**A related paper has been added to:**

#12 - Pairs Trading with Stocks

**Authors: **Mazo, Lafuente, Gimeno

**Title: **Pairs Trading Strategy and Idiosyncratic Risk. Evidence in Spain and Europe.

**Link:** http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2807956

**Abstract:**

Pairs trading strategy’s return depends on the divergence/convergence movements of a selected pair of stocks’ prices. However, if the stable long term relationship of the stocks changes, price will not converge and the trade opened after divergence will close with losses. We propose a new model that, including companies’ fundamental variables that measure idiosyncratic factors, anticipates the changes in this relationship and rejects those trades triggered by a divergence produced by fundamental changes in one of the companies. The model is tested on European stocks and the results obtained outperform those of the base distance model.

**Notable quotations from the academic research paper:**

"The purpose of this research is to propose a pairs trading model that increases return compared to the model of distance (Gatev et al., 2006). We will introduce some rules in the model, based on fundamental variables, so that persistent divergence in the relationship of the prices of the two selected stocks could be foreseen. When we analyze the results of the distance method in previous works, we found that the number of trades with losses was high and the increase of such trades was one of the reasons of the decline of pairs trading strategy return.

Depending on the reason why a divergence on a stock price pair leads to execute the trade, it will be more or less likely that the stock price pair will convergence again. Thus, if the stock price pair divergence is due to irrational investors that leads to liquidity tensions, later convergence is likely to happen. However, if the reason of such divergence is new information about the companies’ fundamentals, divergence is likely to remain and there will be another equivalence relation between both stocks (Andrade et al., 2005). This is the starting point of this paper: beginning from the basic model of distance, we test which variables related to companies’ performance could anticipated if divergence is temporal or permanent.

The variables we use in the model are selected from analysts’ consensus. The data are obtained from FactSet, a financial information provider. The reason to choose the values provided by analysts’ consensus is that they consider the implicit information in analysts’ recommendations that follow a certain stock.

The variables considered in the model are:

a) Earnings per Share in the next 12 months. (EPS).

b) Book Value per Share (BVPS).

c) Target Price (TP).

d) Recommendation.

e) Knowledge of the firm, measured as the number of estimations of each stock.

Empirical analysis of the proposed model confirms the hypothesis of the paper: including in the model variables that represent idiosyncratic risk of a firm outperforms basic pairs trading strategy (distance model). In fact, adding ES, BVPS and TP variables leads to better returns in the analyzed portfolios of IBEX 35 index, Euro Stoxx 50 index and Stoxx Europe 50 Index."

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**The most of the risk premiums are better explained by tail-risk skewness (compared to volatility)... Related to multiple strategies.**

**Authors: **Lemperiere, Deremble, Nguyen, Seager, Potters, Bouchaud

**Title: **Risk Premia: Asymmetric Tail Risks and Excess Returns

**Link:** http://arxiv.org/pdf/1409.7720v3.pdf

**Abstract:**

We present extensive evidence that ``risk premium'' is strongly correlated with tail-risk skewness but very little with volatility. We introduce a new, intuitive definition of skewness and elicit an approximately linear relation between the Sharpe ratio of various risk premium strategies (Equity, Fama-French, FX Carry, Short Vol, Bonds, Credit) and their negative skewness. We find a clear exception to this rule: trend following has both positive skewness and positive excess returns. This is also true, albeit less markedly, of the Fama-French ``Value'' factor and of the ``Low Volatility'' strategy. This suggests that some strategies are not risk premia but genuine market anomalies. Based on our results, we propose an objective criterion to assess the quality of a risk-premium portfolio.

**Notable quotations from the academic research paper:**

"Classical theories identify risk with volatility σ. This (partly) comes from the standard assumption of a Gaussian distribution for asset returns, which is entirely characterised by its first two moments: mean μ and variance σ^2. But in fact fluctuations are known to be strongly non Gaussian, and investors are arguably not much concerned by small fluctuations around the mean. Rather, they fear large negative drops of their wealth, induced by rare, but plausible crashes. These negative events are not captured by the r.m.s. σ but rather contribute to the negative skewness of the distribution. Therefore, an alternative idea that has progressively emerged in the literature is that a large contribution to the “risk premium” is in fact a compensation for holding an asset that provides positive average returns but may occasionally erase a large fraction of the accumulated gains.

Our work is clearly in the wake of the above mentioned literature on skewness preferences and tail-risk aversion. We will present extensive evidence that “risk premium” is indeed strongly correlated with the skewness of a strategy but very little with its volatility, not only in the equity world – as was emphasised by previous authors – but in other sectors as well. We will investigate in detail many classical so-called “risk premium” strategies (in equities, bonds, currencies, options and credit) and elicit a linear relation between the Sharpe ratio of these strategies and their negative skewness. We will find however that some well-known strategies, such as trend following and to a lesser extent the Fama-French “High minus Low” factor and the “Low Vol” strategy, are clearly not following this rule, suggesting that these strategies are not risk premia but genuine market anomalies.

Compared to the previous abundant literature, the present results are new in different respects. First, at variance with most previous investigations (that mostly focusses on stock markets), we do not attempt to frame our empirical analysis within the constraining framework of asset pricing and portfolio theory, but rather let the data speak for itself. This is specially important when studying, as we do here, risk premia across a much larger universe of assets, where the notion of a global “risk factor” (generalizing the market factor in the equity space) is far from clear. Second, we introduce a simple way to plot the returns of a portfolio that reveals its skewness to the “naked eye” and suggests an intuitive and robust definition of skewness that is much less sensitive to extreme events. Third, our empirical conclusion that for a wide spectrum of “risk premia” strategies, skewness rather than volatility is a determinant of returns is, to the best of our knowledge, new, as is the finding that some investment strategies – like trend following – seem to behave quite differently.

We first start in Sect. 2 with the equity market as a whole and revisit the equity risk premium world-wide, and its (negative) correlation with the volatility. We then introduce our new, intuitive definition of skewness that we use throughout the paper and that we justify in the Appendix. We focus on the Fama-French factors in Sect. 3 and study the statistics of market neutral portfolios, including a “Low Volatility” portfolio. We move on to the fixed income world (Sect. 4), where we again build neutral portfolios. Sect. 5 is devoted to an account of risk premia on currencies (the so-called “Carry Trade”), and finally, in Sect. 6, to the paradigmatic case of selling options. We summarise our findings in Sect. 7 with a suggestive linear relation between the Sharpe ratio and the skewness of all the Risk Premium strategies investigated in the paper, and discuss some exceptions to the rule – i.e. positive Sharpe strategies with zero or positive skewness – that we define as “pure α strategies". "

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**Explanatory research paper for all short term contrarian strategies:**

**Title: **Black Monday, Globalization and Trading Behavior of Stock Investors

**Author: **Kim

**Link:** http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2798536

**Abstract:**

Using a simple sign test, we report new empirical evidence, taken from both the US and the German stock markets, showing that trading behavior substantially changed around Black Monday in 1987. It turned out that before Black Monday investors behaved more as in the momentum strategy; and after Black Monday more as in the contrarian strategy. We argue that crashes, in general, themselves are merely a manifestation of uncertainty on stock markets and the high uncertainty due to globalization is mainly responsible for this change.

**Notable quotations from the academic research paper:**

"Research question:

The paper tests whether systematic trading behaviors on stock markets have changed over the long-term. In doing so, the two different trading strategies, momentum and contrarian, serve as the systematic trading strategies. For the empirical part, the daily returns of two sets of stock market data (Deutscher Aktienindex and Dow Jones Index) since 1959 are used. The focus of the analysis is on the distributional property of increases and decreases in returns, especially sequences of the sign. The empirical probability of sequences of the sign is tested by the theoretical distribution resulting from the assumption of the martingale process of return series implying absence of systematic trading strategies.

Results:

The empirical results show that the probabilities of sequences of the same sign (both positive and negative) before Black Monday are significantly higher than those of the theoretical distribution. This means that the investors preferred the momentum strategy. After Black Monday, however, the probabilities of sequences of the same sign are significantly lower than those of theoretical distribution. This means that the investors are tending to trade according to the contrarian strategy.

Table 2 shows the following:

• Results for the DJ

– Before Black Monday, the empirical probabilities of sequences of the same sign for both the positive and negative signs (as given in the second and fifth rows of the first block in the upper panel) are significantly higher than those of the theoretical values (as given in the first and fourth rows of the first block in the upper panel) for all six cases (i.e. two-day to seven-day sequences) for both the DJ and the DAX. The percentage values of the cumulative binomial distribution, evaluated at the number of the corresponding sequences, are equal to or higher than 99% except in one case, namely the seven-day negative sequence (98%).

– After Black Monday, the empirical probabilities of sequences of the same sign for both the positive and negative signs (as given in the second and fifth rows of the second block in the upper panel) are significantly lower than those of the theoretical values (as given in the first and fourth rows of the first block in the upper panel) for all six cases (i.e. two-day to seven-day sequences). The percentage values of the cumulative binomial distribution, evaluated at the number of the corresponding sequences, are equal to or lower than 1% except in two cases, namely the one-day positive sequence (8%) and the oneday negative sequence (6%).

• Results for the DAX

– Before Black Monday, the results for the DAX are almost the same as those of the DJ up to a small difference (no meaning to the main results) in the six-day positive sequence and seven-day negative sequence.

– After Black Monday, the empirical numbers of sequences of the same sign for both the positive and negative signs (as given in the second and fifth rows of the second block in the lower panel) are smaller than those of the theoretical values (as given in the first and fourth rows of the first block in the lower panel). The empirical probabilities in terms of the p-values for the positive sign sequences are weaker than the DJ with a range of significance level from 11% to 39%. The negative sign sequences are still highly significant up to the one-day negative sequence (30%).

From these empirical results, we could draw the conclusion that Black Monday has changed trading behavior on stock markets. Before Black Monday, investors tended to buy when the stock return was positive and to sell when the stock return was negative (a day-to-day momentum strategy) while after Black Monday they tended to buy when the stock return was negative and to sell when the stock return was positive (a day-to-day contrarian strategy)."

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We are really excited that we can announce, that Quantopian started to publish series of articles where they will really deeply analyze some of Quantpedia's suggested strategies.

We think, that Soeng Lee from Quantopian did a really good job with a first article, so we just wanted to point that article to you as something interesting to read for people with an interest in "quant trading". Click on a "View Notebook" button to read a complete analysis:

https://www.quantopian.com/posts/quantpedia-trading-strategy-series-are-earnings-predictable

First article analyses strategy #271 - Earnings Announcements Combined with Stock Repurchases. Quantopian's analysis confirms initial findings of Amini & Singal academic paper:

Earnings are a highly studied event with much of the alpha in traditional earnings strategies squeezed out. However, the research here suggests that there is some level of predictability surrounding earnings and corporate actions (Buyback announcements). In order to validate the authors' research, Soeng Lee from Quantopian attempts an OOS implementation of the methods used in the Amini&Singal whitepaper. He examines share buybacks and earnings announcements from 2011 till 2016 finding similar results to the authors with positive returns of 1.115% in a (-10, +15) day window surrounding earnings. The results hold true for different time windows (0, +15) and sample selection criteria.

Soeng finds the highest positive returns for earnings that are (5, 15) days after a buyback announcement (abnormal returns of __2.67%__). Also, the main study by Amini&Singal was focused on buybacks greater than 5%. However, the robustness test that included all buybacks appears to outperform the main study. The test looking at buybacks 1 ~ 30 days before an earnings announcement also performed better than the 16 ~ 31 days criteria (as suggested in Amini&Singal) with a greater sample size.

The final Quantopian OOS equity curve looks really promising:

This Quantopian's analysis is the first of the longer series of articles. We are already looking forward to the next one ...

**A related paper has been added to:**

#14 - Momentum Effect in Stocks

**Authors: **Bhattacharya, Li, Sonaer

**Title: **Has Momentum Lost Its Momentum?

**Link:** http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2791138

**Abstract:**

We evaluate the robustness of momentum returns in the US stock market over the period 1965 to 2012. We find that momentum profits have become insignificant since the late 1990s partially driven by pronounced increase in the volatility of momentum profits in the last 14 years. Investigations of momentum profits in high and low volatility months address the concerns about unprecedented levels of market volatility in this period rendering momentum strategy unprofitable. Past returns, can no longer explain the cross-sectional variation in stock returns, even following up markets. Investigation of post holding period returns of momentum portfolios and risk adjusted buy and hold returns of stocks in momentum suggests that investors possibly recognize that momentum strategy is profitable and trade in ways that arbitrage away such profits. These findings are partially consistent with Schwert (2003) that documents two primary reasons for the disappearance of an anomaly in the behavior of asset prices, first, sample selection bias, and second, uncovering of anomaly by investors who trade in the assets to arbitrage it away. In further analyses we find evidence that suggest three possible explanations for the declining momentum profits that involve uncovering of the anomaly by investors, decline in the risk premium on a macroeconomic factor, growth rate in industrial production in particular and relative improvement in market efficiency.

**Notable quotations from the academic research paper:**

"In this paper, we investigate whether momentum profits have been driven away or at the very least its pattern altered in the wake of growing knowledge about momentum strategy and competition amongst arbitrageurs who trade on it, if we were to believe momentum profits were caused in the first place due to delayed price reactions to firm-specific information as suggested by Jegadeesh and Titman (1993, 2001).

Our analyses span over the period between 1965 and 2012. We divide the entire time period into three subperiods. The first subperiod corresponds to the Jegadeesh and Titman (1993) sample period, 1965 to 1989, the second subperiod covers the Jegadeesh and Titman (2001) “out of sample period”, 1990 to 1998, the third subperiod corresponds to the period 1999 to 2012. In our study, we choose to examine the persistence of momentum profits while avoiding concerns of data dredging by conducting tests in our out-of-sample period that starts at the beginning of 1999 immediately after Jegadeesh and Titman’s (2001) “out of sample period” ends. Using the data over the 1999 to 2012 sample period, we find that Jegadeesh and Titman (1993) momentum strategies fail to yield profits in the more recent times. This period is particularly interesting as it witnessed the dot-com bust after catching the boom by its tail and also the financial crisis followed by the greatest stock market meltdown since the great depression. One of our concerns in dealing with this unique period is what if the recent turbulence in the economy with a series of high-loss episodes in the US stock market and unprecedented levels of market volatility has rendered momentum strategy unprofitable?

We employ alternate methodologies to scrutinize whether the rapid decline of momentum profits to insignificant levels in this 14 year period is indeed an outcome of the marked rise in market volatility. For instance, we use controls for the periods of unusual volatilities in the capital market, 2007 to 2009 in particular and yet fail to reject the hypothesis that momentum profits have not declined to insignificant levels. Excluding the last financial crisis, 2007 to 2009 serves the additional purpose of excluding spring of 2009 that witnessed the biggest momentum crash in the history of stock market since the summer of 1932 as alluded to by Daniel and Moskowitz (2012). Next, we employ the daily median volatility index, VXO for the period 1986 to 1998 to classify months in the latest subperiod into high and low expected volatility months.5 If momentum profits have declined because of increased volatility of the market, momentum strategy should be profitable at least in months when the implied volatility is as low as in low volatility months in the period 1986 to1998, a period when momentum is profitable. However, what we document is that while momentum strategy is profitable in the period 1986 to 1998 no matter the implied volatility, it fails to generate profit for the period 1999 to 2012 even in the 60 months classified as low volatility months primarily clustered between November 2003 and July 2007.

We also investigate whether momentum profits resurface in this period following up markets as documented by Cooper, Gutierezz and Hameed (2004). Not only are these momentum profits insignificant on average following up markets, their distribution also reveal visible and statistical difference from those in the periods 1965 to 1989 and 1990 to 1998, indicating a deeper and more fundamental change in the underlying process of generation of momentum profits, beyond huge market crashes. The distribution of up market momentum profits in this period is extremely volatile interspersed with huge negative returns that suggest that momentum as a strategy has become riskier in the latest subperiod compared to the two earlier subperiods. Further analysis indicates that the idiosyncratic volatility of momentum portfolio returns has increased compared to the previous periods. We also examine whether cumulative past returns can explain the cross-sectional variation in stock returns. In the presence of return continuation, we expect past stock returns to be positively related to current stock returns, especially following up markets since momentum profits are essentially up market phenomena. As expected in the periods 1965 to 1989 and 1990 to 1998, current stocks returns are positively related to past returns exclusively following up markets. However, in the current subperiod, with decline in momentum profits past returns fail to explain current returns following up markets and show a reliably negative relation following down market.

We suggest three possible explanations for the declining momentum profits that involve uncovering of the anomaly by investors, decline in the risk premium on a macroeconomic factor, growth rate in industrial production in particular, and relative improvement in market efficiency.

The first explanation proposes that momentum profits decline post 1998 because investors become increasingly aware about the profitability of implementing a relatively simple momentum trading strategy, wherein they identify winner (loser) stocks and buy (sell) them. The growing awareness and competition amongst these investors would lead to an increasingly earlier identification and trading of momentum stocks. This explanation predicts intensified reaction to both winner and loser stocks in the identification period itself, which would result in either exhaustion or, at the least, a substantial reduction in return continuation in the holding period.6 We find evidence consistent with this prediction.

The second explanation is based on the findings of Liu and Zhang (2008) who document that growth rate of industrial production, in various specifications, explains over half of the momentum profits. We find that in the latest subperiod although the momentum portfolio’s returns continue to load on this industrial production factor, this particular risk factor is no longer priced.

The third explanation explores the possibility of relative improvement in market efficiency. Following Griffin, Kelley, and Nardari (2010), we compute their DELAY measure, that reflects the degree of response of stock returns to past market returns, and we record a fairly significant reduction in delay in all size portfolios but for the largest one."

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