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.
Coefficient Value Standard Error
Market 1.43 .319000
Dummy 1 .00162 .000675
Dummy 2 -.00132 .000733
What is the p-value for a test of the hypothesis that the beta of the fund is greater than 1?
A) Between 0.05 and 0.10.
B) Between 0.01 and 0.05.
C) Lower than 0.01.
Your answer: A was correct!
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.
I get the math and how to estimate P-Values, but I do not understand why Beta is 1.43. Any help is appreciated.
