How do I calculate portfolio risk for a two-asset portfolio? I keep messing up the formula.

You're right that portfolio risk depends on correlations, and that's exactly why the formula looks more complex than a simple weighted average. Let's break it down.

The two-asset portfolio variance formula:

σ²_p = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρ₁₂σ₁σ₂

Where:

• w₁, w₂ = weights of assets 1 and 2 (must sum to 1)
• σ₁, σ₂ = standard deviations of assets 1 and 2
• ρ₁₂ = correlation between the two assets

Step-by-step example:

Suppose you invest 55% in Orion Industrials (σ = 20%) and 45% in Summit Bonds (σ = 8%), with a correlation of 0.25.

Component	Calculation	Value
w₁²σ₁²	(0.55)²(0.20)²	0.0121
w₂²σ₂²	(0.45)²(0.08)²	0.001296
2w₁w₂ρ₁₂σ₁σ₂	2(0.55)(0.45)(0.25)(0.20)(0.08)	0.00198
Portfolio variance	Sum	0.015376
Portfolio std dev	√0.015376	12.4%

Why this matters: The weighted average standard deviation would be 0.55(20%) + 0.45(8%) = 14.6%. But the actual portfolio risk is only 12.4% — a reduction of 2.2 percentage points purely from diversification.

Three critical scenarios to remember:

1. ρ = +1: No diversification benefit. Portfolio std dev equals the weighted average.
2. ρ = 0: Good diversification. Risk drops meaningfully below the weighted average.
3. ρ = -1: Maximum diversification. You can theoretically reduce portfolio risk to zero with the right weights.

Common mistakes:

• Forgetting to square the weights AND the standard deviations in the first two terms
• Using covariance (Cov₁₂ = ρ₁₂σ₁σ₂) but then also multiplying by ρ again
• Forgetting the factor of 2 in the cross-term

Practice this calculation until it's automatic — CFA Level I frequently tests this in both item set and standalone format.

Check out our CFA Level I course for more portfolio management walkthroughs.