FRM Part II · FRM Exam Part II · Factor Theory
A portfolio has two uncorrelated factor exposures, A and B, with volatilities of 4% and 12% respectively. A manager wants equal risk contribution from each factor (risk parity across factors). Ignoring leverage constraints, what weight ratio w_A to w_B achieves this?
With uncorrelated factors, equal risk contributions require weight times volatility to be equal. The weight ratio is therefore the inverse of the volatility ratio, 12% divided by 4%, which is 3 to 1 in favor of the low-volatility factor.
- A3 to 1Correct
- B1 to 3
- C1 to 1
- D9 to 1
Explanation
With zero correlation, risk contribution of each factor is proportional to w²σ². Equal contributions require wAσA = wBσB, so wA/wB = 12/4 = 3. A 1 to 3 ratio inverts this, and 9 to 1 wrongly squares the ratio.
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