FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods
A single-factor model gives a portfolio a beta of 0.9 to a market index with 20% annual volatility. The portfolio's residual (idiosyncratic) volatility is 8%, uncorrelated with the market. What is the portfolio's total annual volatility, to the nearest 0.1%?
Total volatility is about 19.7%. Systematic volatility is 0.9 times 20%, or 18%. Because residual risk is uncorrelated, variances add: 324 plus 64 equals 388, whose square root is 19.7%. Simply adding volatilities to get 26% would be wrong.
- A17.7%
- B19.7%Correct
- C26.0%
- D28.0%
Explanation
Systematic volatility = 0.9 x 20% = 18%. Total variance = 18%^2 + 8%^2 = 324 + 64 = 388 (in %^2), so volatility = sqrt(388) = 19.7%. Adding volatilities (26%) ignores that uncorrelated risks add in variance.
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