VARGAMMA: A UNIFIED MEASURE OF PORTFOLIO RISK

Kent Osband

Most portfolio risk analysis implicitly assumes that risks are stable, despite copious evidence of instability. This article presents an alternative, “VarGamma”, that provides neat formulas for expected risk-adjusted returns even with stochastic volatility and volatility-dependent drift. VarGamma measures are far more flexible and robust than standard mean–variance formulations or quantiles (VaR), with minimal extra complexity. Parameters can be readily inferred from either historical data or options prices. In portfolio optimization, VarGamma is particularly useful in integrating mean–variance analysis with stress tests. In estimation of tail risks, VarGamma-related techniques tend to be significantly more precise than standard empirical measures. Their predictions of near-exponential decay in outer tail risks (far slower than normality suggests) sit well with crisis theory and practice. VarGamma also discourages wasteful regulatory arbitrage.