Quantopian & Quantpedia Trading Strategy Series: Cross-Sectional Equity Mean Reversion Thursday, 29 December, 2016

Quantopian & Quantpedia Trading Strategy Series continues ... Now with a 4th article, again written by Matthew Lee, focused on Cross-Sectional Equity Mean Reversion (Strategy #13):

https://www.quantopian.com/posts/quantpedia-trading-strategy-series-an-analysis-on-cross-sectional-mean-reversion-strategies

Cross-sectional mean reversion in stocks (strong tendency of stocks with strong gains/losses to reverse in a short-term time frame - up to one month) is a well-known market observation and the main reason why so many academic researchers generally use a 2-12 momentum measurement (returns over the past 12 months, excluding the previous one) when examining momentum anomaly. Many academic papers examined this effect, the most notable are papers by Jagadesh, and Bruce Lehmann (see "Other papers" section on Quantpedia subpage for this reversal strategy for additional academic research papers). The most academics speculate that the fundamental reasons for the anomaly are market-microstructure frictions (bid-ask bounce) or investors' cognitive biases - overreaction to past information and a correction of that reaction after a short time horizon.

But is this simple equity strategy still profitable?

Matthew Lee from Quantopian performed an independed analysis during an out of sample period from 12-01-2011 to 12-01-2016. Overall, the performance of simple short-term equity reversal strategy is below the market. But, it's to be noted that this strategy is long/short compared to just long-only equity benchmark (which is the SPY). So if we want to compare total performance of that strategy, we should compare long only reversal of the "loser stocks decile". Long/short equity reversal strategy has a Sharpe ratio 0.84 and Beta of 0.15. Sharpe ratio of long/short version is comparable to market portfolio and a low correlation of equity reversal strategy makes it a possible addon to investment portfolio.

However ... Reversal strategy is very active (weekly, bi-weekly rebalancing) which means high transaction costs and slippage. So really high caution should be paid in a real-world implementation and steps which tries to limit strategy's turnover should be taken.

The final OOS equity curve:

Strategy's performance

Thanks for the analysis Matthew!

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

An Effect of Monetary Conditions on Carry Trades Thursday, 22 December, 2016

A related paper to:

#5 - FX Carry Trade

Authors: Falconio

Title: Carry Trades and Monetary Conditions

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2854134

Abstract:

This paper investigates the relation between monetary conditions and the excess returns arising from an investment strategy that consists of borrowing low-interest rate currencies and investing in currencies with high interest rates, so-called "carry trade". The results indicate that carry trade average excess return, Sharpe ratio and 5% quantile differ substantially across expansive and restrictive conventional monetary policy before the onset of the recent financial crisis. By contrast, the considered parameters are not affected by unconventional monetary policy during the financial crisis.

Notable quotations from the academic research paper:

"My main result is that carry trade portfolio average return, Sharpe ratio and 5% quantile di ffer substantially across expansive and restrictive conventional monetary policy before the onset of the recent financial crisis. Speci fically, I find that expansive periods are characterised by signi cantly higher average returns and Sharpe ratios and lower downside risk. Concerning this, I argue that expansive conventional monetary policy is able to improve market expectations across countries and in this way lower FX volatility risk. This generates a currency appreciation for net debtor nations and an increase in carry trade pro fits.

Second, I present evidence suggesting that the considered parameters are similar across aggressive and stabilising unconventional monetary policy during the recent financial crisis. So, the Federal Reserve could not a ffect market expectations during this time.

For investors, this evidence suggests that rewards from carry trade vary with changes in monetary conditions only during "normal" times. For researchers, this evidence suggests that recognising the relevance of monetary policy is crucial to understanding the pricing implications of FX volatility risk for carry trade."


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An Interesting Analysis of Shiller's CAPE Ratio Saturday, 17 December, 2016

An interesting new academic paper related to an actual issue - a high valuation of us equities:

Authors: Dimitrov, Jain

Title: Shiller's CAPE: Market Timing and Risk

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2876644

Abstract:

Robert Shiller shows that Cyclically Adjusted Price to Earnings Ratio (CAPE) is strongly associated with future long-term stock returns. This result has often been interpreted as evidence of market inefficiency. We present two findings that are contrary to such an interpretation. First, if markets are efficient, returns on average, even when conditional on CAPE, should be higher than the risk-free rate. We find that even when CAPE is in its ninth decile, future 10-year stock returns, on average, are higher than future returns on 10-year Treasurys. Thus, the results are largely consistent with market efficiency. Only when CAPE is very high, say, CAPE is in the upper half of the tenth decile (CAPE higher than 27.6), future 10-year stock returns, on average, are lower than those on 10-year U.S. Treasurys. Second, we provide a risk-based explanation for the association between CAPE and future stock returns. We find that CAPE and future stock returns are positively associated with future stock market volatility. Overall, CAPE levels do not seem to reflect market inefficiency and do reflect risk (volatility).

Notable quotations from the academic research paper:

"Among various market valuation indicators proposed over the history of the stock market, one of the most popular ones is Robert Shiller’s Cyclically Adjusted Price to Earnings Ratio (CAPE). CAPE is defined as the current price of the S&P 500 index divided by the S&P 500 index’s ten-year average inflation-adjusted earnings. John Campbell and Robert Shiller have analyzed the relationship between CAPE and future stock returns in a series of articles. They show that future 10-year stock returns on the S&P 500 index are negatively associated with CAPE. Shiller (1996, p. 2) concludes that “…the association seems so strong as to suggest that this relation is not consistent with the efficient markets or random walk model.” In contrast, proponents of market efficiency argue that this evidence is consistent with “rational swings in expected returns” (Fama). The debate continues unabated to this day and interest in understanding CAPE remains high.

In this paper, we present two sets of analyses to shed light on this ongoing debate on market efficiency. First, if markets are efficient, knowing CAPE should not help investors earn superior future returns by selling (buying) stocks and buying (selling) a risk-free asset when CAPE is high (low). In other words, market timing strategies using CAPE should not be profitable. However, we are not aware of any formal tests of such strategies. We find that with the exception of the periods when CAPE is in the upper half of its 10th decile (CAPE higher than 27.6), on average, it is not beneficial to time the market. For the most part, investors cannot profit from the evidence that CAPE is associated with future 10-year stock returns. Second, if markets are efficient, CAPE (and future stock market returns) should be associated with overall risk in the stock market. We test this hypothesis by analyzing the association between CAPE (and future stock market returns) and future stock return volatility (risk). We find that CAPE (and 10-year future stock returns) is associated with future 10-year volatility of stock returns. Thus, risk as measured by volatility seems to be a potential explanation for CAPE-based patterns in stock returns. Overall, the ability of CAPE to forecast future stock market returns appears consistent with a positive association between risk and returns. It does not seem to imply that markets are inefficient."


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Sources of Return for CTAs - A Brief Survey of Relevant Research Friday, 9 December, 2016

A related paper has been added to:

#118 - Time Series Momentum Effect

Authors: Till

Title: What are the Sources of Return for CTAs and Commodity Indices? A Brief Survey of Relevant Research

Link: 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.

Notable quotations from the academic research paper:

"In the academic literature, one can find strong evidence – historically at least – for there being persistent returns in futures programs due to momentum, roll yield, and also due to rebalancing. This is actually the case across asset classes, and not just for commodity futures contracts.

The AQR authors theorised that “price trends exist in part due to long-standing behavioural biases exhibited by investors, such as anchoring and herding, as well as the trading activity of  non-profit seeking participants, such as  central banks and corporate hedging programs.” Assuming these factors continue, the long-term profitability from momentum strategies might also continue, and not just be a matter of history.

“However, the ... strategy also exposed investors to large losses ... during both [historical] periods,” noted the Federal Reserve Bank of Chicago paper (Chabot et al. (2014)).  Interestingly,  “[m]omentum  ...  [losses]  were [apparently]  predictable”.  In  both  historical  periods,  losses  were  “more  likely  when  momentum recently performed well.” For the 1867 to 1907 period, losses were more likely when “interest rates were relatively low.” And for the 1927 to 2012 period, losses were more likely when “momentum had recently outperformed the stock market”. Each of these periods were “times when borrowing or attracting return chasing  ‘blind  capital’  would  have been  easier.”  The authors argue that the periodic large losses, associated with the strategy plausibly becoming too popular, “play an important role in sustaining” the momentum strategy’s historical returns.

In  addition to momentum,  the empirical literature also documents that “roll yield” can be considered a structural source of return, at least over long periods of time. For example, Campbell & Company  (2013) described a proprietary trend-following benchmark, in which they calculated returns from 1972 through November 2012, and which included a selection of equity, fixed income, foreign exchange, and commodity markets. Over this 40-year period, approximately half of the benchmark’s cumulative performance was due to spot return, and the other half was due to roll yield. Over long horizons, the roll yield is important mainly for commodity futures contracts. This is because of another structural feature of commodity markets: mean reversion. If a commodity has a tendency over long enough timeframes to mean-revert, then by construction, returns cannot be due to a long-term appreciation (or depreciation) in spot prices. In that case, over  a  sufficient time frame, the futures-only return for a futures contract would have to basically collapse to its roll yield. Can we observe this historically in commodity futures markets? The  answer is essentially yes.

The mean-reversion of commodity prices can also have meaningful consequences for returns at the portfolio- or index-level. Specifically, this feature is at the root of an additional source of return, quite separate from trends in spot prices or the potential persistence of curve-structure effects. That potential additional source of return is the return from rebalancing. Erb and Harvey (2006) discussed how there can be meaningful returns from rebalancing a  portfolio of lowly-correlated, high-variance instruments. The rebalancing effect was explained Greer et al. (2014), as follows: “[A] ‘rebalancing return’ ... can naturally accrue from periodically resetting a portfolio of assets back to its strategic weights, causing the investor to sell assets that have gone up in value and buy assets that have declined.”

One caveat is that one’s holding period may have to be quite long term in order for these return effects to be apparent. However, even structurally positive returns may be insufficient to motivate investors to consider futures products. A CTA (or global macro) investor may require that the program’s return profile is also long-options-like; and an institutional investor will expect that a commodity index will provide diversification for a stock-and-bond portfolio. The paper also noted that how these programs are benchmarked will depend on whether a futures program is considered a beta, an alternative beta, pure alpha, or well-timed beta. This paper correspondingly provided recommendations for benchmarks for each of these types of investment exposures."


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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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