FRM Part II · FRM Exam Part II · Portfolio Construction
A manager building a minimum-variance portfolio of two uncorrelated assets finds asset X has volatility 20% and asset Y has volatility 10%. What weight in X minimizes portfolio variance?
With uncorrelated assets, the minimum-variance weight in X is σY² divided by the sum of both variances: 0.01/0.05 = 20%. The lower-volatility asset Y receives the larger 80% weight, giving variance of 0.008.
- A20%Correct
- B33%
- C50%
- D80%
Explanation
With zero correlation, wX = σY²/(σX²+σY²) = 0.01/(0.04+0.01)=0.20. Check: variance = 0.04(0.04)+0.64(0.01)=0.0016+0.0064=0.008, lower than at 50/50 (0.0125). The 80% option reverses the weights.
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