FRM Part II · FRM Exam Part II · Factor Theory
An investor builds a portfolio of three uncorrelated factor strategies, each with an expected volatility of 10%, and allocates equal capital (one-third each) with no leverage. What is the portfolio volatility?
The portfolio volatility is about 5.77%. With uncorrelated, equally weighted strategies each at 10% volatility, volatility falls by the square root of the number of strategies, so 10% divided by the square root of three gives roughly 5.77%.
- A10.00%
- B5.77%Correct
- C3.33%
- D8.16%
Explanation
With zero correlation, variance = 3 × (1/3)^2 × 10%^2 = 0.3333 × 1% = 0.3333%, wait: 3 × 0.1111 × 0.01 = 0.003333; the square root is 5.77%. Using 10%/√3 confirms 5.77%. A 10% answer assumes perfect correlation, and 3.33% divides volatility by three, which ignores the square-root effect.
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