Time Series Momentum Effect

Traditional cross-sectional momentum is a popular and very well-documented anomaly. Traditional momentum uses a universe of assets to pick past winners, and it predicts that those winners will continue to outperform their peers in the future as well. However, recent academic research shows that we do not need the whole universe of assets to exploit the momentum effect. A new version of this anomaly (Time Series Momentum) shows that each security’s (or asset's) own past return is a future predictor. The past 12-month excess return of each instrument is a positive predictor of its future return. A diversified portfolio of time series momentum across all assets is remarkably stable and robust, yielding a high Sharpe ratio with little correlation to passive benchmarks. An additional advantage is that time series momentum returns appear to be largest when the stock market's returns are most extreme; hence, time series momentum may be a hedge for extreme events.

Fundamental reason

Academic research states that the time series momentum effect is consistent with behavioral theories of investors' initial under-reaction and delayed over-reaction applied to information dissemination.

Markets traded
equities, bonds, commodities, currencies
Confidence in anomaly's validity
Strong
Notes to Confidence in anomaly's validity
Period of rebalancing
Monthly
Notes to Period of rebalancing
Number of traded instruments
58
Notes to Number of traded instruments
Complexity evaluation
Moderately complex strategy
Notes to Complexity evaluation
Financial instruments
futures, CFDs
Backtest period from source paper
1965-2009
Indicative performance
16.21%
Notes to Indicative performance
per annum, estimated alpha (using Fama&French factors) , annualized (geometrically) monthly return of 1,26%, data from Table 3 Panel A
Estimated volatility
11.73%
Notes to Estimated volatility
estimated from t-statistic 8.55, data from Table 3 Panel A
Maximum drawdown
not stated
Notes to Maximum drawdown
Sharpe Ratio
1.04

Keywords:

momentum

Simple trading strategy

The investment universe consists of 24 commodity futures, 12 cross-currency pairs (with 9 underlying currencies), 9 developed equity indices, and 13 developed government bond futures.

Every month, the investor considers whether the excess return of each asset over the past 12 months is positive or negative and goes long on the contract if it is positive and short if negative. The position size is set to be inversely proportional to the instrument’s volatility. A univariate GARCH model is used to estimated ex-ante volatility in the source paper. However, other simple models could probably be easily used with good results (for example, the easiest one would be using historical volatility instead of estimated volatility). The portfolio is rebalanced monthly.

Source Paper

Moskowitz, Ooi, Pedersen: Time Series Momentum
http://pages.stern.nyu.edu/~lpederse/papers/TimeSeriesMomentum.pdf
Abstract:
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 1 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. We show that the returns to time series momentum are closely linked to the trading activities of speculators and hedgers, where speculators appear to profit from it at the expense of hedgers.

Other Papers

Baltas, Kosowski: Trend-following and Momentum Strategies in Futures Markets
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1968996
Abstract:
Constructing a time-series momentum strategy involves the volatility-adjusted aggregation of univariate strategies and therefore relies heavily on the efficiency of the volatility estimator and on the quality of the momentum trading signal. Using a dataset with intra-day quotes of 12 futures contracts from November 1999 to October 2009, we investigate these dependencies and their relation to timeseries momentum profitability and reach a number of novel findings. First, momentum trading signals generated by fitting a linear trend on the asset price path maximise the out-of-sample performance while minimizing the portfolio turnover, hence dominating the ordinary momentum trading signal in literature, the sign of past return. Second, the results show strong momentum patterns at the monthly frequency of rebalancing, relatively strong momentum patterns at the weekly frequency and relatively weak momentum patterns at the daily frequency. In fact, significant reversal effects are documented at the very short-term horizon. Finally, regarding the volatility-adjusted aggregation of univariate strategies, the Yang-Zhang range estimator constitutes the optimal choice for volatility estimation in terms of maximizing efficiency and minimizing the bias and the ex-post portfolio turnover.

Baltas, Kosowski: Improving Time-Series Momentum Strategies: The Role of Trading Signals and Volatility Estimators
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2140091
Abstract:
Constructing a time-series momentum strategy involves the volatility-adjusted aggregation of uni- variate strategies and therefore relies heavily on the efficiency of the volatility estimator and on the quality of the momentum trading signal. Using a dataset with intra-day quotes of 12 futures contracts from November 1999 to October 2009, we investigate these dependencies and their relation to time-series momentum profitability and reach a number of novel findings. Momentum trading signals generated by fitting a linear trend on the asset price path maximise the out-of-sample performance while minimizing the portfolio turnover, hence dominating the ordinary momentum trading signal in literature, the sign of past return. Regarding the volatility-adjusted aggregation of univariate strategies, the Yang-Zhang range estimator constitutes the optimal choice for volatility estimation in terms of maximizing efficiency and minimizing the bias and the ex-post portfolio turnover.

Baltas, Kosowski: MOMENTUM STRATEGIES IN FUTURES MARKETS AND TREND-FOLLOWING FUNDS
https://workspace.imperial.ac.uk/business-school/Public/RiskLab/wp11.pdf
Abstract:
In this paper we study time-series momentum strategies in futures markets and their relationship to commodity trading advisors (CTAs). First, we construct one of the most comprehensive sets of time-series momentum portfolios by extending existing studies in three dimensions: time-series (1974-2002), cross-section (71 contracts) and frequency domain (monthly, weekly, daily). Our timeseries momentum strategies achieve Sharpe ratios of above 1.20 and provide important diversification benefits due to their counter-cyclical behaviour. We find that monthly, weekly and daily strategies exhibit low cross-correlation, which indicates that they capture distinct return continuation phenomena. Second, we provide evidence that CTAs follow time-series momentum strategies, by showing that time-series momentum strategies have high explanatory power in the time-series of CTA returns. Third, based on this result, we investigate whether there exist capacity constraints in time-series momentum strategies, by running predictive regressions of momentum strategy performance on lagged capital flows into the CTA industry. Consistent with the view that futures markets are relatively liquid, we do not find evidence of capacity constraints and this result is robust to different asset classes. Our results have important implications for hedge fund studies and investors.

Hurst, Ooi, Pedersen: A Century of Evidence on Trend - Following Investing
http://www.scribd.com/doc/110704069/A-Century-of-Evidence-on-Trend-Following-AQR
Abstract:
We study the performance of trend-following investing across global markets since 1903, extending the existing evidence by more than 80 years. We fnd that trend-following has delivered strong positive returns and realized a low correlation to traditional asset classes each decade for more than a century. We analyze trend-following returns through various economic environments and highlight the diversifcation benefits the strategy has historically provided in equity bear markets.Finally, we evaluate the recent environment for the strategy in the context of these long-term results.

Du Plesis, Hallerbach, Spreij: Demystifying momentum: Time-series and cross-sectional momentum, volatility and dispersion
http://www.science.uva.nl/onderwijs/thesis/centraal/files/f233479199.pdf
Abstract:
Variations of several momentum strategies are examined in an asset-allocation setting as well as for a set of industry portfolios. Simple models of momentum returns are considered. The difference between time-series momentum and cross-sectional momentum, with particular regard to the sources of profit for each, is clarified both theoretically and empirically. Theoretical and empirical grounds for the efficacy of volatility weighting are provided and the relationship of momentum with cross-sectional dispersion and volatility is examined.

Maymin, Maymin, Fisher: Momentum's Hidden Sensitivity to the Starting Day
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1899000
Abstract:
We show that the profitability of time-series momentum strategies on commodity futures across their entire history is strongly sensitive to the starting day. Using daily returns with 252-day formation periods and 21-day holding periods, the Sharpe ratio depends on whether one starts on the first day, the second day, and so on, until the twenty first day. This sensitivity is higher for shorter trading periods. The same results also hold in simulation of independent and identically lognormally distributed returns, showing that this is not only an empirical pattern but a fundamental issue with momentum strategies. Portfolio managers should be aware of this latent risk: starting trading the same strategy on the same underlying but one day later could, even after many decades, turn a successful strategy into an unsuccessful one.

Hurst, Ooi, Pedersen: Demystifying Managed Future
http://pages.stern.nyu.edu/~lpederse/papers/DemystifyingManagedFutures.pdf
Abstract:
We show that the returns of Managed Futures funds and CTAs can be explained by simple trend-following strategies, specifically time series momentum strategies. We discuss the economic intuition behind these st rategies, including the potential sources of profit due to initial under-reaction and delayed over-reaction to news. We show empirically that these trend-following strategies explain Managed Futures returns. Indeed, time series momentum strategies produce large correlations and high R-squares with Managed Futures indices and individual manager returns, including the largest and most successful managers. While the largest Managed Futures managers have realized significant alphas to traditional long-only benchmarks, controlling for time series momentum strategies drives their alphas to zero. Finally, we consider a number of implementation issues relevant to time series momentum strategies, including risk management, risk allocation across asset classes and trend horizons, portfolio rebalancing frequency, transaction costs, and fees.

Zhou, Zhu: An Equilibrium Model of Moving-Average Predictability and Time-Series Momentum
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2326650
Abstract:
In an equilibrium model with rational informed investors and technical investors, we show that the moving average of past market prices can forecast the future price, explaining the strong predictive power found in many empirical studies. Our model can also explain the time series momentum that the market prices tend to be positively correlated in the short-run and negatively correlated in the long-run.

Hutchinson, O'Brien: Is This Time Different? Trend Following and Financial Crises
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2375733
Abstract:
Following large positive returns in 2008, CTAs received increased attention and allocations from institutional investors. Subsequent performance has been below its long term average. This has occurred in a period following the largest financial crisis since the great depression. In this paper, using almost a century of data, we investigate what typically happens to the core strategy pursued by these funds in global financial crises. We also examine the time series behaviour of the markets traded by CTAs during these crisis periods. Our results show that in an extended period following financial crises trend following average returns are less than half those earned in no-crisis periods. Evidence from regional crises shows a similar pattern. We also find that futures markets do not display the strong time series return predictability prevalent in no-crisis periods, resulting in relatively weak returns for trend following strategies in the four years immediately following the start of a financial crisis.

Dudler, Gmuer, Malamud: Risk Adjusted Time Series Momentum
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2457647
Abstract:
We introduce a new class of momentum strategies that are based on the long-term averages of risk-adjusted returns and test these strategies on a universe of 64 liquid futures contracts. We show that this risk adjusted momentum strategy outperforms the time series momentum strategy of Ooi, Moskowitz and Pedersen (2012) for almost all combinations of holding- and look-back periods. We construct measures of momentum-specific volatility (risk), (both within and across asset classes) and show that these volatility measures can be used both for risk management and it momentum timing. We find that momentum risk management significantly increases Sharpe ratios, but at the same time leads to more pronounced negative skewness and tail risk; by contrast, combining risk management with momentum timing practically eliminates the negative skewness of momentum returns and significantly reduces tail risk. In addition, momentum risk management leads to a much lower exposure to market, value, and momentum factors. As a result, risk-managed momentum returns offer much higher diversification benefits than the standard momentum returns.

Hutchinson, O'Brien: Trend Following and Macroeconomic Risk
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2550718
Abstract:
We examine the relationship between the returns of trend following and macroeconomic risk. Our results demonstrate that macroeconomic factors do have a statistically significant relationship with trend following, when we allow for the dynamic exposures of the strategy. We find that this time varying risk exposure allows trend following to generate positive returns across a wide range of bond and equity market cycles. Prior research has documented that the majority of cross sectional momentum returns are derived from macroeconomic risk exposures. However, the same is not true for trend following where at least half of performance comes from the unexplained components of futures returns. When we relate performance to the conditional volatility of macroeconomic variables, our results show that trend following generates higher returns in periods where economic uncertainty is low.

Goyal, Jegadeesh: Cross-Sectional and Time-Series Tests of Return Predictability: What Is the Difference?
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2610288
Abstract:
We analyze the differences between past-return based strategies that differ in conditioning on past returns in excess of zero (time-series strategy, TS) and past returns in excess of the cross-sectional average (cross-sectional strategy, CS). We find that the return difference between these two strategies is mainly due to time-varying long positions that the TS strategy takes in the aggregate market and, consequently, do not have any implications for the behavior of individual asset prices. However, TS and CS strategies based on financial ratios as predictors are sometimes different due to asset selection.

Levine, Pedersen: Which Trend Is Your Friend?
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2603731
Abstract:
Managed-futures funds (sometimes called CTAs) trade predominantly on trends. There are several ways of identifying trends, either using heuristics or statistical measures often called “filters.” Two important statistical measures of price trends are time series momentum and moving average crossovers. We show both empirically and theoretically that these trend indicators are closely connected. In fact, they are equivalent representations in their most general forms, and they also capture many other types of filters such as the HP filter, the Kalman filter, and all other linear filters. Further, we show how trend filters can be equivalently represented as functions of past prices vs. past returns. Our results unify and broaden a range of trend-following strategies and we discuss the implications for investors.

Georgopoulou, Wang: The Trend is Your Friend: Time-Series Momentum Strategies Across Equity and Commodity Markets
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2618243
Abstract:
Using a dataset of 67 equity and commodity indices from 1969 to 2013, this study documents a significant time-series momentum effect across international equity and commodity markets. This paper further documents that international mutual funds have a tendency to buy instruments that have been performing well in recent months, but they do not systematically sell those that have been performing poorly in the same periods. We also find that a diversified long-short momentum portfolio realizes its largest profits in extreme market conditions, but the market interventions by central banks in recent years seem to challenge the performance of such portfolios.

Dudler, Gmur, Malamud: Momentum and Risk Adjustment
http://www.iijournals.com/doi/pdfplus/10.3905/jai.2015.2015.1.044
Abstract:
The goal of this article is therefore to study this inefficiency within the time series momentum (TSMOM) strategies introduced in an important article by Moscowitz, Ooi, and Pedersen [2012]. To this end, we introduce a new class of momentum strategies, risk-adjusted time series momentum (RAMOM) strategies, which are based on averages of past futures returns, normalized by their volatility. We test these strategies on a universe of 64 liquid futures contracts and demonstrate that RAMOM strategies outperform the TSMOM strategies of Moscowitz, Ooi, and Pedersen [2012] for short-, medium-, and long-term momentum strategies. Additionally, RAMOM trading signals have another useful and important feature: They are naturally less dependent on high volatility. In other words, standard TSMOM strategies tend to positively correlate (see, e.g., Hurst et al. [2013]) with a long-straddle position (long-call, long-put) and, as a result, perform better in volatile market environments. As we show, this is much less the case for the RAMOM returns because, by risk-adjusting the trading signals according to volatility, we render RAMOM returns more sensitive to new information precisely at the time when volatility is low. As a result, outperformance of RAMOM relative to TSMOM tends to be negatively related to volatility.

Baltas: Trend-Following, Risk-Parity and the Influence of Correlations
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2673124
Abstract:
Trend-following strategies take long positions in assets with positive past returns and short positions in assets with negative past returns. They are typically constructed using futures contracts across all asset classes, with weights that are inversely proportional to volatility, and have historically exhibited great diversification features especially during dramatic market downturns. However, following an impressive performance in 2008, the trend-following strategy has failed to generate strong returns in the post-crisis period, 2009-2013. This period has been characterised by a large degree of co-movement even across asset classes, with the investable universe being roughly split into the so-called Risk-On and Risk-Off subclasses. We examine whether the inverse-volatility weighting scheme, which effectively ignores pairwise correlations, can turn out to be suboptimal in an environment of increasing correlations. By extending the conventionally long-only risk-parity (equal risk contribution) allocation, we construct a long-short trend-following strategy that makes use of risk-parity principles. Not only do we significantly enhance the performance of the strategy, but we also show that this enhancement is mainly driven by the performance of the more sophisticated weighting scheme in extreme average correlation regimes.

Kim, Tse, Wald: Time Series Momentum and Volatility Scaling
http://world-finance-conference.com/papers_wfc2/468.pdf
Abstract:
Moskowitz, Ooi, and Pedersen (2012) show that time series momentum delivers a large and significant alpha for a diversified portfolio of various international futures contracts over the 1985 to 2009 period. Although we confirm these results with similar data, we find that their results are driven by the volatility-scaled returns (or the so-called risk parity approach to asset allocation) rather than by time series momentum. The alpha of time series momentum monthly returns drops from 1.27% with volatility-scaled weights to 0.41% without volatility scaling, which is significantly lower than the cross-sectional momentum alpha of 0.95%. Using volatility-scaled positions, the cumulative return of a time series momentum strategy is higher that that of the buy-and-hold strategy; however, timeseriesmomentuman buy-and-hold offer similar cumulative returns if they are not scaled by volatility. The superior performance of the time series momentum strategy also vanishes in the more recent post-crisis period of 2009 to 2013.

Blocher, Cooper, Molyboga: Benchmarking Commodity Investments
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2744766
Abstract:
While much is known about the financialization of commodities, less is known about how to profitably invest in commodities. Existing studies of Commodity Trading Advisors (CTAs) do not adequately address this question because only 19% of CTAs invest solely in commodities, despite their name. We compare a novel four-factor asset pricing model to existing benchmarks used to evaluate CTAs. Only our four-factor model prices both commodity spot and term risk premia. Overall, our four-factor model prices commodity risk premia better than the Fama-French three-factor model prices equity risk premia, and thus is an appropriate benchmark to evaluate commodity investment vehicles.

Ferreira, Silva, Yen: Information ratio analysis of momentum strategies
http://arxiv.org/abs/1402.3030
Abstract:
In the past 20 years, momentum or trend following strategies have become an established part of the investor toolbox. We introduce a new way of analyzing momentum strategies by looking at the information ratio (IR, average return divided by standard deviation). We calculate the theoretical IR of a momentum strategy, and show that if momentum is mainly due to the positive autocorrelation in returns, IR as a function of the portfolio formation period (look-back) is very different from momentum due to the drift (average return). The IR shows that for look-back periods of a few months, the investor is more likely to tap into autocorrelation. However, for look-back periods closer to 1 year, the investor is more likely to tap into the drift. We compare the historical data to the theoretical IR by constructing stationary periods. The empirical study finds that there are periods/regimes where the autocorrelation is more important than the drift in explaining the IR (particularly pre-1975) and others where the drift is more important (mostly after 1975). We conclude our study by applying our momentum strategy to 100 plus years of the Dow-Jones Industrial Average. We report damped oscillations on the IR for look-back periods of several years and model such oscilations as a reversal to the mean growth rate.

Hamill, Rattray, Hemert: Trend Following: Equity and Bond Crisis Alpha
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2831926
Abstract:
We study time-series momentum (trend-following) strategies in bonds, commodities, currencies and equity indices between 1960 and 2015. We find that momentum strategies performed consistently both before and after 1985, periods which were marked by strong bear and bull markets in bonds respectively. We document a number of important risk properties. First, that returns are positively skewed, which we argue is intuitive by drawing a parallel between momentum strategies and a long option straddle strategy. Second, performance was particularly strong in the worst equity and bond market environments, giving credence to the claim that trend-following can provide equity and bond crisis alpha. Putting restrictions on the strategy to prevent it being long equities or long bonds has the potential to further enhance the crisis alpha, but reduces the average return. Finally, we examine how performance has varied across momentum strategies based on returns with different lags and applied to different asset classes.

Peltomaki, Agerback, Gudmundsen-Sinclair: The Long and Short of Trend Followers
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2836389
Abstract:
We propose the use of short and long portfolios of trend-following strategies to analyze their risk and return characteristics. We find that their exposures are time-varying, depend on the market state, and that returns to their long and short sides in the same asset are not comparable. In addition, we present evidence for occasional long-biased discretion by CTA managers. Our findings are in line with the adaptive markets hypothesis, and the main lesson of our study is that the long and short sides should be differentiated in the analysis of dynamic investment strategies.

Till: What are the Sources of Return for CTAs and Commodity Indices? A Brief Survey of Relevant Research
http://www.oxfordstrat.com/coasdfASD32/uploads/2016/03/Sources-of-Return-for-CTAs.pdf
Abstract:
This survey paper will discuss the (potential) structural sources of return for both CTAs and commodity indices based on a review of empirical research articles from both academics and practitioners. The paper specifically covers (a) the long-term return sources for both managed futures programs and for commodity indices; (b) the investor expectations and the portfolio context for futures strategies; and (c) how to benchmark these strategies.

Hoffman, Kaminski: The TAMING of the SKEW
http://www.valuewalk.com/wp-content/uploads/2016/06/The_Taming_of_the_Skew___Campbell__Company.pdf
Abstract:
Investors are often concerned about the negative skewness, or left-tail asymmetry, of equity returns. In response, they seek risk-mitigating strategies to provide offsetting returns when equity markets fall. Due to their association with positive skewness, trend-following strategies are popular candidates for risk-mitigation or crisis-offset. This paper explores how a trend-following portfolio can achieve positive skewness, and finds that time variation in risk is the primary factor. In fact, any portfolio with a positive Sharpe ratio can achieve positive skewness simply by varying the level of risk taken through time.

Hurst, Ooi, Pedersen: A Century of Evidence on Trend-Following Investing
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2993026
Abstract:
In this article, the authors study the performance of trend-following investing across global markets since 1880, extending the existing evidence by more than 100 years using a novel data set. They find that in each decade since 1880, time series momentum has delivered positive average returns with low correlations to traditional asset classes. Further, time-series momentum has performed well in 8 out of 10 of the largest crisis periods over the century, defined as the largest drawdowns for a 60/40 stock/bond portfolio. Lastly, time series momentum has performed well across different macro environments, including recessions and booms, war and peacetime, high- and low-interest rate regimes, and high- and low-inflation periods.

Cook, Hoyle, Sargaison, Taylor, Hemert: The Best Strategies for the Worst Crises
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2986753
Abstract:
Hedging equity portfolios against the risk of large drawdowns is notoriously difficult and expensive. Holding, and continuously rolling, at-the-money put options on the S&P 500 is a very costly, if reliable, strategy to protect against market sell-offs. Holding ‘safe-haven’ US Treasury bonds, while providing a positive and predictable long-term yield, is generally an unreliable crisis-hedge strategy, since the post-2000 negative bond-equity correlation is a historical rarity. Long gold and long credit protection portfolios appear to sit between puts and bonds in terms of both cost and reliability. In contrast to these passive investments, we investigate two dynamic strategies that appear to have generated positive performance in both the long-run but also particularly during historical crises: futures time-series momentum and quality stock factors. Futures momentum has parallels with long option straddle strategies, allowing it to benefit during extended equity sell-offs. The quality stock strategy takes long positions in highest-quality and short positions in lowest-quality company stocks, benefitting from a ‘flight-to-quality’ effect during crises. These two dynamic strategies historically have uncorrelated return profiles, making them complementary crisis risk hedges. We examine both strategies and discuss how different variations may have performed in crises, as well as normal times, over the years 1985 to 2016.

Jusselin, Lezmi, Malongo, Masselin, Roncalli, Dao: Understanding the Momentum Risk Premium: An In-Depth Journey Through Trend-Following Strategies
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3042173
Abstract:
Momentum risk premium is one of the most important alternative risk premia. Since it is considered a market anomaly, it is not always well understood. Many publications on this topic are therefore based on backtesting and empirical results. However, some academic studies have developed a theoretical framework that allows us to understand the behavior of such strategies. In this paper, we extend the model of Bruder and Gaussel (2011) to the multivariate case. We can find the main properties found in academic literature, and obtain new theoretical findings on the momentum risk premium. In particular, we revisit the payoff of trend-following strategies, and analyze the impact of the asset universe on the risk/return profile. We also compare empirical stylized facts with the theoretical results obtained from our model. Finally, we study the hedging properties of trend-following strategies.