Residual momentum

https://doi.org/10.1016/j.jempfin.2011.01.003Get rights and content

Abstract

Conventional momentum strategies exhibit substantial time-varying exposures to the Fama and French factors. We show that these exposures can be reduced by ranking stocks on residual stock returns instead of total returns. As a consequence, residual momentum earns risk-adjusted profits that are about twice as large as those associated with total return momentum; is more consistent over time; and less concentrated in the extremes of the cross-section of stocks. Our results are inconsistent with the notion that the momentum phenomenon can be attributed to a priced risk factor or market microstructure effects.

Introduction

Conventional momentum strategies, as described in the seminal work of Jegadeesh and Titman, 1993, Jegadeesh and Titman, 2001, are based on total stock returns. In this study we investigate in detail a momentum strategy based on residual returns estimated using the Fama and French three-factor model. One of our main findings is that the Sharpe ratio of residual momentum is approximately double that of total return momentum, mainly due to lower return variability. The reason is related to the fact that momentum has substantial time-varying exposures to the Fama and French factors, as illustrated by Grundy and Martin (2001). Specifically, momentum loads positively (negatively) on systematic factors when these factors have positive (negative) returns during the formation period of the momentum strategy. As a consequence, a total return momentum strategy experiences losses when the sign of factor returns over the holding period is opposite to the sign over the formation period. By design, residual momentum exhibits smaller time-varying factor exposures, which reduces the volatility of the strategy.

Residual momentum does not only improve upon total return momentum in terms of higher long-run average Sharpe ratios, but also in several other ways. First, total return momentum strategies appear to have lost their profitability in the most recent years. In fact, we find a return of − 8.5% per annum over the period January 2000 to December 2009. Residual momentum, on the other hand, has remained profitable, generating a return of 4.7% per annum over the same time period. To illustrate that the negative returns of total return momentum strategies can largely be attributed to their time-varying exposures to the Fama and French factors we point at the large losses of momentum in the first half of 2009. The negative market returns in the credit crisis of 2008 caused total return momentum to be tilted towards the low-beta segment of the market in early 2009. When the market recovered in the first quarter of 2009, total return momentum's negative market beta caused large losses. Because residual momentum was less negatively exposed to the market, the strategy was less negatively affected.

Second, a variety of papers argue that momentum displays characteristics that are often associated with priced risk factors. Chordia and Shivakumar (2002), for example, argue that the profits of momentum strategies exhibit strong variation across the business cycle. Over the period January 1930 to December 2009, total return momentum earns 14.7% per annum during expansions and loses − 8.7% during recessions. We show that these results can largely be attributed to the strategy's time-varying exposures to the Fama and French factors. A total return momentum strategy is typically titled towards low-beta stocks after the early stage of a recession, while market returns during the later stage of a recession are, on average, highly positive. Because residual momentum is nearly market-neutral by construction, the strategy delivers positive returns not only during expansions, but also during recessions. In particular, the return of residual momentum during recessions is a positive 5.6% per annum.

Third, another risk-based explanation for momentum is that the strategy is concentrated in the smallest firms in the cross-section, see for example Jegadeesh and Titman (1993). Residual momentum, on the other hand, is nearly neutral to the Fama and French size factor, indicating that the success of momentum strategies is not critically dependent on a structural tilt towards small-caps. Moreover, because, unlike total return momentum, residual momentum is not concentrated in small-cap stocks, trading costs are likely to have a smaller impact on the profitability of the strategy.

Finally, residual momentum is less prone to the tax-loss selling effect compared to total return momentum. Fund managers tend to sell small-cap loser stocks in December, causing a large positive return for a total return momentum strategy during that month, followed by a large negative return in January (see, e.g., Ferris et al., 2001, Griffiths and White, 1993, Roll, 1983). Because residual momentum is closer to being size neutral than total return momentum, this December/January effect is much less pronounced, as a result of which the strategy earns more stable returns within a calendar year.

Our work extends the research by Grundy and Martin (2001) who show that momentum has dynamic exposures to the Fama and French factors. The authors find a significantly improved performance for a hypothetical strategy which hedges these exposures by adding positions in zero-cost hedge portfolios based on ex post estimates of factor exposures. However, when they evaluate a feasible strategy which uses information that is available ex ante they only find a marginal improvement in performance. The residual momentum strategy described in this paper, on the other hand, succeeds in improving upon a total return momentum strategy without using any information or instruments that would not have been available to investors in reality.

Our work also extends the research by Gutierrez and Pirinsky (2007), who document that momentum's long-term reversal in months 13 to 60 after portfolio formation can be attributed to the strategy's common-factor exposures. For a momentum strategy based on residual stock returns the authors observe that performance over the first year after formation is similar to that of total return momentum, but, contrary to total return momentum, long-run performance does not revert. This suggests that the difference between residual and total return momentum is negligible in the first year after formation and only becomes significant during subsequent years. However, we show that when risks are taken into account the momentum strategies' performances are in fact also different during the first 12 months after portfolio formation. As discussed above, we find that the risk-adjusted performance of residual momentum is double that of total return momentum; more consistent over time; more consistent over the business cycle; and less concentrated in the extremes of the cross-section.

Our findings are consistent with the gradual-information-diffusion hypothesis that states that information diffuses only gradually across the investment public and that investor under-reaction is more strongly pronounced for firm-specific events than for common events (see, e.g., Barberis et al., 1998, Daniel et al., 1998, Gutierrez and Pirinsky, 2007, Hong and Stein, 1999, Hong et al., 2000). Moreover, our results present an even more serious challenge to the view that markets are weak-form efficient than the total return momentum results in the literature.

Our findings also have implications for the practical implementation of momentum trading strategies. Our results imply that momentum investors in practice are more likely to achieve a superior risk-adjusted performance by adopting a residual momentum strategy than by following a conventional total return momentum strategy.

In what follows, Section 2 discusses our motivation to look at residual momentum. Section 3 describes our data and construction of momentum portfolios. 4 Empirical results, 5 Robustness checks and follow-up empirical tests document the results of our empirical analyses and robustness tests, respectively. Finally Section 6 concludes.

Section snippets

Residual momentum versus total return momentum

A conventional momentum strategy first ranks stocks on their total return over the preceding period and then buys the past winner stocks and sells the past loser stocks. We argue that such a strategy implicitly places a bet on persistence in common-factor returns, which will affect its risk and return characteristics. To illustrate this, consider the following example. If the market premium was positive during the formation period, a momentum strategy will typically be long in high-beta stocks

Data and methodology

Consistent with most of the momentum literature, we extract our data from the CRSP database and consider all domestic, primary stocks listed on the New York (NYSE), American (AMEX), and Nasdaq stock markets in our study. Closed-end funds, Real Estate Investment Trusts (REITs), unit trusts, American Depository Receipts (ADRs), and foreign stocks are excluded from the analysis. Our sample period covers the period January 1926 to December 2009. We exclude stocks during the month(s) that their

Empirical results

This section contains an extensive comparison of the empirical characteristics of residual and total return momentum strategies.

Robustness checks and follow-up empirical tests

In this final section we perform a range of tests to examine the robustness of our results to various choices we made with respect to the design of our research.

Summary and concluding comments

We present a momentum strategy based on residual stock returns that significantly improves upon conventional total return momentum strategies. Our approach begins with estimating residual returns for each stock relative to the Fama and French factors. We find that ranking stocks on their residual returns is a very effective approach to isolate the stock-specific component of momentum. Our results show that residual momentum exhibits risk-adjusted profits that are about twice as large as those

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    We are grateful for the comments of the referee and the editor, Chrisitan Wolff. The usual disclaimer applies.

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