Risk Metrics
A comprehensive collection of risk measurement methodologies used in portfolio analysis. These metrics quantify different dimensions of risk -- from tail losses and drawdowns to distributional shape and tracking deviation -- enabling a multi-faceted understanding of portfolio risk that goes beyond simple volatility.
Value at Risk (VaR)
The maximum loss expected over a given time horizon at a specified confidence level, providing a single-number summary of downside risk.
Conditional VaR (CVaR / Expected Shortfall)
The expected loss conditional on the loss exceeding the VaR threshold, capturing the severity of tail losses beyond VaR.
Entropic Value at Risk (EVaR)
An upper bound on both VaR and CVaR derived from the Chernoff inequality, providing a coherent and computationally tractable risk measure.
Maximum Drawdown (MDD)
The largest peak-to-trough decline in portfolio value over a given period, measuring the worst cumulative loss an investor would have experienced.
Drawdown at Risk (DaR)
The maximum drawdown expected at a given confidence level, combining the drawdown concept with the probabilistic framework of Value at Risk.
Conditional Drawdown at Risk (CDaR)
The expected drawdown conditional on the drawdown exceeding the DaR threshold, analogous to CVaR but applied to the drawdown distribution.
Ulcer Index
A volatility measure that focuses exclusively on downside risk by computing the root mean square of percentage drawdowns from prior peaks.
Skewness
The third standardized moment of the return distribution, measuring the asymmetry of returns around the mean. Negative skewness implies larger downside tail risk.
Kurtosis
The fourth standardized moment of the return distribution, measuring the thickness of the tails. Excess kurtosis indicates more frequent extreme outcomes than a normal distribution.
Tracking Error
The standard deviation of the difference between portfolio and benchmark returns, measuring the consistency of active return and the degree of deviation from the benchmark.