FRM Part II · FRM Exam Part II · Factor Theory
An investor holds a portfolio split equally between two uncorrelated factor strategies. Each strategy has an annualized volatility of 10%. What is the portfolio's annualized volatility, approximately?
The portfolio volatility is about 7.07%. With zero correlation and 50% weights, variance is 0.25×0.01 + 0.25×0.01 = 0.005, and the square root of that is 7.07%. Diversification across uncorrelated factors cuts risk below the 10% of each individual strategy.
- A10.0%
- B7.07%Correct
- C5.00%
- D14.14%
Explanation
Variance = 0.5^2(0.10^2) + 0.5^2(0.10^2) + 0 = 0.0025 + 0.0025 = 0.005. Volatility = sqrt(0.005) = 7.07%. The 10% option ignores diversification, 5% wrongly squares the weights without summing both terms and taking the root properly, and 14.14% adds variances without weighting.
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