Time-Series Momentum: A Monte Carlo Approach

Abstract

In this article the authors develop a Monte Carlo backtesting procedure for risk premium strategies and employ it to study time-series momentum (TSM). Relying on time-series models, empirical residual distributions, and copulas, the authors address two key drawbacks of conventional backtesting procedures. They create 10,000 paths of different TSM strategies based on the S&P 500 and a cross-asset-class futures portfolio. The simulations reveal a probability distribution that shows that strategies that outperform buy-and-hold in-sample using historical backtests may (1) exhibit tail risks and (2) underperform or outperform when out-of-sample. The results are robust to using different time-series models, time periods, asset classes, and risk measures.

TOPICS: Statistical methods, simulations, big data/machine learning

Key Findings

• • Historical backtests suffer from the problem that they contain few tail events which may be an important driver for the performance of risk premium strategies.

• • We develop a Monte-Carlo procedure that uses a combination of copulas, time-series models, and empirical residual distributions to overcome this problem.

• • Applied to time-series momentum, we find that this strategy may (1) exhibit tail risks (2) underperform or outperform in the long run.