### CFA Practice Question

A portfolio manager pursues an active strategy. Over a period of 12 months, she achieves a return of 0.95% per month. The risk of her portfolio implies her return should be 0.45% per month. The sample standard deviation is 0.64%. The Null Hypothesis is that the portfolio manager earns a return equal to or lower than 0.45% per month. (That is, alpha is zero or negative). You are provided the following values for t-distribution and Z-distribution.

t-distributed with 12 dof test statistic for 1% one-tailed = 2.681
t-distributed with 11 dof test statistic for 1% one-tailed = 2.718
t-distributed with 12 dof test statistic for 1% two-tailed = 3.054

t-distributed with 11 dof test statistic for 1% two-tailed = 3.106

Can the Null Hypothesis be rejected at the 99% level of significance test?
A. Yes
B. No
C. Insufficient information.
Explanation: This is a one-tailed test. The test statistic = (0.95% - 0.45%)/(0.64%/12^0.5) = 2.7063. This is smaller than 2.718, so we fail to reject the Null.

### User Contributed Comments3

User Comment
Luizillo 2.681 is the t-distribution with 12dof fot 1% one tailed. This number should not be used because is not considering the n-1 dof from the t- distribution.
bantoo Test statistic value is 2.71739 which is lower than t-statistic value by a extremely thin margin so we fail to reject null hypothesis.
Coowy t calc: 2.70633
t crit 11df: 2.718

Therefore we fail to reject Ho and conclude the Return is not statistical singnificant higher than 0.45%