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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
σp=wTΣw\sigma_p = \sqrt{w^T \Sigma w}
Where
σp\sigma_p=Portfolio volatility
ww=Portfolio weights vector
Σ\Sigma=Covariance matrix
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
Related Terms

Covariance Matrix

Captures how asset returns move together — the foundation of diversification.

Efficient Frontier

The set of portfolios offering the highest return for each level of risk.

Sharpe Ratio

Risk-adjusted return: excess return divided by volatility.

Minimum Variance Portfolio

The portfolio with the lowest possible volatility.

Maximum Sharpe Portfolio

The portfolio with the highest risk-adjusted return.

Capital Market Line (CML)

The line from the risk-free rate through the optimal portfolio.