# Detailed study of a moving average trading rule

## TL;DR

This paper analyzes the performance of a moving average trading rule on stock indexes, linking it to the stochastic properties of asset returns and identifying effects of autocorrelation and drift over different time horizons.

## Contribution

It provides a theoretical and empirical analysis of how autocorrelation and drift influence the Sharpe ratio of moving average strategies across various look-back periods.

## Key findings

- Sharpe ratio varies with look-back period due to autocorrelation and drift effects.
- Autocorrelation dominates short-term performance, while drift influences long-term results.
- Oscillations in Sharpe ratio are observed and modeled as non-stationary phenomena.

## Abstract

We present a detailed study of the performance of a trading rule that uses moving average of past returns to predict future returns on stock indexes. Our main goal is to link performance and the stochastic process of the traded asset. Our study reports short, medium and long term effects by looking at the Sharpe ratio (SR). We calculate the Sharpe ratio of our trading rule as a function of the probability distribution function of the underlying traded asset and compare it with data. We show that if the performance is mainly due to presence of autocorrelation in the returns of the traded assets, the SR as a function of the portfolio formation period (look-back) is very different from performance due to the drift (average return). The SR shows that for look-back periods of a few months the investor is more likely to tap into autocorrelation. However, for look-back larger than few months, the drift of the asset becomes progressively more important. Finally, our empirical work reports a new long-term effect, namely oscillation of the SR and propose a non-stationary model to account for such oscillations.