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Downside Deviation

Volatility of returns below a minimum acceptable return.

Downside deviation only considers returns below a threshold (usually 0% or the risk-free rate), ignoring positive deviations. This provides a more intuitive measure of risk for investors who are primarily concerned about losses. It's used in the Sortino ratio as a replacement for standard deviation.

Formula
σd=1N∑ri<MAR(ri−MAR)2\sigma_d = \sqrt{\frac{1}{N} \sum_{r_i < \text{MAR}} (r_i - \text{MAR})^2}
Where
σd\sigma_d=Downside deviation
rir_i=Return at observation i
MAR\text{MAR}=Minimum acceptable return
NN=Number of observations
Related Terms

Sortino Ratio

Risk-adjusted return using only downside volatility.

Portfolio Volatility

Standard deviation of portfolio returns — total risk including diversification effects.

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.

Covariance Matrix

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

Minimum Variance Portfolio

The portfolio with the lowest possible volatility.