Reading 12- LOS b: Q7- 9

7.David Black wants to test whether the estimated beta in a market model is equal to one. He collected a sample of 60 monthly returns on a stock and estimated the regression of the stock’s returns against those of the market. The estimated beta was 1.1, and the standard error of the coefficient is equal to 0.4. What should Black conclude regarding the beta if he uses a 5 percent level of significance? The null hypothesis that beta is:

A)   equal to one is rejected.

B)   equal to one cannot be rejected or accepted.

C)   NOT equal to one cannot be rejected.

D)   equal to one cannot be rejected.

The correct answer was D)

The calculated t-statistic is t = (1.1 – 1.0) / 0.4 = 0.25. The critical t-value for 60-2 = 58 degrees of freedom is approximately 2.0. Therefore, the null hypothesis that beta is equal to one cannot be rejected.

8.Seventy-two monthly stock returns for a fund between 1997 and 2002 are regressed against the market return, measured by the Wilshire 5000, and two dummy variables. The fund changed managers on January 2, 2000. Dummy variable one is equal to 1 if the return is from a month between 2000 and 2002. Dummy variable number two is equal to 1 if the return is from the second half of the year. There are 36 observations when dummy variable one equals 0, half of which are when dummy variable two also equals 0. The following are the estimated coefficient values and standard errors of the coefficients.

What is the p-value for a test of the hypothesis that the new manager outperformed the old manager?

A)   Lower than 0.01.

B)   Between 0.05 and 0.10.

C)   Between 0.01 and 0.05.

D)   Greater than 0.10.

The correct answer was A)

Dummy variable one measures the effect on performance of the change in managers. The t-statistic is equal to 0.00162 / 0.000675 = 2.400, which is higher than the t-value (with 72 - 3 - 1 = 68 degrees of freedom) of approximately 2.39 for a p-value of between 0.01 and 0.005 for a 1 tailed test.

9.An analyst is investigating the hypothesis that the beta of a fund is equal to one. The analyst takes 60 monthly returns for the fund and regresses them against the Wilshire 5000. The test statistic is 1.97 and the p-value is 0.05. Which of the following is TRUE?

A)   If beta is equal to 1, the likelihood that the absolute value of the test statistic is equal to 1.97 is less than or equal to 5%.

B)   If beta is equal to 1, the likelihood that the absolute value of the test statistic would be greater than or equal to 1.97 is 5%.

C)   For a sample of 100 beta values, the expected number of times beta would be equal to 1 is less than or equal to 5%.

D)   The proportion of occurrences when the absolute value of the test statistic will be higher when beta is equal to 1 than when beta is not equal to 1 is less than or equal to 5%.

The correct answer was B)

A statistical test computes the likelihood of a test statistic being higher than a certain value assuming the null hypothesis is true.