FRM Part I · FRM Exam Part I · Linear Regression
A regression of a stock's return on a market index gives an intercept (alpha) estimate of 0.60% per month with a standard error of 0.40% based on 32 observations. The two-sided 5% critical t-value with 30 degrees of freedom is 2.04. Which conclusion is correct?
Fail to reject the null that alpha is zero. The t-statistic is 0.60 divided by 0.40, which equals 1.5, and this is smaller than the critical value of 2.04. The alpha is therefore not statistically significant at the 5% level.
- AReject H0: alpha = 0, because the t-statistic of 1.5 exceeds 1.0
- BFail to reject H0: alpha = 0, because the t-statistic of 1.5 is below 2.04Correct
- CReject H0: alpha = 0, because the t-statistic of 2.40 exceeds 2.04
- DFail to reject H0: alpha = 0, because the t-statistic of 0.67 is below 2.04
Explanation
t = 0.60/0.40 = 1.5, which is less than 2.04 in absolute value, so the null of zero alpha is not rejected at 5%. The 1.0 threshold is arbitrary. 2.40 and 0.67 come from inverting or mis-scaling the ratio.
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