Bias-corrected sharpe ratios: closing the gap between in-sample & out-of-sample
File(s)
Author(s)
Mulligan, Joseph
Type
Thesis
Abstract
This thesis investigates how we should correct in-sample Sharpe ratios in practice. It is well observed that out-of-sample Sharpe ratios are typically lower than their in-sample equivalents, sometimes significantly so. This phenomenon has historically been studied from multiple testing perspectives (``p-hacking'') or attributed to alpha decay (opportunities being arbitraged away). Existing literature on fund and factor performance has separately investigated how complexity and statistical bias can cause this effect within their respective domains. This work unifies these strands, offering both theoretical and practical results to aid in the correction of over-optimistic in-sample Sharpe ratios.
First, we address the problem from a structural perspective. By adopting a linear model for returns and a classical Markowitz portfolio construction, we derive theoretical expressions for the in- and out-of-sample mean and variance of the proposed trading strategy. We explicitly quantify the inflation experienced by the in-sample Sharpe ratio as the number of parameters in the model increases, and demonstrate how this is mitigated through additional data points and stronger signals. These theoretical results are validated through both simulation and empirical studies.
Second, we shift to a statistical approach, where the construction of the backtest is unknown. We propose a Bayesian method to estimate the true Sharpe ratio of new candidate investments by modelling the observed distribution of in- and out-of-sample Sharpe ratios of suitably homogeneous comparable investments. This method accounts for both selection bias (a form of overfitting) and alpha decay, yielding significantly more accurate estimates of out-of-sample performance. This is evidenced through an in-depth application of the model to a large dataset of hedge fund returns, where it significantly improves upon naive baselines.
First, we address the problem from a structural perspective. By adopting a linear model for returns and a classical Markowitz portfolio construction, we derive theoretical expressions for the in- and out-of-sample mean and variance of the proposed trading strategy. We explicitly quantify the inflation experienced by the in-sample Sharpe ratio as the number of parameters in the model increases, and demonstrate how this is mitigated through additional data points and stronger signals. These theoretical results are validated through both simulation and empirical studies.
Second, we shift to a statistical approach, where the construction of the backtest is unknown. We propose a Bayesian method to estimate the true Sharpe ratio of new candidate investments by modelling the observed distribution of in- and out-of-sample Sharpe ratios of suitably homogeneous comparable investments. This method accounts for both selection bias (a form of overfitting) and alpha decay, yielding significantly more accurate estimates of out-of-sample performance. This is evidenced through an in-depth application of the model to a large dataset of hedge fund returns, where it significantly improves upon naive baselines.
Version
Open Access
Date Issued
2026-01-31
Date Awarded
2026-04-01
Copyright Statement
Attribution-NonCommercial 4.0 International Licence (CC BY-NC)
License URL
Advisor
Jacquier, Antoine
Muhle-Karbe, Johannes
Sponsor
Qube Research & Technologies (Firm)
Engineering and Physical Sciences Research Council
Grant Number
EP/S023925/1
Publisher Department
Department of Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)