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.

Coefficient

Value

Standard error

Market

 

1.43000

0.319000

Dummy 1

 

0.00162

0.000675

Dummy 2

 

0.00132

0.000733

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.?
Answer: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).