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FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)

A regression of stock A's excess returns on the market's excess returns gives a slope of 1.20 and an R-squared of 0.64. The market's return standard deviation is 15%. What is the standard deviation of the stock's firm-specific (residual) risk, to the nearest 0.1%?

Residual standard deviation is 13.5%. Systematic variance is 1.44 times 225, or 324. Dividing by R-squared of 0.64 gives total variance of 506.25, so residual variance is 182.25, whose square root is 13.5%.

  1. A10.8%Correct
  2. B13.5%
  3. C18.0%
  4. D7.8%

Explanation

Systematic variance = 1.2^2 x 15^2 = 1.44 x 225 = 324, so total volatility variance = 324/0.64 = 506.25 (total sd 22.5%). Residual variance = 506.25 - 324 = 182.25, sd = 13.5%. Check: 13.5% is the residual sd, so the answer is 13.5%, not 10.8%.

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