CFA Level IPortfolio ManagementHard
An analyst is constructing the global minimum-variance portfolio from two assets: Asset 1 with a standard deviation of 20% and Asset 2 with a standard deviation of 30%, given a correlation of 0.20 between the two assets. What weight should be allocated to Asset 1 to minimize portfolio variance?
- A50.0%
- B73.6%
- C64.0%
- D26.4%
Show answer & explanationAnswer & explanation
Correct answer: B. 73.6%
The minimum-variance weight formula is w1 = (σ2² − σ1σ2ρ) / (σ1² + σ2² − 2σ1σ2ρ). Using σ1=20, σ2=30, ρ=0.20: σ1²=400, σ2²=900, σ1σ2=600, σ1σ2ρ=120. Numerator = 900 − 120 = 780. Denominator = 400 + 900 − 240 = 1,060. w1 = 780/1,060 ≈ 73.6%, with w2 ≈ 26.4%.
Why the other options are wrong
- A. An equal-weight assumption ignores the differing volatilities and correlation.
- C. Results from an arithmetic slip in the denominator calculation.
- D. This is the weight for Asset 2 (1 − 73.6%), not Asset 1.
Global Minimum-Variance Portfolio (Two Assets)
The two-asset combination that minimizes overall portfolio variance, weighting more heavily toward the lower-volatility asset given their correlation.
- Formula: w1 = (σ2² − σ1σ2ρ) / (σ1² + σ2² − 2σ1σ2ρ)
- Lower-volatility asset typically receives a higher weight
- Sits at the leftmost point of the efficient frontier
Memory trick: Least risk lives left — lean weight toward the calmer asset.