FRM Part I · FRM Exam Part I · Linear Regression
An analyst regresses monthly excess returns of a fund (Y) on monthly excess returns of a market index (X) using 60 observations. The sample statistics are: covariance of X and Y = 0.0036, variance of X = 0.0040, mean of X = 0.010, mean of Y = 0.012. What is the OLS estimate of the intercept?
The intercept is 0.003. The OLS slope equals covariance divided by the variance of X, which is 0.90. The intercept is the mean of Y minus the slope times the mean of X, so 0.012 minus 0.009 gives 0.003.
- A0.003Correct
- B0.009
- C-0.003
- D0.021
Explanation
Slope = Cov(X,Y)/Var(X) = 0.0036/0.0040 = 0.90. Intercept = mean Y - slope x mean X = 0.012 - 0.90 x 0.010 = 0.003. The option 0.021 adds the slope term instead of subtracting it, and 0.009 mistakenly uses the slope itself as the term subtracted without scaling.
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