Portfolio Variance (2-Asset)
Portfolio Variance (2-Asset)
Variance of a two-asset portfolio. Combines individual variances with the covariance term that captures diversification benefits when correlation is below 1.
When to use: Compute two-asset portfolio variance; its square root is portfolio volatility, used by Sharpe. Treynor uses beta instead. Weights must sum to 1; negative weights represent short positions.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PortVar | Portfolio Variance | Variance of a 2-asset portfolio return as a decimal² | variance |
| w1 | Weight 1 | Portfolio weight in asset 1 as a decimal | % |
| w2 | Weight 2 | Portfolio weight in asset 2 as a decimal (typically 1 − w1) | % |
| Sigma1 | Volatility 1 | Standard deviation of asset 1 returns as a decimal | % |
| Sigma2 | Volatility 2 | Standard deviation of asset 2 returns as a decimal | % |
| Rho | Correlation | Correlation between the two assets, between −1 and 1 | integer |
Real-Life Examples
Example 1: 60/40 Stock-Bond
60% stocks (σ=18%), 40% bonds (σ=6%), correlation 0.20.
Given
Step-by-Step
Portfolio variance 0.01328 → volatility ~11.5%. Far below a weighted average of the components (60%×18% + 40%×6% = 13.2%) thanks to diversification. The lower the correlation, the bigger the benefit.
Example 2: Two Equities (High Correlation)
50/50 split between two large-cap equity funds, both σ=20%, correlation 0.85.
Given
Step-by-Step
High correlation means almost no diversification benefit — portfolio volatility (19.2%) is barely below either standalone (20%). Real diversification requires low or negative correlation.
Frequently Asked Questions
Variance is in squared decimal-return units. Take its square root to obtain volatility as a decimal return, then multiply by 100 to express volatility as a percentage.
Weights sum to 1, each volatility is nonnegative, and correlation lies between −1 and 1. Negative weights are allowed for an explicitly leveraged or short allocation.