Detailed study of a moving average trading rule

Abstract

We present a detailed study of the performance of a trading rule that uses moving averages 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 proposes a non-stationary model to account for such oscillations.

Keywords:

• Momentum strategies
• Reversal strategies
• Moving averages
• Sharpe ratio
• Trading strategies
• Investment strategies
• Time series analysis

JEL Classification:

• C13
• C15
• C51

Acknowledgements

ACS would like to thank the participants of R/Finance 2013 at UIC and QCMC 2015 at the Max Planck Institute for comments and the organizers for financial support to present preliminary versions of this paper. FFF acknowledges financial support from Fundação Amparo à Pesquisa do Estado de São Paulo (FAPESP) grant number 2013/18942-2 - Coordination for the Improvement of Higher Education Personnel (CAPES) and Fundação Instituto de Física Teórica (FIFT) for hospitality. We thank Constantin Unanian for detailed comments. J-YY is grateful to Academia Sinica Institute of Mathematics (Taipei, Taiwan) for their hospitality and support during some extended visit.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Cross-sectional momentum is not the focus of this article, but it has been studied extensively if compared to time-series momentum or trend following. Since the work of Jegadeesh and Titman (1993), momentum has been extended to different asset classes, portfolios, and other markets abroad. Momentum has been reported in international equity markets by Doukas and McKnight (2005), Forner and Marhuenda (2003), Nijman et al. (2004), Rouwenhorst (1998); in industries by Lewellen (2002), Moskowitz and Grinblatt (1999); in indexes by Bhojraj and Swaminathan (2006), Asness et al. (1997); and in commodities by Erb and Harvey (2006), Moskowitz et al. (2012). Single risky asset momentum is analysed in Daniel et al. (1998), Barberis et al. (1998), Hong and Stein (1999), Berk et al. (1999), Johnson (2002), Ahn et al. (2003), Liu and Zhang (2008), Sagi and Seasholes (2007) to cite a few. Recently, momentum has also been studied linking its performance to business cycles and regimes by Chordia and Shivakumar (2002), Kim et al. (2014), Griffin et al. (2003), Guidolin (2011), Barroso and Santa-Clara (2015).

2 Alternatively to under and overreaction (Barberis et al. 1998, Daniel et al. 1998, Hong and Stein 1999), there are other causes that have been cited as possible explanations. Lewellen (2002) suggests that the lead-lag cross-serial correlation should explain cross-sectional momentum. Conrad and Kaul (1998) point to the cross-sectional variation of asset returns. Chordia and Shivakumar and others (Chordia and Shivakumar 2002, Griffin et al. 2003, Guidolin 2011, Kim et al. 2014, Barroso and Santa-Clara 2015) study business cycles and suggest that time-varying expected returns can explain momentum.

3 There is no guarantee that such an algorithm represents well trend-following strategies; however, we defer the question of how to represent a class of strategies for future study. For now, we consider that our algorithm is able to capture the main mathematical features present in a general moving average-based strategy.

4 It is usual to define the Sharpe ratio by removing the interest rate from the mean return. However, note that we have assumed that the interest rate is zero. It is also worth noting that the Sharpe ratio (SR) is a special case of the Information ratio (IR). The IR measures performance against a benchmark which might be in general a risky portfolio. However, for the purpose of this study our benchmark is cash. Therefore, SR is equal to IR for us.

5 Data download uses ‘quantmod’ library in R (R Core Team 2016).

6 Transactions costs are a very important issue that has to be addressed whenever a high turnover strategy is advocated as superior. Therefore, our comparison here is merely hypothetical.