Momentum

Momentum is the tendency of investments to persist in their performance. Assets that perform well over a 3 to 12 month period tend to continue to perform well into the future. The momentum effect of Jegadeesh and Titman (1993) is one of the strongest and most pervasive financial phenomena. Momentum investment strategies have been mostly applied to equities (see momentum in equities), however there is large evidence documenting momentum across different asset classes. Typical strategy consists of a universe of major indices on equity, bonds, real estate and commodities. The aim is to keep long only portfolio where an index with positive past 12 month returns is bought and negative returns sold. A well-known example of trend following momentum strategy is from Faber (2007). He creates 10 month moving average for which assets are sold and bought every month based on price being above or below the moving average. Using a 100 years of data, Faber claims to outperform the market with the mean return of 10.18% , 11.97 % volatility and max draw-down of 50.29%, compared to S&P 500 return of 9.32%, volatility of 17.87% and max draw-down of 83.46%.

In general, we distinguish between absolute and relative momentum. Absolute momentum is captured by trend following strategies that adjusts weights of assets based on past returns such as relative level of current prices compared to moving averages. Relative or cross sectional momentum, on the other hand, use long and short positions applied to both the long and short side of a market simultaneously. It makes little difference whether the studied markets go up or down, since short momentum positions hedge long ones, and vice versa. When looking only at long side momentum, however, it is desirable to be long only when both absolute and relative momentum are positive, since long-only momentum results are highly regime dependent. In order to increase performance, the simple momentum strategy is expanded to capture both relative and absolute momentum creating a long short portfolio.

Various extensions to the simple strategies shown above have been suggested. For example we can deploy mean-variance optimisation to re-weight our assets to minimise the risk given return. Moreover, we can diversify the strategy by restricting the weights to different asset classes and risk factors as well as adding various risk management practices to decrease leverage during heightened volatility periods. Furthermore, taking into account the cyclicality and idiosyncratic momentum of various sub-indices to Faber’s original asset classes produces even stronger improvements to risk-adjusted returns. Unfortunately, cross-sectional strategies use high number of stocks resulting in high trading costs. Luckily, it has been found that using sectors and indices instead of individual stocks still earns similar momentum returns while having lower trading costs.

Numerous empirical studies report on benefits of extending momentum strategy across asset classes (see Rouwenhorst 1998, Blake 1999, Griffin, Ji, and Martin 2003, Gorton, Hayashi, and Rouwenhorst 2008, Asness, Moskowitz, and Pedersen 2009). For example, including commodities in a momentum strategy can achieve better diversification and protection from inflation while having equity like returns (Erb and Harvey, 2006). Foreign exchange is another asset class with published momentum effects. Okunev and White (2003) find the well-documented profitability of momentum strategies with equities to hold for currencies throughout the 1980s and the 1990s. Contrary to already mentioned asset classes, bond returns have generally not displayed momentum. However, some later evidence suggests that assorting bonds with volatility adjusted returns leads to observation of momentum. Using 68,914 individual investment-grade and high-yield bonds, Jostova et al. (2013) find strong evidence of momentum profitability in US corporate bonds over the period from 1973 to 2008. Past six-month winners outperform past six-month losers by 61 basis points per month over a six-month holding period. Last but not least, momentum has been documented in real estate with a cross-sectional momentum buy/sell strategy significantly reducing volatility and drawdown of a long only REIT fund.

An often cited benefit of momentum strategies is their sustainable performance attributed to a true anomaly rather than skewedness in the return probability distribution that is cited to be responsible for value and carry strategy. Reasons explaining the momentum anomaly include analyst coverage, analyst forecast dispersion, illiquidity, price level, age, size, credit rating, return chasing and confirmation bias, market-to-book, turnover and others.

Factor Investing in Currency Markets

26.July 2019

A new research paper related to multiple currency strategies:

#5 – FX Carry Trade
#8 – Currency Momentum Factor
#9 – Currency Value Factor – PPP Strategy

Authors: Baku, Fortes, Herve, Lezmi, Malongo, Roncalli, Xu

Title: Factor Investing in Currency Markets: Does it Make Sense?

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3415700

Abstract:

The concept of factor investing emerged at the end of the 2000s and has completely changed the landscape of equity investing. Today, institutional investors structure their strategic asset allocation around five risk factors: size, value, low beta, momentum and quality. This approach has been extended to multi-asset portfolios and is known as the alternative risk premia model. This framework recognizes that the construction of diversified portfolios cannot only be reduced to the allocation policy between asset classes, such as stocks and bonds. Indeed, diversification is multifaceted and must also consider alternative risk factors. More recently, factor investing has gained popularity in the fixed income universe, even though the use of risk factors is an old topic for modeling the yield curve and pricing interest rate contingent claims. Factor investing is now implemented for managing portfolios of corporate bonds or emerging bonds.

In this paper, we focus on currency markets. The dynamics of foreign exchange rates are generally explained by several theoretical economic models that are commonly presented as competing approaches. In our opinion, they are more complementary and they can be the backbone of a Fama-French-Carhart risk factor model for currencies. In particular, we show that these risk factors
may explain a significant part of time-series and cross-section returns in foreign exchange markets. Therefore, this result helps us to better understand the management of forex portfolios. To illustrate this point, we provide some applications concerning basket hedging, overlay management and the construction of alpha strategies.

Notable quotations from the academic research paper:

"In this paper, we propose analyzing foreign exchange rates using three main risk factors: carry, value and momentum. The choice of these market risk factors is driven by the economic models of foreign exchange rates. For instance, the carry risk factor is based on the uncovered interest rate parity, the value risk factor is derived from equilibrium models of the real exchange rate, and the momentum risk factor bene fits from the importance of technical analysis, trading behavior and overreaction/underreaction patterns. Moreover, analyzing an asset using these three dimensions helps to better characterize the fi nancial patterns that impact an asset: its income, its price and its trend dynamics. Indeed, carry is associated with the yield of the asset, value measures the fair price or the fundamental risk and momentum summarizes the recent price movements.

FX Carry

FX Value

FX Momentum

By using carry, value and momentum risk factors, we are equipped to study the cross-section and time-series of currency returns. In the case of stocks and bonds, academics present their results at the portfolio level because of the large universe of these asset classes. Since the number of currencies is limited, we can show the results at the security level.

For each currency, we can then estimate the sensitivity with respect to each risk factor, the importance of common risk factors, when speci fic risk does matter, etc. We can also connect statistical figures with monetary policies and regimes, illustrating the high interconnectedness of market risk factors and economic risk factors. The primary goal of building an APT model for currencies is to have a framework for analyzing and comparing the behavior of currency returns. This is the main objective of this paper, and a more appropriate title would have been "Factor Analysis of Currency Returns". By choosing the title "Factor Investing in Currency Markets", we emphasize that our risk factor framework can also help to manage currency portfolios as security analysis always comes before investment decisions.

This paper is organized as follows. Section Two is dedicated to the economics of foreign exchange rates. We fi rst introduce the concept of real exchange rate, which is central for understanding the di fferent theories of exchange rate determination. Then, we focus on interest rate and purchasing power parities. Studying monetary models and identifying the statistical properties of currency returns also helps to defi ne the market risk factors, which are presented in Section Three. These risk factors are built using the same approach in terms of portfolio composition and rebalancing. Section Four presents the cross-section and time-series analysis of each currency. We can then estimate a time-varying APT-based model in order to understand the dynamics of currency markets. The results of this dynamic model can be used to manage a currency portfolio. This is why Section Five considers hedging and
overlay management."


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Two Versions of CAPM

19.July 2019

This week's analysis of selected financial research paper contains more text and no picture, but we still think it's worth reading …

Authors: Siddiqi

Title: CAPM: A Tale of Two Versions

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3350280

Abstract:

Given that categorization is the core of cognition, we argue that investors do not view firms in isolation. Rather, they view them within a framework of categories that represent prior knowledge. This involves sorting a given firm into a category and using categorization-induced inferences to form earnings and discount-rate expectations. If earnings-aspect is categorization-relevant, then earnings estimates are refined, whereas discount-rates are confounded with the category-exemplar. The opposite happens when discount-rates are categorization relevant. Earnings-focused approach such as DCF, generally used by institutional investors, leads to a version of CAPM in which the relationship between average excess return and stock beta is flat (possibly negative). Value effect and size premium (controlling for quality) arise in this version. Discount-rate focused approach such as multiples or comparables valuation, typically used by individual investors, leads to a second version in which the relationship is strongly positive with growth stocks doing better. The two-version CAPM accounts for several recent empirical findings including fundamentally different intraday vs overnight behavior, as well as behavior on macroeconomic announcement days. Momentum is expected to be an overnight phenomenon, which is consistent with empirical findings. We argue that, perhaps, our best shot at observing classical CAPM in its full glory is a laboratory experiment with subjects who have difficulty categorizing (such as in autism spectrum disorders).

Notable quotations from the academic research paper:

"Consider the following two empirical observations:

Firstly, stock prices behave very differently with respect to their sensitivity to market risk (beta) at specific times. Typically, average excess return and beta relationship is flatter than expected. It could even be negative. However, during specific times, this relationship is strongly positive, such as on days when macroeconomic announcements are made or during the night.

Secondly, a hue, which is halfway between yellow and orange, is seen as yellow on a banana and orange on a carrot. In this article, we argue that the two observations are driven by the same underlying mechanism.

The second observation is an example of the implications of categorization for color calibration. In this article, we argue that the first observation is also due to categorization, which gives rise to two versions of CAPM. In one version, the relationship between expected return and stock beta is flatter than expected or could even be negative, whereas in the second version, this relationship is strongly positive.

Categorization is the mental operation by which brain classifies objects and events. We do not experience the world as a series of unique events. Rather, we make sense of our experiences within a framework of categories that represent prior knowledge. That is, new information is only understood in the context of prior knowledge.

Here, in accord with cognitive science literature, we present a view of categorization that has both an upside as well as a downside, and apply this nuanced perspective to the capital asset pricing model (CAPM). If categorization is fundamental to how our brains make sense of information, then investor behavior, like any other domain of human behaviour, should also be viewed through this lens. This means that the traditional view that each firm is viewed in isolation needs to be altered. When an investor considers a firm, she views it within a framework of categories that represent prior knowledge. This involves sorting a given firm into a category based on attributes that are deemed categorization-relevant. Categorization-induced inferences help refine such attributes while confounding categorization-irrelevant attributes with the category-exemplar.

Valuation requires estimating earnings (cash-flows) potential and estimating discount-rates. Even among firms that sell similar products (same sector) some may have more similar earnings potential, whereas other may have more similar discount-rates. The former type may include firms with similar earnings-related fundamentals but very different levels of debt ratio and equity betas. Also, their multiples (generally related to inverse of the discount-rate) such as P/E, EV/Sales or EV/EBITDA could be very different. The latter type may include firms with similar debt ratios and equity betas or similar P/E and EV/EBITDA but quite different earnings or cash-flows fundamentals.

We argue that, an earnings-focused approach, such as discounted cash-flows (DCF), tends to categorize the former type of firms together, whereas, the relative valuation approach (RV) based on multiples such as P/E or EV/EBITDA tends to categorize the latter types of firms together. In other words, the choice of a valuation approach introduces a bias in how firms are categorized.

In this paper, we take discounted cash-flows (DCF) as the prototype of an earnings-potential focused approach, and valuation by multiples or relative valuation (RV) as the prototype discount-rate focused approach.

We show that when earnings aspect is categorization-relevant (as in DCF analysis), a version of CAPM is obtained, which displays a flatter or even negative relationship between stock beta and expected excess returns. Betting-against-beta anomaly is observed along with the value effect, as well as the size premium after controlling for quality (consistent with the findings in Asness et al 2018). We argue that this is the default version which typically prevails. While categorizing firms, if investors are focused on the discount rate aspect (as in RV analysis), then the discount-rates are refined whereas earnings estimates are confounded with the category-exemplar. A second version of CAPM arises. In this version, there is a strong positive relationship between beta and expected excess return.

One way to make sense of the co-existence of two versions is to classify investors as either earnings-focused or discount rate-focused. If earnings-focused investors dominate, then the first version is observed. If the discount-rate-focused investors dominate, then the second version is observed. Note, that earnings-focused approach (such as DCF) is typically employed by large institutional investors, whereas RV approach is associated with individual investors (and with sell-side equity analysts who publish research reports for individual investors).

If institutional investors are earnings-focused and individual investors are discount rate-focused, then the trading behavior of each type can be observed to make specific predictions:

1) Institutional investors typically avoid trading at the open and prefer to trade in the afternoon near the market close. The objective is to time the trade when the market is most liquid to avoid any adverse price impact. This means that trade at open is dominated by individual investors. So, one expects to see the relationship between stock beta and average return to be strongly positive (second version) overnight and flat or even negative (first version) intraday.

2) Institutional traders typically trade in the right direction prior to macroeconomic announcement days (suggesting superior information) with institutional trading volume falling sharply on macro-announcement days. As trade on such days is dominated by individual investors, one expects to see a strongly positive relationship (second version) on macro-announcement days.

3) The first version generally dominates intraday due to institutional investors being dominant. As the corresponding CAPM version comes with size and value effects, the prediction is that size and value are primarily intraday phenomena.

4) We show that, all else equal, discount rate-focused investors have higher willingness-to-pay than earnings-focused investors. If discount rate-focused investors dominate trade at open, whereas earnings-focused investors are active intraday, then one expects prices to typically rise overnight from close-to-open and fall intraday between open-to-close.

5) If momentum traders, who buy past winners and short past losers, are primarily individual investors, then one expects momentum to be an overnight phenomenon observed between close-to-open. This is because individual traders dominate trade at or near open.

"


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Equity Factor Strategies In Frontier Markets

12.July 2019

A new research paper related to all equity factor strategies …

Authors: Zaremba, Maydybura, Czapkiewicz, Arnaut

Title: Explaining Equity Anomalies In Frontier Markets: A Horserace of Factor Pricing Models

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3378785

Abstract:

We are the first to compare the explanatory power of the major empirical asset pricing models over equity anomalies in the frontier markets. We replicate over 160 stock market anomalies in 23 frontier countries for years 1996–2017, and evaluate their performance with the factor models. The Carhart’s (1997) four-factor model outperforms both the recent Fama and French (2015) five-factor model and the q-model by Hou, Xue, and Zhang (2015). Its superiority is driven by the ability to explain the momentum-related anomalies. Inclusion of additional profitability and investment factors lead to no further major improvement in the performance. Nonetheless, none of the models is able to fully explain the abnormal returns on all of the anomaly portfolios.

Notable quotations from the academic research paper:

"In times of soaring correlations among global stocks and increasing controversies on anomaly performance in emerging stock markets, one specific asset class may offer a remedy: frontier equities. Deemed the least developed emerging markets, the frontier countries are scattered around the globe, with presence in Africa, Asia, Europe, and Latin America. Being very diverse both economically and geographically, they range from the wealthy oil-producing kingdoms in the Gulf to some of the poorest countries in Africa. While the current size of the frontier stock markets is still fairly small – the total capitalization of the MSCI Frontier Market Index constituents equaled $134 billion in May 2018 (MSCI, 2018), accounting for less than 0.4% of developed markets – yet, the interest in them is growing quickly.

Considering the future potential, along with the soaring interest of the international community, and the investment opportunities, it is surprising how underresearched – if not ignored – the frontier equities are. The number of academic studies on this stock market class seems astonishingly modest. This leaves numerous important questions, which may be of huge importance for global investors, unanswered. Which equity anomalies – discovered originally in developed countries – work also in the frontier stock markets? Could they be translated into profitable strategies using easily-to-implement quantitative methods? Finally, which asset pricing models and factors best summarize the cross-sectional return patterns and the equity anomalies in frontier countries? Could the recent five-factor framework by Fama and French (2015) or the q-model by Hou, Xue, and Zhang (2015) be also applied in this growing asset class? The principal target of this study is to close this gap in the existing body of literature at least partially.

Research sample

The elevated liquidity constraints, higher trading costs, short sale unavailability accompanied by less sophisticated investors may potentially result in larger mispricing and more pronounced stock market anomalies.

Our research aims to contribute in three primary ways. Our first goal is to conduct the most comprehensive test on which equity anomalies, discovered originally in the developed countries, are also present in the frontier equities. Thus, we examine the performance of 167 anomalies from the finance literature, encompassing different classes of patterns related to value, trend following, investment, profitability, risk, and many others. The large-scale analysis available in broadly-accessible journals was either limited to the few most prominent strategies, such as size, value, and momentum (Blackburn and Cakici 2017, De Groot, Pang, and Swinkels 2012). Our study aims to take a substantial leap forward in understanding the multidimensionality of equity returns in the frontier markets.

Second, we research which of the broadly-acknowledged asset pricing models serve best in explaining the cross-section of anomaly returns in the frontier markets. In particular, we consider seven factor pricing models: the capital asset pricing model (Sharpe 1964), abbreviated CAPM, the three-factor model (Fama and French 1993), abbreviated FF3, the four-factor model (Carhart 1997), abbreviated C4, the five-factor model (Fama and French 2015), abbreviated FF5, the q-model by Hou, Xue, and Zhang (2015), the six-factor model by Fama and French (2018), abbreviated FF6, and the six-factor model by Barillas and Shanken (2018), abbreviated BS6.

Last but not least, our research may be regarded as a large out-of-sample test of equity anomalies.

To answer our research questions, we replicate the 167 equity anomalies from Zaremba et al. (2018) in an extensive sample of over 3,600 companies from frontier markets from all over the world for years 1996 – 2017. We form the long-short anomaly portfolios and evaluate their returns using the seven considered factor pricing models: CAPM, FF3, C4, FF5, Q4, FF6, and BS6. We compare the models’ performance by employing a range of tools and statistics that assess their ability to explain the risk and mean returns jointly.

The principal findings of this study could be summarized as follows. First, out of the 167 anomaly portfolios, only 38% (19%) of the equal-weighted (value-weighted) long-short strategies produce profits significantly departing from zero at the 5% level. The successful return patterns are usually linked to the “value vs. growth” or trend following effects, verifying positively the arguments of Asness, Moskowitz, and Pedersen (2013) that value and momentum are everywhere.

Second, we demonstrate that Carhart’s (1997) four-factor model best explains the anomaly returns in frontier markets, outperforming other models in many ways. It displays lower average absolute intercepts and largest number of explained anomalies. Its cross-sectional and time-series R2 is higher CAPM, FF3, FF5, or Q4, and only marginally lower than in the case of FF6 and BS6.

Returns of long short portfolios

"


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The Best of Strategies for the Times of Crisis

26.June 2019

We at Quantpedia are not the only ones who are interested in finding strategies that can be used to mitigate the impacts of the large equity corrections. We have already written a short article about a lottery/skewness strategy in commodities, which offers some protection in a time of crisis. Our users can also screen a list of strategies that can be used as a hedge/diversification for equity markets during downturns. A new research paper written by Harvey, Hoyle, Rattray, Sargaison, Taylor and Van Hemert explores the same question and analyzes the performance of different tools that investors could deploy during equity bear markets. We sincerely recommend it …

Authors: Harvey, Hoyle, Rattray, Sargaison, Taylor, Van Hemert

Title: The Best of Strategies for the Worst of Times: Can Portfolios be Crisis Proofed?

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3383173

Abstract:

In the late stages of long bull markets, a popular question arises: What steps can an investor take to mitigate the impact of the inevitable large equity correction? However, hedging equity portfolios is notoriously difficult and expensive. We analyze the performance of different tools that investors could deploy. For example, continuously holding short-dated S&P 500 put options is the most reliable defensive method but also the most costly strategy. Holding ‘safe-haven’ US Treasury bonds produces a positive carry, but may be an unreliable crisis-hedge strategy, as the post-2000 negative bond-equity correlation is a historical rarity. Long gold and long credit protection portfolios sit in between puts and bonds in terms of both cost and reliability. Dynamic strategies that performed well during past drawdowns include: futures time-series momentum (which benefits from extended equity sell-offs) and a quality strategy that takes long/short positions in the highest/lowest quality company stocks (which benefits from a ‘flight-to-quality’ effect during crises). We examine both large equity drawdowns and recessions. We also provide some out-of-sample evidence of the defensive performance of these strategies relative to an earlier, related paper.

Notable quotations from the academic research paper:

"The typical investment portfolio is highly concentrated in equities leaving investors vulnerable to large drawdowns. We examine the performance of a number of candidate defensive strategies, both active and passive, between 1985 and 2018, with a particular emphasis on the eight worst drawdowns (the instances where the S&P 500 fell by more than 15%) and three US recessions. To guard against overfitting, we provide out-of-sample evidence of the performance of these strategies in the 2018Q4 drawdown that occurred after we wrote an earlier, related paper.

We begin with two passive strategies, both of which benefit directly from a falling equity market. A strategy that buys, and then rolls, one-month S&P 500 put options performs well in each of the eight equity drawdown periods. However, it is very costly during the ‘normal’ times, which constitute 86% of our sample and expansionary (non-recession) times, which constitute 93% of our observations. As such, passive option protection seems too expensive to be a viable crisis hedge. A strategy that is long credit protection (short credit risk) also benefits during each of the eight equity drawdown periods, but in a more uneven manner, doing particularly well during the 2007-2009 Financial Crisis, which was a credit crisis. Nevertheless, the credit protection strategy is less costly during normal times and non-recessions than the put buying strategy.

Next, we consider so-called ‘safe-haven’ investments. A strategy that holds long positions in 10-year US Treasuries performed well in the post-2000 equity drawdowns, but was less effective during previous equity sell-offs. This is consistent with the negative bond-equity correlation witnessed post-2000, which is atypical from the longer historical perspective. As we move beyond the extreme monetary easing that has characterized the post-Financial Crisis period, it is possible that the bond-equity correlation may revert to the previous norm, rendering a long bond strategy a potentially unreliable crisis hedge. A long gold strategy generally performs better during crisis periods than at normal times, consistent with its reputation as a safe-haven security. However, its appeal as a crisis hedge is diminished by the fact that its long-run return, measured over the 1985-2018 period, is close to zero and that it carries substantial idiosyncratic risk unrelated to equity markets.

We then turn our attention to dynamic strategies.

Time-series momentum strategies add to winning positions (ride winners) and reduce losing positions (cut losers), much like a dynamic replication of an option straddle strategy. We show that such strategies performed well over the eight equity drawdowns and three recessions. We also explore limiting the equity exposure (no long positions allowed), which we find enhances the crisis performance.

Next, we consider long-short US equity strategies. A review of the factors proposed in the academic literature suggests that those that take long positions in high-quality and short positions in low-quality companies are most promising as crisis hedges, since they benefit from flights to quality when panic hits markets. The definition of a quality business is, of course, open to debate. However, broadly speaking, such companies will be profitable, growing, have safer balance sheets, and run investor-friendly policies in areas such as payout ratios. We examine a host of quality metrics, and illustrate the importance of a beta-neutral (common in practice) rather than a dollar-neutral (common in academic studies) portfolio construction.

performance of passive trading strategies

performance over drawdown period

"


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Using Deep Neural Networks to Enhance Time Series Momentum

22.June 2019

A new research paper related to:

#118 – Time Series Momentum

Authors: Lim, Zohren, Roberts

Title: Enhancing Time Series Momentum Strategies Using Deep Neural Networks

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3369195

Abstract:

While time series momentum is a well-studied phenomenon in finance, common strategies require the explicit definition of both a trend estimator and a position sizing rule. In this paper, we introduce Deep Momentum Networks — a hybrid approach which injects deep learning based trading rules into the volatility scaling framework of time series momentum. The model also simultaneously learns both trend estimation and position sizing in a data-driven manner, with networks directly trained by optimising the Sharpe ratio of the signal. Backtesting on a portfolio of 88 continuous futures contracts, we demonstrate that the Sharpe-optimised LSTM improved traditional methods by more than two times in the absence of transactions costs, and continue outperforming when considering transaction costs up to 2-3 basis points. To account for more illiquid assets, we also propose a turnover regularisation term which trains the network to factor in costs at run-time.

Notable quotations from the academic research paper:

"While numerous papers have investigated the use of machine learning for financial time series prediction, they typically focus on casting the underlying prediction problem as a standard regression or classification task – with regression models forecasting expected returns, and classification models predicting the direction of future price movements. This approach, however, could lead to suboptimal performance in the context time-series momentum for several reasons.

Firstly, sizing positions based on expected returns alone does not take risk characteristics into account – such as the volatility or skew of the predictive returns distribution — which could inadvertently expose signals to large downside moves. This is particularly relevant as raw momentum strategies without adequate risk adjustments, such as volatility scaling, are susceptible to large crashes during periods of market panic. Furthermore, even with volatility scaling – which leads to positively skewed returns distributions and long-option-like behaviour – trend following strategies can place more losing trades than winning ones and still be profitable on the whole – as they size up only into large but infrequent directional moves. The fraction of winning trades is a meaningless metric of performance, given that it cannot be evaluated independently from the trading style of the strategy. Similarly, high classification accuracies may not necessarily translate into positive strategy performance, as profitability also depends on the magnitude of returns in each class. In light of the deficiencies of standard supervised learning techniques, new loss functions and training methods would need to be explored for position sizing – accounting for tradeoffs between risk and reward.

In this paper, we introduce a novel class of hybrid models that combines deep learning-based trading signals with the volatility scaling framework used in time series momentum strategies – which we refer to as the Deep Momentum Networks (DMNs). This improves existing methods from several angles.

Firstly, by using deep neural networks to directly generate trading signals, we remove the need to manually specify both the trend estimator and position sizing methodology – allowing them to be learnt directly using modern time series prediction architectures.

Secondly, by utilising automatic differentiation in existing backpropagation frameworks, we explicitly optimise networks for risk-adjusted performance metrics, i.e. the Sharpe ratio, improving the risk profile of the signal on the whole.

Lastly, retaining a consistent framework with other momentum strategies also allows us to retain desirable attributes from previous works – specifically volatility scaling, which plays a critical role in the positive performance of time series momentum strategies. This consistency also helps when making comparisons to existing methods, and facilitates the interpretation of different components of the overall signal by practitioners.

performance of trading strategies

Referring to the cumulative returns plots for the rescaled portfolios in Exhibit 4, the benefits of direct outputs with Sharpe ratio optimisation can also be observed – with larger cumulative returns observed for linear, MLP and LSTM models compared to the reference benchmarks. Furthermore, we note the general underperformance of models which use standard regression and classification methods for trend estimation – hinting at the difficulties faced in selecting an appropriate position sizing function, and in optimising models to generate positions without accounting for risk."


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Time-Series Momentum Works Everywhere

16.June 2019

It looks that time series momentum is one of the most prevalent effects in finance. Once again, an academic paper shows that it works in every corner of financial markets – in traditional assets, alternative assets and even in long short equity factors …

Authors: Babu, Levine, Ooi, Pedersen, Stamelos

Title: Trends Everywhere

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3386035

Abstract:

We provide new out-of-sample evidence on trend-following investing by studying its performance for 82 securities not previously examined and 16 long-short equity factors. Specifically, we study the performance of time series momentum for emerging market equity index futures, fixed income swaps, emerging market currencies, exotic commodity futures, credit default swap indices, volatility futures, and long-short equity factors. We find that time series momentum has worked across these asset classes and across several trend horizons. We examine the co-movement of trends across asset classes and factors, the performance during different market environments, and discuss the implications for investors.

Notable quotations from the academic research paper:

"Our full data contains 156 assets, of which 58 are the “traditional assets” studied in the literature cited above, 82 are “alternative assets,” meaning futures, forwards, and swaps not previously studied, and 16 are “factors” constructed as long-short equity portfolios. In other words, we collect so much new data that the number of new assets outnumbers the “traditional assets” studied in the literature. While we broaden the universe, we only consider investable liquid assets or strategies.

We find strong evidence for time series momentum across the assets and factors that we study. Over our sample period, the gross Sharpe ratio of 12-month time series momentum for traditional assets is 1.17, and the strategy delivers an even higher Sharpe ratio of 1.34 for the alternative assets. The Sharpe ratio for long-short equity factors is 0.95, and, when we diversify across all three asset groups, the combined trend-following strategy yields a gross Sharpe ratio of 1.60.

Figure 1 reports the t-statistics from the regression, using lags ranging from 1 month to 60 months. Panel A reports the results for traditional assets. The positive t-statistics for the first 12 months indicate return continuation – that is, trends – and t-statistics larger than 2 in magnitude are statistically significant, consistent with earlier findings. For lags above 12 months, we see some negative coefficients, indicating trend reversals, although these tend to be statistically insignificant. Panel B extends the analysis to alternative assets, which also display strong return continuation for the first 12 months, and more mixed returns beyond 12 months. Panel C extends the analysis to equity factor portfolios, showing that time series predictability is feature of more than just traditional and alternative assets, but also of equity factors, with positive t-statistics across the most recent 12 months. These results demonstrate the remarkable pervasiveness of return continuation for the most recent 12 months, but not for returns beyond 12 months, across a range of assets and equity factors.

Traditional assets. Our data for traditional assets are the prices of 58 liquid futures and forwards, consisting of 9 developed equity index futures, 13 developed bond futures, 12 cross-currency forward pairs (from nine underlying currencies), and 24 commodity futures.

t-stat for traditional assets

Alternative assets. Our data for alternative assets consist of prices for 7 emerging market equity index futures, 17 fixed income swaps, 24 emerging market cross currency pairs, 21 commodity futures, 5 credit default swap indices, and 8 volatility futures.

t-stat for alternative assets

Equity factors. For equity factors, our data consist of 16 of the most well-cited and robust single-name stock selection factors

t-stat for factors

"


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