Signal-to-Noise Ratio Inference under Volatility Clustering and Heavy Tails

ADIA Lab Research Paper Series

Authors: Marcos López de Prado, Emilio Porcu, Vincent Zoonekynd, Robert F. Engle

Date Published: April 2026

We develop a closed-form asymptotic theory for inference on the Sharpe ratio under conditional heteroskedasticity. Building on a general central limit framework for joint sample moments, we establish the asymptotic distribution of the plug-in Sharpe estimator for strictly stationary GARCH(1,1) processes under mild moment and dependence conditions. The resulting variance admits an explicit parametric representation that captures the effect of volatility clustering and higher-order moments of the innovation distribution. We further show that the classical √ n-Gaussian asymptotics of the Sharpe ratio impose a structural restriction on the underlying return process, namely the root-n regularity of quadratic functionals.