CFA Level I · CFA Level I Exam · Applications of Simple Linear Regression in Finance
An analyst estimates a lin-log model: Y = 12 + 6.0 × ln(X), where Y is a fund's annual return in percent and X is its assets under management in millions. The expected change in Y for a 1% increase in X is closest to:
In a lin-log model, a 1% increase in X raises ln(X) by about 0.01, so Y changes by about 6.0 times 0.01, or 0.06 percentage points. The slope divided by 100 gives the effect of a 1% change in X.
- A0.06 percentage points.Correct
- B6.00 percentage points.
- C0.60 percentage points.
Explanation
In a lin-log model, a 1% change in X changes ln(X) by about 0.01, so Y changes by about b1 × 0.01 = 6.0 × 0.01 = 0.06 units. Since Y is measured in percent, that is 0.06 percentage points. The 6.00 figure treats the slope as the effect of a 100% change in X, and 0.60 corresponds to a 10% change.
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