An interesting academic paper related to a lot of seasonality strategies, but mainly to:

#7 – Volatility Effect in Stocks – Long-Only Version
#14 – Momentum Effect in Stocks
#26 – Value (Book-to-Market) Anomaly
#229 – Earnings Quality Factor

Authors: de Carvalho, Xiao, Soupe, Dugnolle

Title: Diversify and Purify Factor Premiums in Equity Markets

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2894171

Abstract:

In this paper we consider the question of how to improve the efficacy of strategies designed to capture factor premiums in equity markets and, in particular, from the value, quality, low risk and momentum factors. We consider a number of portfolio construction approaches designed to capture factor premiums with the appropriate levels of risk controls aiming at increasing information ratios. We show that information ratios can be increased by targeting constant volatility over time, hedging market beta and hedging exposures to the size factor, i.e. neutralizing biases in the market capitalization of stocks used in factor strategies. With regards to the neutralization of sector exposures, we find this to be of importance in particular for the value and low risk factors. Finally, we look at the added value of shorting stocks in factor strategies. We find that with few exceptions the contributions to performance from the short leg are inferior to those from the long leg. Thus, long-only strategies can be efficient alternatives to capture these factor premiums. Finally, we find that factor premiums tend to have fatter tails than what could be expected from a Gaussian distribution of returns, but that skewness is not significantly negative in most cases.

Notable quotations from the academic research paper:

"In this paper we show the importance of portfolio construction when it comes to capturing factor premiums efficiently. We first show that the simplest and most traditional approaches to factor investing tend to generate lower risk-adjusted returns because of uncontrolled risk and unwanted exposure to the market index or market capitalization biases. We show that strategies that target constant volatility and hedge the market beta and exposure to size deliver higher information ratios. This is in particular due to a reduction in volatility.

We also show the importance of removing sector exposure as an additional source of risk without return in factor investing. And we explain why long only factor investing can rather efficiently capture factor premiums, in particular from the low risk and momentum factors. Additionally, we demonstrate the importance of diversifying factors in each style thanks to the decorrelation of factor returns even within the same style.

Finally, we show that factor premiums tend to exhibit fat tails, but also a relatively small skewness.

Overall, we defend the importance of purifying and diversifying factor exposures in factor investing as one way of significantly improving risk-adjusted returns from factor strategies. And although this causes turnover to increase due to the need for additional trades, we highlight the fact that most of the benefits shown in this paper can be captured in practice by using clever approaches to contain turnover."

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An interesting academic paper related to a lot of seasonality strategies, but mainly to:

#125 – 12 Month Cycle in Cross-Section of Stocks Returns

Authors: Hirschleifer, Jiang, Meng

Title: Mood Beta and Seasonalities in Stock Returns

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2880257

Abstract:

Existing research has documented cross-sectional seasonality of stock returns – the periodic outperformance of certain stocks relative to others during the same calendar month, weekday, or pre-holiday periods. A model based on the differential sensitivity of stocks to investor mood explains these effects and implies a new set of seasonal patterns. We find that relative performance across stocks during positive mood periods (e.g., January, Friday, the best-return month realized in the year, the best-return day realized in a week, pre-holiday) tends to persist in future periods with congruent mood (e.g., January, Friday, pre-holiday), and to reverse in periods with non-congruent mood (e.g., October, Monday, post-holiday). Stocks with higher mood betas estimated during seasonal windows of strong moods (e.g., January/October, Monday/Friday, or pre-holidays) earn higher expected returns during future positive mood seasons but lower expected returns during future negative mood seasons.

Notable quotations from the academic research paper:

"We propose here a theory based on investor mood to offer an integrated explanation for known seasonalities at both the aggregate and cross-sectional levels, and to offer new empirical implications which we also test. In our model, investor positive (negative) mood swings cause periodic optimism (pessimism) in evaluating signals about assets’ systematic and idiosyncratic payoff components. This results in seasonal variation in mispricing and return predictability.

Consistent with the model predictions, we uncover a set of new cross-sectional return seasonalities based on the idea that stocks that have been highly sensitive to seasonal mood fluctuations in the past will also be sensitive in the future. In other words, we argue that some stocks have higher sensitivities to mood changes (higher mood betas) than others, which creates a linkage between mood-driven aggregate seasonalities and seasonalities in the cross-section of returns. In particular, we argue that investor mood varies systematically across calendar months, weekdays, and holidays. In consequence, a mood beta estimated using security returns in seasons with mood changes helps to predict future seasonal returns in other periods in which mood is expected to change.

During our sample period 1963-2015. the average stock excess return (measured by CRSP equal-weighted index return minus the riskfree rate) is highest in January and lowest in October. Thus, we focus on January as a proxy for an investor high-mood state and October for a low-mood state. Using Fama-MacBeth regressions, we verify the finding of Heston and Sadka (2008) for January and October—historical January (October) relative performance tends to persist in future January (October) for the following ten or more years. In our interpretation, stocks that do better than others during one month will tend to do better again in the same month in the future because there is a congruent mood at that time.

Furthermore, we find a new reversal effect that crosses months with incongruent moods; historical January (October) returns in the cross section tends to significantly reverse in subsequent Octobers (Januaries). A stock that did better than other stocks last January tends to do worse than other stocks in October for the next five years or so. A one-standard-deviation increase in the historical congruent (incongruent)-calendar-month leads an average 23% increase (17% decrease) in the next ten years, relative to the mean January/October returns.

Our explanation for these effects is not specific to the monthly frequency. A useful way to challenge our theory is therefore to test for comparable cross-sectional seasonalities at other frequencies. Moving to the domain of daily returns, we document a similar set of congruent/incongruent-mood-weekday return persistence and reversal effects.

We confirm this return persistence effect for Monday and Friday returns, and then show, analogous to the monthly results, that a congruent-mood-weekday return persistence effect applies: relative performance across stocks on the best-market-return (worst-market-return) day realized in a week tends to persist on subsequent ten Fridays (Mondays) and beyond, when good (bad) market performance is expected to continue. A one-standard-deviation increase in historical congruent-weekday or congruent-mood-weekday return is associated an average with a 4% or 12% higher return in the subsequent ten Mondays/Fridays.

At the level of individual stocks, there is pre-holiday cross-sectional seasonality, wherein stocks that historically have earned higher pre-holiday returns on average earn higher pre-holiday returns for the same holiday over the next ten years.

The cross-sectional return persistence and reversal effects across months, weekdays, and holidays are overall consistent with our theoretical predictions that investors’ seasonal mood fluctuations cause seasonal misperceptions about factor and firm-specific payoffs and lead to cross-sectional return seasonalities. These predictions are based on the idea that different stocks have different mood beta—a stock’s return sensitivity to factor mispricing induced by mood shocks. We argue that the concept of mood beta integrates various seasonality effects. We therefore perform more direct tests of the model prediction that mood betas will help forecast the relative performance of the stocks in seasons with different moods."

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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:

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 …

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 differ 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 affect 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 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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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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