FRM Part II · FRM Exam Part II · Portfolio Construction
Two risky assets have equal expected returns of 8% and equal volatilities of 15%. Their correlation is 0.2. An investor fully invested in the two assets wants the minimum-variance portfolio. What are the optimal weights?
With identical volatilities, the minimum-variance weight formula reduces to one half for each asset regardless of the correlation, as long as correlation is below one. The portfolio is symmetric, so an equal 50/50 split minimizes variance.
- AWeights depend on the risk-free rate and favor the asset with a higher beta
- BShort one asset and go long the other since correlation is positive
- C50% in each assetCorrect
- D70% in one asset and 30% in the other
Explanation
For two assets with equal variances, the minimum-variance weight is w = (σ² − ρσ²)/(2σ² − 2ρσ²) = 0.5. Positive correlation below one does not call for shorting. The weights are symmetric, so equal weights minimize variance.
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