The Sharpe Stability Ratio: Temporal Consistency of Risk-Adjusted Performance

This paper introduces the Sharpe Stability Ratio (SSR), a performance metric that evaluates the temporal consistency of risk-adjusted returns. While the Sharpe ratio (SR) summarizes average excess return per unit of risk over a fixed sample, it cannot distinguish persistent skill from episodic outperformance: two strategies may display identical ex-post SR yet differ sharply in their temporal profiles, with one delivering stable performance across subperiods and the other concentrating gains in a few favourable episodes. SSR addresses this gap by treating the rolling Sharpe ratio as a time-series object and defining stability as the ratio of mean rolling performance to its heteroskedasticity-and autocorrelation-consistent (HAC) standard deviation. We show that this temporal-stability metric has several practical applications. First, SSR reveals that strategies with similar point-in-time SR and Probabilistic Sharpe Ratio (PSR) can exhibit markedly different stability profiles, providing information that is critical for due diligence and manager selection. Second, it quantifies the strong serial correlation induced by overlapping rolling windows and documents that naive dispersion measures severely understate uncertainty, implying that HAC correction is indispensable for valid temporal inference. Third, SSR supports formal hypothesis testing on stability via block bootstrap procedures that preserve the dependence structure of returns. Fourth, it demonstrates that statistically credible aggregate performance (PSR close to one) does not guarantee temporal consistency: high average SR may be generated by concentrated episodic strength rather than sustained skill. Evidence from controlled simulations and hedge fund index data shows that SSR delivers complementary insights relative to SR and PSR, separating genuinely stable performance from volatile profiles that appear credible under static evaluation.