Security Analysis and Portfolio Management
Diversification
Can two risky assets make a calmer portfolio?
Portfolio risk depends on how assets move together as well as their individual volatility.
σₚ² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ
w is a portfolio weight, σ is volatility, and ρ is the correlation between returns. With 50/50 weights and zero correlation, variance is 2 × (0.5 × 0.20)² = 0.02. Take the square root to get 14.14%.
Two equally weighted 20%-volatility assets with zero correlation give about 14.14% portfolio volatility.
w is a portfolio weight, σ is volatility, and ρ is the correlation between returns. With 50/50 weights and zero correlation, variance is 2 × (0.5 × 0.20)² = 0.02. Take the square root to get 14.14%.
What is volatility if the same assets have perfect positive correlation?