FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)
A regression of a stock's excess returns on market excess returns gives a slope of 1.2 and an R-squared of 0.36. The market return volatility is 15% annually. What is the stock's total annual volatility?
The stock's total volatility is 30%. Systematic volatility is beta times market volatility, 1.2 x 15% = 18%. Since R-squared of 0.36 is the systematic share of variance, total variance is 0.0324 divided by 0.36, which is 0.09, so volatility is 30%.
- A18.0%
- B30.0%Correct
- C10.8%
- D21.6%
Explanation
Systematic volatility = 1.2 x 15% = 18%. R-squared = systematic variance / total variance, so total variance = 0.0324/0.36 = 0.09, giving total volatility of 30%. Choosing 18% ignores the R-squared and treats systematic volatility as total.
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