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CFA Level I · CFA Level I Exam · Applications of Simple Linear Regression in Finance

An analyst estimates a regression of a stock's return (Y) on an index return (X) using 5 observations. The sums are: ΣX = 10, ΣY = 20, ΣX² = 30, ΣXY = 50 (all in percent units). The estimated slope coefficient is closest to:

The slope is the cross-product of deviations divided by the sum of squared deviations of X. Sxy = 50 − 5×2×4 = 10 and Sxx = 30 − 5×4 = 10, giving a slope of 1.00. Skipping the mean adjustment would give an incorrect answer.

  1. A0.50
  2. B1.00
  3. C2.00Correct

Explanation

Sxy = ΣXY − n·X̄·Ȳ = 50 − 5×2×4 = 10. Sxx = ΣX² − n·X̄² = 30 − 5×4 = 10. Slope = 10/10 = 1.00. Check: intercept = 4 − 1×2 = 2, consistent with the means. Using ΣXY/ΣX² = 1.67 would be a mistake of skipping the mean adjustment.

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