# Avoiding Backtesting Overfitting by Covariance-Penalties: an empirical investigation of the ordinary and total least squares cases

## TL;DR

This paper introduces a Covariance-Penalty correction method to prevent backtesting overfitting in trading strategies, demonstrating its effectiveness through empirical tests on over 1300 assets, with Total Least Squares outperforming Ordinary Least Squares.

## Contribution

It proposes a novel Covariance-Penalty correction approach for avoiding backtesting overfitting in financial strategies, validated through extensive empirical analysis.

## Key findings

- Covariance-Penalties effectively reduce backtesting overfitting.
- Total Least Squares outperforms Ordinary Least Squares in strategy performance.
- The proposed method is validated on over 1300 assets.

## Abstract

Systematic trading strategies are rule-based procedures which choose portfolios and allocate assets. In order to attain certain desired return profiles, quantitative strategists must determine a large array of trading parameters. Backtesting, the attempt to identify the appropriate parameters using historical data available, has been highly criticized due to the abundance of misleading results. Hence, there is an increasing interest in devising procedures for the assessment and comparison of strategies, that is, devising schemes for preventing what is known as backtesting overfitting. So far, many financial researchers have proposed different ways to tackle this problem that can be broadly categorised in three types: Data Snooping, Overestimated Performance, and Cross-Validation Evaluation. In this paper, we propose a new approach to dealing with financial overfitting, a Covariance-Penalty Correction, in which a risk metric is lowered given the number of parameters and data used to underpins a trading strategy. We outlined the foundation and main results behind the Covariance-Penalty correction for trading strategies. After that, we pursue an empirical investigation, comparing its performance with some other approaches in the realm of Covariance-Penalties across more than 1300 assets, using Ordinary and Total Least Squares. Our results suggest that Covariance-Penalties are a suitable procedure to avoid Backtesting Overfitting, and Total Least Squares provides superior performance when compared to Ordinary Least Squares.