Portfolio Volatility
Standard deviation of portfolio returns — total risk including diversification effects.
Portfolio volatility measures how much your portfolio's returns fluctuate — it's the standard deviation of returns. Unlike simply averaging individual asset volatilities, portfolio vol accounts for correlations: assets that don't move in lockstep reduce total risk. For example, a 50/50 portfolio of two 20%-vol assets with 0.3 correlation has ~16% vol, not 20%. This is the diversification benefit—the whole is less risky than the sum of parts. The formula σₚ = √(wᵀΣw) shows portfolio vol depends on weights (w), individual vols (Σ diagonal), and correlations (Σ off-diagonal). Lower correlation = better diversification. This is why global portfolios (stocks + bonds + alternatives) can achieve lower vol than stock-only portfolios.
Formula
Where
=Portfolio volatility
=Portfolio weights vector
=Covariance matrix
Variables
| \sigma_p^2 | Portfolio variance |
| \mathbf{w} | Vector of asset weights (sum to 1) |
| \mathbf{\Sigma} | Covariance matrix of asset returns |
| \sigma_{ij} | Covariance between assets i and j |
Assumptions
- Weights sum to 1 (fully invested)
- Returns are multivariate normal
- Covariance matrix is estimated from historical data
- Past correlations persist in the future
vs. Industry Tools
Bloomberg PORT — Uses same formula; may apply shrinkage to covariance matrix
BARRA — Uses factor model covariance instead of sample covariance