## An Impact of Correlation and Volatility on a Pairs Trading Strategy Thursday, 1 December, 2016

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

#12 - Pairs Trading with Stocks

**Authors: **Riedinger

**Title: **Idiosyncratic Risk, Costly Arbitrage and Asymmetry: Evidence from Pairs Trading

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2833800

**Abstract:**

This paper explains the idiosyncratic risk puzzle in a novel test setting with a combination of arbitrage risk and arbitrage asymmetry as in Stambaugh/Yu/Yuan (2015). We utilize the popular investment strategy pairs trading to identify a different kind of mispricing and find a dominant negative (positive) relationship among overpriced (underpriced) stocks between idiosyncratic volatility and returns in the US stock market between 1990 and 2014. The return rises for higher idiosyncratic risk levels, however not monotonically contrary to related papers. We clarify this issue with a profound analysis of the pairs trading’s algorithm and demonstrate how the technical drivers, volatility and correlation, influence returns. Our findings reveal why pairs trading’s profitability varies across markets, industries, over time, and firm characteristics, and how to improve the trading strategy. Double-sorted portfolios on volatility and correlation earn significant risk-adjusted monthly returns of up to 76bp, which is 43bp more than the traditional portfolio earns.

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

"Our first research proposition claims that higher IVOL increases the total return, similar to findings for other investment strategies8. In terms of IVOL, pairs trading is basically a long-short strategy, which profits from the positive IVOL effect among underpriced stocks, but also from the negative IVOL effect among overpriced stocks. We compute the monthly pairs trading return for different volatility levels. To decide whether bearing IVOL is compensated, we must also consider whether our pairs trading portfolio is diversified. A portfolio, which includes a short and a long position of two highly correlated stocks, is for instance almost perfectly diversified. We therefore not only control for different levels of volatility, but we also control for different levels of pair correlation in the following analyzes. We challenge the traditional selection procedure and form twenty-five double sorted portfolios out of five pair volatility9 (σAB = σA2 + σB2) quintiles and five pair correlation ρAB quintiles. Afterwards, we apply the traditional trading procedure for twenty pairs out of each portfolio and compute monthly returns. Analysis compares the monthly development of a 1$ investment in the traditionally selected portfolio with the performance of two alternatively formed portfolios in January 2011. Both alternative portfolios include highly correlated pairs, however one includes highly volatile pairs whereas the other one includes pairs with low volatility. Both alternative portfolios clearly outperform the traditional portfolio. The cumulative return of the portfolio with highly volatile correlated stocks earns four times more than the traditional SSD portfolio and two times more than a portfolio with less volatile pairs. Overall, we find that twenty out of twenty-five portfolios (risk-adjusted return of 39bp - 209bp) outperform the traditional SSD selected portfolio (37bp). The monthly pairs trading returns are higher for higher levels of volatility. However, it comes as a surprise that not the most volatile stocks earn the highest return, but stocks with a medium to high volatility. The return increase with IVOL is not monotonically in contrast to previous studies, which represents a puzzle that we address in the second part of the paper.

Our second research proposition conjectures that the IVOL effect of overpriced securities dominates. We calculate the short leg return (overpriced stocks) and the long leg return (un-derpriced stocks) for each trade and determine the percentage contribution of the long leg to the total trade return for each volatility level. Consistent with arbitrage asymmetry, our short leg contributes 29% on average more to the total trade return than the long leg among pairs with high IVOL. In contrast, both legs’ contribution is on average equal among low IVOL stocks, which confirms the our research proposition.

We derive three further research propositions from financial and stochastic literature, which we confirm empirically: Firstly, up to 88% of SSD’s variation are explained by pair correla-tion (positive relationship) and pair volatility (negative relationship). Strictly speaking, the traditionally selected pairs with the lowest SSD are highly correlated with little volatility. High correlation and low volatility in turn affect the return per trade and the trading frequen-cy. Secondly, the 2σ-trading rule induces the following relationship: Highly volatile (less vol-atile) pairs and negatively (positively) correlated pairs increase (decrease) the return per trade. Thirdly, low pair volatility and high pair correlation during the identification period, coupled with higher volatility and lower correlation during the trading period, increase the number of trades. Consistent with the theory of mean-reverting volatility, pair volatility increases are more likely for pairs with currently low volatility. Likewise, correlation declines are more likely for highly correlated pairs. Combining these insights, we get the following big picture: The influence of high volatility and negative correlation is positive for the return per trade on the one hand, but at the same time negative for the trading frequency on the other hand. We expect a monotonically increasing return for higher IVOL levels based on the arbitrage risk argument. However, the negative effects of high volatility on the trading frequency and strong correlation on the return per trade reduce the returns for highly volatile and highly correlated stock pairs. In a perfect world, without the influence of the trading rule, we would probably see a linear IVOL effect in pairs trading."

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## A Market Leverage as an Explanation of Low Volatility Anomaly Friday, 25 November, 2016

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

#7 - Volatility Effect in Stocks - Long-Only Version

#77 - Beta Factor in Stocks

#78 - Beta Factor in Country Equity Indexes

**Authors: **Andricopoulos

**Title: **Leverage As A Weapon of Mass Shareholder-Value Destruction; Another Look at the Low-Beta Anomaly

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2859363

**Abstract:**

The 'low-beta' or 'low-volatility anomaly' is one of the most researched in the field of 'alternative beta'. Despite strong published evidence going back to the 1970s that high beta/volatility stocks underperform relative to expectations generated by the Capital Asset Pricing Model (CAPM), the anomaly still persists. The explanations given for this are all behavioural; that investor biases lead to overpricing of high volatility stocks. This paper shows that investor biases cannot be the explanation for the anomaly. Instead, it is proposed that the anomaly stems from a destruction of shareholder value. The strong implication is that the more market leverage a firm has, the more shareholder value is destroyed. Although the prevailing view for a long time has been that adding debt is good for shareholders, making balance sheets more 'efficient', there is in fact a considerable volume of evidence that the opposite is true; evidence which has been incorrectly interpreted for many years. Some possible mechanisms for this shareholder-value destruction are proposed.

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

"There is a large body of evidence that stocks with a low volatility persistently outperform versus stocks with a high volatility on a risk-adjusted basis, and in many cases on an absolute basis. Current explanations focus on behavioral reasons that could lead to mispricings (this will be given the umbrella term, the 'mispricing argument'). For example, it is suggested that mutual fund managers have a bias in favor of high beta stocks. Whilst these may be true; the major contribution of this paper is to show why these arguments cannot explain the phenomenon. The only remaining explanation is that high beta is highly correlated to a future shareholder-value destruction. Some

ways that this could happen are explored.

Empirical data are then also presented which suggests that it is high beta and not high idiosyncratic volatility that leads to this shareholder value destruction. One way of looking at this is to say that companies which outperform based on luck (the market going up) destroy shareholder value relative to those for which any outperformance is based on manager skill.

The signicance of this work is two-fold. From a corporate structure point of view, there has long been the idea that adding debt can make a balance sheet more efficient, and that it is in the interest of shareholders. This finding implies that the opposite is true. Adding leverage, on average, leads to more shareholder value being destroyed. The suggestion here is that the reasons for this are largely to do with manager behavior, but could also have other causes. Despite the low-beta anomaly being known about since the 1970s, the prevailing (behaviorally-driven mispricing) explanations have served, for many years, to hide the damage caused by leverage to shareholder value. From an investment point of view, the implication is that the low-beta anomaly will persist indefinitely; or at least until the causes are discovered and corporate practices are changed to counteract them. If the cause of the anomaly were related to pricing, then the mispricing would no longer exist if enough investors bet against it. If, as this paper shows, it is due to future shareholder value destruction, then there is no reason that low-beta stocks will not continue to out-perform high-beta stocks in the future. Although at times a market-neutral low-beta vs high-beta portfolio can be relatively over-valued or under-valued by market sentiment, in the long term it should always have positive return."

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## What is the Capacity of Smart Beta Strategies ? Wednesday, 16 November, 2016

**An academic paper related to multiple smart beta strategies:**

**Authors: **Ratcliffe, Miranda, Ang

**Title: **Capacity of Smart Beta Strategies: A Transaction Cost Perspective

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2861324

**Abstract:**

Using a transaction cost model, and an assumption for the smart beta premium observed in data, we estimate the capacity of momentum, quality, value, size, minimum volatility, and a multi-factor combination of the first four strategies. Flows into these factor strategies incur transaction costs. For a given trading horizon, we can find the fund size where the associated transaction costs negate the smart beta premium, assuming current rebalancing trends and holding constant other market structure characteristics. With a trading horizon of one day, we find that momentum is the strategy with the smallest assets under management (AUM) capacity of $65 billion, and size is the largest with an AUM capacity of $5 trillion. Extending the trading horizon to five days increases capacity in momentum and size to $320 billion and over $10 trillion, respectively.

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

"We study the capacity, in terms of AUM, of smart beta strategies—momentum, quality, size, value, and minimum volatility. We also study a strategy combining the first four of these factors. All of these smart beta strategies can be implemented with transparent, third-party indices and directly traded as ETFs. The strategies are also long only.

We base our analysis on a transaction cost model developed by BlackRock, Inc. that is used on a daily basis by different investment teams. In line with a sizeable microstructure literature building on Glosten and Harris (1988) and Hasbrouck (1991), the transaction cost model includes both fixed-cost and non-linear market impact components. The parameters of the model are updated on a daily basis, based on trading executed by BlackRock across all of its portfolios. For example, BlackRock traded over $340 billion in US equities during January to March 2016, an indication of the amount of data that is used to calibrate the model. Thus, the transaction cost model gives an estimation that a large asset manager would face in executing trades in ETF securities.

We define capacity as the breakeven hypothetical AUM at which the associated turnover transaction costs exactly offsets the historically observed style premium.6 Since this calculation is sensitive to the assumption of the magnitude of the premium, we present results varying the premiums. A key variable that determines smart beta capacity is the turnover of the factor, and we assume recent rebalancing trends are a good representation of the expected turnover going forward.

The exercise we conduct in this paper is hypothetical and involves several unrealistic assumptions. We assume that all trading takes place in a given interval—over one day, and over a longer horizon of five days. We assume that market structure characteristics of the factor vehicles, like turnover (measured as two-way, annualized), and of the market itself, like no entry and exit of stocks in these strategies, are held fixed as the flows come in. We gauge capacity only by transaction costs incurred by inflows, and so ignore the funding costs of those flows (which could come from other stocks or asset classes). We are not saying the transaction cost estimates are definitive measures of capacity of smart beta strategies—but they are informative in that they measure an important real-world trading friction that reduces returns earned by investors.

As expected, the strategy with the smallest capacity is momentum—the style factor with the highest turnover. Momentum has an estimated breakeven AUM of $65 billion. If trading occurs over one day, we find that the breakeven AUM for size is the largest, at approximately $5 trillion, followed by minimum volatility, which is above $1 trillion. However, if trading is allowed to occur over five days, which is common for larger trades, instead of over one day, the capacity of momentum increases from $65 billion to $324 billion. Finally, the combination of value, size, momentum, and quality factors has an estimated breakeven AUM of $316 billion and $1.5 trillion over trading horizons of one and five days, respectively. In reality, it is likely that many aspects of the markets—including the composition of the stocks in the factor strategies themselves—will change before flows of this magnitude are realized. What is important is the large size of these numbers, rather than the absolute numbers themselves, which indicate that transaction costs have to be very large in order to have a significant effect in reducing returns to investors in smart beta strategies. Put another way, capacity considerations in smart beta are likely to come from economic sources other than trading costs."

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## A Reversal-Based Trading Strategy around Earnings Announcements Wednesday, 2 November, 2016

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

#307 - Reversal During Earnings-Announcements

**Authors: **Jansen, Nikiforov

**Title: **Fear and Greed: a Returns-Based Trading Strategy around Earnings Announcements

**Link:** http://www.wsj.com/public/resources/documents/FearandGreedJPM0922.pdf

**Abstract:**

This study documents that earnings announcements serve as a reality check on short-term, fear and greed driven price development: stocks with extreme abnormal returns in the week before an earnings announcement experience strong price reversal around the announcement. A trading strategy that exploits this reversal is profitable in 40 of the last 42 years and earns abnormal returns in excess of 1.3% over a two day-window.

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

"In this study, we develop a trading strategy around earnings announcements that seeks to profit from predictable reversals of fear and greed driven price development in individual stocks. We argue that earnings announcements are logical events around which to center such a trading strategy, because they convey fundamental information about asset prices and thus have the potential to “break” irrational price development. Moreover, because of heightened information asymmetry in the period just before an earnings announcement, price development is probably particularly susceptible to excessive fear or greed. That is, if uninformed investors observe sharp price changes just before an earnings announcement, they may attribute these to the informed trading of insiders; start to excessively trade in the same direction themselves; and thus cause an overreaction. We therefore predict—in the spirit of Warren Buffett’s advice—that stocks that experience sharp price changes just before an earnings announcement will experience price reversal at the time of the announcement itself. We test this prediction with a trading strategy that on the earnings announcement date takes (1) a long position in stocks that experienced extreme negative abnormal returns in the week prior, and (2) a short position in stocks that experienced extreme positive abnormal returns in the week prior.

We find that, over the two day window of the earnings announcement date and the day following, both positions are highly profitable. On average, the long position earns abnormal returns of 1.49%, and the short position earns 1.20%. We furthermore show that these return reversals are about 60% larger than around non-earnings announcement dates, and thus are significantly more pronounced than short-term return reversals documented in the prior literature. We also show that our strategy (1) is profitable in 40 of the 42 years in our sample; (2) is similarly profitable in “bear” and “bull” markets; (3) and is significantly profitable for both large firms and high volume stocks. Since the year 2000—using a conservative transactions costs estimate of 70 basis points for a round trip trade—we find that our strategy generates abnormal returns of 0.76% after transaction costs, or 95% on an annualized basis. We conclude, therefore, that prices are subject to sentiment-driven price development in the period of elevated information asymmetry just before earnings announcements, and that the announcements themselves serve as a reality check on that price development."

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## Quantopian & Quantpedia Trading Strategy Series: Reversals in the PEAD Friday, 28 October, 2016

Our sucessful __ Quantopian & Quantpedia Trading Strategy Series__ continues with a third article, written by Matthew Lee, focused on Reversal During Post-Earnings Announcement Drift (Strategy #238):

https://www.quantopian.com/posts/quantpedia-trading-strategy-series-reversals-in-the-pead

(Click on a "View Notebook" button to read a complete analysis)

What is the logic behind this strategy? Jonathan A. Milian in his paper "Overreacting to a History of Underreaction" explores the possibility that well known cross sectional anomalies can reverse over time. And he picks the premier anomaly - Post Earnings Announcement Drift. He finds that stocks with the most negative previous earnings surprise actually exhibit the most positive returns very shortly after the subsequent earnings announcement.

The academic paper speculates that it seems that due to well-documented history of investors underreacting to earnings news, investors are now overreacting to earnings announcement news. Investors position themselves in alignment with the expectation of the PEAD effect so when the next earnings announcement comes, the overcrowding of investors pushes the market beyond efficient, resulting in the correction of investor sentiment and a negative correlation for firm's earnings news in the following days. However classical PEAD (post-earnings announcement drift) literature examines mainly quarterly portfolio returns while this academic paper focuses on 2-days retun therefore it is probable that PEAD still holds and both anomalies exists concurrently.

Matthew Lee from Quantopian performed an independed analysis of initial findings of Jonathan A. Milian's original academic paper (over a sample period from 2011 - 2016 compared to the Milian's 2003 - 2010). What Matthew found? Overall, he found his results to be consistent with Milian's results for all strategy's holding periods from 2-10 days. The best result was a hold period of 9 or 10 days following the Earnings Announcement, rather than 2 days. Firms in the highest decile of past earnings surprise underperform stocks in the lowest decile by -1.78% over a hold period of 10 days (compared to -1.59% over a hold period of 3 days found in the paper).

So, what is the trading algorithm?

1. Each day, pick stocks in the S&P500 which have Earnings Announcements the next day

2. Go short on stocks in the highest decile of previous earnings surprise, long on stocks in the lowest decile of previous earnings surprise

3. Hold for a period of 10 days, then close the position

As always, the final OOS equity curve looks really good:

Nice work Matthew!

You may also check first or second article in this series if you liked the current one. And stay tuned for the next ...