The Mathematical Failure of Risk-Adjusted Performance Metrics in Cryptocurrency Markets

Abstract

This investigation reveals fundamental mathematical and theoretical flaws in the application of Sharpe and Sortino ratios to cryptocurrency trading strategies, particularly when targeting high values (Sharpe > 2, Sortino > 3). It demonstrates that these metrics create dangerous illusions of safety through interconnected failure modes: systematic violation of distributional assumptions, mathematical instability in estimation, non-ergodic behaviour that invalidates ensemble-based calculations, and behavioural gaming described by Goodhart’s Law. Cryptocurrency returns exhibit heavy-tailed distributions with power-law exponents between 2 and 2.5, violating the normality assumptions crucial for meaningful interpretation, while the pursuit of high ratio targets introduces optimization-induced fragility that guarantees out-of-sample deterioration.

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