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FRM Part II · FRM Exam Part II · Factors

Asset A has a beta of 0.8 and residual (idiosyncratic) volatility of 10%. The market volatility is 20%. The risk-free rate is 2% and the market expected return is 8%. What are asset A's total volatility and its CAPM expected return?

Total volatility is about 18.9% because systematic volatility of 16% and idiosyncratic volatility of 10% combine in variance terms, giving the square root of 356. The CAPM expected return is 2% plus 0.8 times 6%, or 6.8%.

  1. ATotal volatility 16.0%; expected return 6.8%
  2. BTotal volatility 18.9%; expected return 6.8%Correct
  3. CTotal volatility 18.9%; expected return 8.0%
  4. DTotal volatility 26.0%; expected return 4.8%

Explanation

Systematic volatility = 0.8 x 20% = 16%. Total variance = 16%^2 + 10%^2 = 256 + 100 = 356 (in %^2), so volatility = 18.87%, about 18.9%. Expected return = 2% + 0.8 x 6% = 6.8%. Option one ignores idiosyncratic risk; the 26% option adds volatilities linearly.

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