شتاب سری های زمانی

We document significant “time series momentum” in equity index, currency, commodity, and bond futures for each of the 58 liquid instruments we consider. We find persistence in returns for one to 12 months that partially reverses over longer horizons, consistent with sentiment theories of initial under-reaction and delayed over-reaction. A diversified portfolio of time series momentum strategies across all asset classes delivers substantial abnormal returns with little exposure to standard asset pricing factors and performs best during extreme markets. Examining the trading activities of speculators and hedgers, we find that speculators profit from time series momentum at the expense of hedgers.

We document an asset pricing anomaly we term “time series momentum,” which is remarkably consistent across very different asset classes and markets. Specifically, we find strong positive predictability from a security's own past returns for almost five dozen diverse futures and forward contracts that include country equity indexes, currencies, commodities, and sovereign bonds over more than 25 years of data. We find that the past 12-month excess return of each instrument is a positive predictor of its future return. This time series momentum or “trend” effect persists for about a year and then partially reverses over longer horizons. These findings are robust across a number of subsamples, look-back periods, and holding periods. We find that 12-month time series momentum profits are positive, not just on average across these assets, but for every asset contract we examine (58 in total). Time series momentum is related to, but different from, the phenomenon known as “momentum” in the finance literature, which is primarily cross-sectional in nature. The momentum literature focuses on the relative performance of securities in the cross-section, finding that securities that recently outperformed their peers over the past three to 12 months continue to outperform their peers on average over the next month. 1 Rather than focus on the relative returns of securities in the cross-section, time series momentum focuses purely on a security's own past return. We argue that time series momentum directly matches the predictions of many prominent behavioral and rational asset pricing theories. Barberis, Shleifer, and Vishny (1998), Daniel, Hirshleifer, and Subrahmanyam (1998), and Hong and Stein (1999) all focus on a single risky asset, therefore having direct implications for time series, rather than cross-sectional, predictability. Likewise, rational theories of momentum (Berk et al., 1999, Johnson, 2002, Ahn et al., 2003, Liu and Zhang, 2008 and Sagi and Seasholes, 2007) also pertain to a single risky asset. Our finding of positive time series momentum that partially reverse over the long-term may be consistent with initial under-reaction and delayed over-reaction, which theories of sentiment suggest can produce these return patterns.2 However, our results also pose several challenges to these theories. First, we find that the correlations of time series momentum strategies across asset classes are larger than the correlations of the asset classes themselves. This suggests a stronger common component to time series momentum across different assets than is present among the assets themselves. Such a correlation structure is not addressed by existing behavioral models. Second, very different types of investors in different asset markets are producing the same patterns at the same time. Third, we fail to find a link between time series momentum and measures of investor sentiment used in the literature (Baker and Wurgler, 2006 and Qiu and Welch, 2006). To understand the relationship between time series and cross-sectional momentum, their underlying drivers, and relation to theory, we decompose the returns to a time series and cross-sectional momentum strategy following the framework of Lo and Mackinlay (1990) and Lewellen (2002). This decomposition allows us to identify the properties of returns that contribute to these patterns, and what features are common and unique to the two strategies. We find that positive auto-covariance in futures contracts' returns drives most of the time series and cross-sectional momentum effects we find in the data. The contribution of the other two return components—serial cross-correlations and variation in mean returns—is small. In fact, negative serial cross-correlations (i.e., lead-lag effects across securities), which affect cross-sectional momentum, are negligible and of the “wrong” sign among our instruments to explain time series momentum. Our finding that time series and cross-sectional momentum profits arise due to auto-covariances is consistent with the theories mentioned above.3 In addition, we find that time series momentum captures the returns associated with individual stock (cross-sectional) momentum, most notably Fama and French's UMD factor, despite time series momentum being constructed from a completely different set of securities. This finding indicates strong correlation structure between time series momentum and cross-sectional momentum even when applied to different assets and suggests that our time series momentum portfolio captures individual stock momentum. To better understand what might be driving time series momentum, we examine the trading activity of speculators and hedgers around these return patterns using weekly position data from the Commodity Futures Trading Commission (CFTC). We find that speculators trade with time series momentum, being positioned, on average, to take advantage of the positive trend in returns for the first 12 months and reducing their positions when the trend begins to reverse. Consequently, speculators appear to be profiting from time series momentum at the expense of hedgers. Using a vector auto-regression (VAR), we confirm that speculators trade in the same direction as a return shock and reduce their positions as the shock dissipates, whereas hedgers take the opposite side of these trades. Finally, we decompose time series momentum into the component coming from spot price predictability versus the “roll yield” stemming from the shape of the futures curve. While spot price changes are mostly driven by information shocks, the roll yield can be driven by liquidity and price pressure effects in futures markets that affect the return to holding futures without necessarily changing the spot price. Hence, this decomposition may be a way to distinguish the effects of information dissemination from hedging pressure. We find that both of these effects contribute to time series momentum, but only spot price changes are associated with long-term reversals, consistent with the idea that investors may be over-reacting to information in the spot market but that hedging pressure is more long-lived and not affected by over-reaction. Our finding of time series momentum in virtually every instrument we examine seems to challenge the “random walk” hypothesis, which in its most basic form implies that knowing whether a price went up or down in the past should not be informative about whether it will go up or down in the future. While rejection of the random walk hypothesis does not necessarily imply a rejection of a more sophisticated notion of market efficiency with time-varying risk premiums, we further show that a diversified portfolio of time series momentum across all assets is remarkably stable and robust, yielding a Sharpe ratio greater than one on an annual basis, or roughly 2.5 times the Sharpe ratio for the equity market portfolio, with little correlation to passive benchmarks in each asset class or a host of standard asset pricing factors. The abnormal returns to time series momentum also do not appear to be compensation for crash risk or tail events. Rather, the return to time series momentum tends to be largest when the stock market's returns are most extreme—performing best when the market experiences large up and down moves. Hence, time series momentum may be a hedge for extreme events, making its large return premium even more puzzling from a risk-based perspective. The robustness of time series momentum for very different asset classes and markets suggest that our results are not likely spurious, and the relatively short duration of the predictability (less than a year) and the magnitude of the return premium associated with time series momentum present significant challenges to the random walk hypothesis and perhaps also to the efficient market hypothesis, though we cannot rule out the existence of a rational theory that can explain these findings. Our study relates to the literature on return autocorrelation and variance ratios that also finds deviations from the random walk hypothesis (Fama and French, 1988, Lo and Mackinlay, 1988 and Poterba and Summers, 1988). While this literature is largely focused on US and global equities, Cutler, Poterba, and Summers (1991) study a variety of assets including housing and collectibles. The literature finds positive return autocorrelations at daily, weekly, and monthly horizons and negative autocorrelations at annual and multi-year frequencies. We complement this literature in several ways. The studies of autocorrelation examine, by definition, return predictability where the length of the “look-back period” is the same as the “holding period” over which returns are predicted. This restriction masks significant predictability that is uncovered once look-back periods are allowed to differ from predicted or holding periods. In particular, our result that the past 12 months of returns strongly predicts returns over the next one month is missed by looking at one-year autocorrelations. While return continuation can also be detected implicitly from variance ratios, we complement the literature by explicitly documenting the extent of return continuation and by constructing a time series momentum factor that can help explain existing asset pricing phenomena, such as cross-sectional momentum premiums and hedge fund macro and managed futures returns. Also, a significant component of the higher frequency findings in equities is contaminated by market microstructure effects such as stale prices ( Richardson, 1993 and Ahn et al., 2002). Focusing on liquid futures instead of individual stocks and looking at lower frequency data mitigates many of these issues. Finally, unique to this literature, we link time series predictability to the dynamics of hedger and speculator positions and decompose returns into price changes and roll yields. Our paper is also related to the literature on hedging pressure in commodity futures (Keynes, 1923, Fama and French, 1987, Bessembinder, 1992 and de Roon et al., 2000). We complement this literature by showing how hedger and speculator positions relate to past futures returns (and not just in commodities), finding that speculators’ positions load positively on time series momentum, while hedger positions load negatively on it. Also, we consider the relative return predictability of positions, past price changes, and past roll yields. Gorton, Hayashi, and Rouwenhorst (2008) also link commodity momentum and speculator positions to the commodities' inventories. The rest of the paper is organized as follows. Section 2 describes our data on futures returns and the positioning of hedgers and speculators. Section 3 documents time series momentum at horizons less than a year and reversals beyond that. Section 4 defines a time series momentum factor, studying its relation to other known return factors, its performance during extreme markets, and correlations within and across asset classes. Section 5 examines the relation between time series and cross-sectional momentum, showing how time series momentum is a central driver of cross-sectional momentum as well as macro and managed futures hedge fund returns. Section 6 studies the evolution of time series momentum and its relation to investor speculative and hedging positions. Section 7 concludes.

We find a significant time series momentum effect that is remarkably consistent across the nearly five dozen futures contracts and several major asset classes we study over the last 25 years. The time series momentum effect is distinct from cross-sectional momentum, though the two are related. Decomposing both time series and cross-sectional momentum profits, we find that the dominant force to both strategies is significant positive auto-covariance between a security's excess return next month and it's lagged 1-year return. This evidence is consistent with initial under-reaction stories, but may also be consistent with delayed over-reaction theories of sentiment as the time series momentum effect partially reverses after one year. Time series momentum exhibits strong and consistent performance across many diverse asset classes, has small loadings on standard risk factors, and performs well in extreme periods, all of which present a challenge to the random walk hypothesis and to standard rational pricing models. The evidence also presents a challenge to current behavioral theories since the markets we study vary widely in terms of the type of investors, yet the pattern of returns remains remarkably consistent across these markets and is highly correlated across very different asset classes. Indeed, correlation among time series momentum returns is stronger than the correlation of passive long positions across the same asset classes, implying the existence of a common component to time series momentum that is not present in the underlying assets themselves. Finally, the link between time series momentum returns and the positions of speculators and hedgers indicates that speculators profit from time series momentum at the expense of hedgers. This evidence is consistent with speculators earning a premium via time series momentum for providing liquidity to hedgers. Decomposing futures returns into the effect of price changes, which captures information diffusion, and the roll return, which captures how hedging pressure affects the shape of the futures curve, we find that shocks to both price changes and roll returns are associated with time series momentum profits. However, only shocks to price changes partially reverse, consistent with behavioral theories of delayed over-reaction to information, and not hedging pressure. Time series momentum represents one of the most direct tests of the random walk hypothesis and a number of prominent behavioral and rational asset pricing theories. Our findings present new evidence and challenges for those theories and for future research.