Detailed study of a moving average trading rule

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. * ferfff@usp.br † csilva@idatafactory.com ‡ ju-yi.yen@uc.edu 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 [41], momentum has been extended to different asset classes, portfolios, and other markets abroad. Momentum has been reported in international equity markets by [22,28,62,65]; in industries by [50,60]; in indexes by [8,2]; and in commodities by [24,61]. Single risky asset momentum is analyzed in [21,5,39,7,44,1,52,66] to cite a few. Recently, momentum has also been studied linking its performance to business cycles and regimes by [16,46,33,35,6]. arXiv:1907.00212v1 [q-fin.ST]

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