hard · FRM Part 1 Quantitative Analysis
An analyst estimates a factor model for a hedge fund's excess returns using n = 42 monthly observations and k = 5 independent factors. The estimated coefficient on the momentum factor is hatβ_MOM = 1.18 with standard error SE(hatβ_MOM) = 0.075.
The analyst wants to test whether the fund's true momentum exposure differs from a beta of 1.0 (not zero) at the 5% two-tailed significance level, using t_0.025,36 ≈ 2.028. What is the correct test statistic and conclusion?
- t = 15.73; since 15.73 > 2.028, reject H_0 — this incorrectly tests against 0 rather than 1.0 as the null.
- t = 0.37; fail to reject H_0 — this results from mistakenly multiplying the SE by √(n) before dividing.
- t = 2.40; since |t| = 2.40 > 2.028, reject H_0 — the momentum exposure is significantly different from 1.0.
- t = -2.40; since -2.40 < 2.028, fail to reject H_0 — comparing the signed statistic directly instead of |t|.
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