Questions / Quant research, Portfolio & factor risk
Minimum variance weights
Two uncorrelated assets have volatilities 10% and 20%. For a fully invested two-asset minimum-variance portfolio with no other constraints, what percentage goes in the 10% asset?
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Answer: 80% (4/5)
- Let w be the first-asset weight, so the second weight is 1−w. With zero correlation, variance is 0.01w² + 0.04(1−w)².
- Differentiate: 0.02w − 0.08(1−w)=0. This yields 0.10w=0.08.
- Therefore w=0.8, or 80%. Diversification makes a nonzero weight in the more volatile asset worthwhile here.
Interview shortcut. Uncorrelated min-variance weight ∝ 1/σ²: (1/100)/(1/100 + 1/400).
Takeaway. For uncorrelated assets, minimum-variance weights are proportional to inverse variance.
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