proxy for the market portfolio at time t, and mu_t, is an iid random disturbance term. The coefficient 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, beta was 1.147. The standard error associated with this coefficient SE(beta) 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?

Explanation / Answer

Null Hypothesis : Stock is not risky

Alternate Hypothesis : Stock is risky

p value = beta/std dev of beta

to test hypothesis we need to compare p value and level of significance

p value = 1.147/0.0548 = 20.93

As p value > 0.05 (level of significance)

we accept Null hypothesis and state that stock is not risky

thus analyst's claim is right at 5% significance level

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