Reading 12- LOS b: Q1- 4

1.63 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 performance in the second half of the year is different than performance in the first half of the year?

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 B)

The difference between performance in the second and first half of the year is measured by dummy variable 2. The t-statistic is equal to 0.00132 / 0.000733 = 1.800, which is between the t-values (with 63 − 3 − 1 = 59 degrees of freedom) of 1.671 for a p-value of 0.10, and 2.00 for a p-value of 0.05 (note that the test is a two-sided test).

2.A dependent variable is regressed against three independent variables across 25 observations. The regression sum of squares is 119.25, and the total sum of squares is 294.45. The following are the estimated coefficient values and standard errors of the coefficients.

For which of the coefficients can the hypothesis that they are equal to zero be rejected at the 0.05 level of significance?

A)   1 and 2 only.

B)   3 only.

C)   2 and 3 only.

D)   1, 2, and 3.

The correct answer was B)

The values of the t-statistics for the three coefficients are equal to the coefficients divided by the standard errors, which are 2.43 / 1.42 = 1.711, 3.21 / 1.55 = 2.070, and 0.18 / 0.0818 = 2.200. The statistic has 25 - 3 - 1 = 21 degrees of freedom. The critical value for a p-value of 0.025 (because this is a two-sided test) is 2.080, which means only coefficient 3 is significant.

3.Consider the following estimated regression equation, with standard errors of the coefficients as indicated:

Sales_i = 10.0 + 1.25 R&D_i + 1.0 ADV_i – 2.0 COMP_i + 8.0 CAP_i
where the standard error for R&D is 0.45, the standard error for ADV is 2.2, the standard error for COMP 0.63, and the standard error for CAP is 2.5.

The equation was estimated over 40 companies. Using a 5 percent level of significance, what are the hypotheses and the calculated test statistic to test whether the slope on R&D is different from 1.0?

A)   H₀: b_R&D = 1 versus H_a: b_R&D≠1; t = 2.778.

B)   H₀: b_R&D = 1 versus H_a: b_R&D≠ 1; t = 0.556.

C)   H₀: b_R&D ≠ 1 versus H_a: b_R&D = 1; t = 2.778.

D)   H₀: b_R&D ≠ 1 versus H_a: b_R&D = 1; t = 0.556.

The correct answer was B)

The test for “is different from 1.0” requires the use of the “1” in the hypotheses and requires 1 to be specified as the hypothesized value in the test statistic. The calculated t-statistic = (1.25-1)/.45 = 0.556

4.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 zero. 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 beta of the fund is greater than 1?

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 B)

The beta is measured by the coefficient of the market variable. The test is whether the beta is greater than 1, not zero, so the t-statistic is equal to (1.43 − 1) / 0.319 = 1.348, which is in between the t-values (with 72 - 3 - 1 = 68 degrees of freedom) of 1.29 for a p-value of 0.10 and 1.67 for a p-value of 0.05.