Once again, our favorite type of study – an out of sample research study based on data from 19th and beginning of 20th century.  Interesting research paper related to all equity momentum strategies …

Authors: Trigilia, Wang

Title: Momentum, Echo and Predictability: Evidence from the London Stock Exchange (1820-1930)

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3373164

Abstract:

We study momentum and its predictability within equities listed at the London Stock Exchange (1820-1930). At the time, this was the largest and most liquid stock market and it was thinly regulated, making for a good laboratory to perform out-of-sample tests. Cross-sectionally, we find that the size and market factors are highly profitable, while long-term reversals are not. Momentum is the most profitable and volatile factor. Its returns resemble an echo: they are high in long-term formation portfolios, and vanish in short-term ones. We uncover momentum in dividends as well. When controlling for dividend momentum, price momentum loses significance and profitability. In the time-series, despite the presence of a few momentum crashes, dynamically hedged portfolios do not improve the performance of static momentum. We conclude that momentum returns are not predictable in our sample, which casts some doubt on the success of dynamic hedging strategies.

Notable quotations from the academic research paper:

"This paper studies momentum and its predictability in the context of the rst modern stock market, the London Stock Exchange (LSE), from the 1820s to the 1920s.

Factors' performance. Compared to the U.S. post-1926, we find that the market has been less profitable – averaging 5% annually (but also less volatile). Its Sharpe ratio has been 0.34, not too far from the 0.43 of CRSP. The Small-Minus-Big (SMB) factor delivered a 4.85% average annual return, much higher than that found in U.S. post-1926. The risk-free rate, as proxied by the interest on British Government's consols, has been close to 3.3% throughout the period, despite the many large changes in supply (i.e., in the outstanding stock of public debt). As for momentum (UMD), consistent with the existing evidence it has been the most profitable factor – with an average annual return close to 9% – and the most volatile – with 20% annual standard deviation.

Dissecting momentum returns. Recent literature debates whether momentum is long or short term. In our sample, UMD profits strongly depend on the formation period: they average at 10.6% annually for long-term formation (12 to 7 months) and 3.8% for short-term formation (6 to 2 months). So, our out-of-sample test confirms that momentum is better described as a within-year echo.

To investigate the role of fundamentals as drivers of price momentum, we construct two sets of earnings momentum portfolio. The first earnings momentum portfolio is constructed based on the past dividend paid by the firm relative to its market cap. The portfolio buys stocks of the highest dividend-paying firms over a 12 to 2 months formation period, and shorts the stocks of the lowest ones. We find strong evidence that our dividend momentum (DIV) strategy is profitable across our sample: it yields a 5% average annual return with a standard deviation of 12%.

The second earnings momentum portfolio is constructed based on the dividend innovations. Specically, we look at the change of dividend year to year, and construct the DIV portfolio. The portfolio buys stocks with the highest change in dividend paid and shorts the stocks with the lowest ones. The
DIV portfolio yield an over 24% return with a standard deviation of only 13.2%.

To discern whether price momentum seems driven by dividend momentum, we also test whether the alpha of the static UMD portfolio remains significant and positive after we control for the Fama-French three factors plus the dividend momentum portfolio. In the EW sample, price momentum delivers excess returns of about 8.8% after controlling for the Fama-French three factors, significant at the 1%. However, introducing DIV momentum reduces the alpha to 2.9%, and the alpha is insignificantly different from zero. As for VW portfolios, they deliver higher alphas but are less precisely estimated. In this case, the annualized alpha of price momentum drops by half from 11.2% to 5.8% after controlling for
DIV momentum.

Momentum crashes. We find that the distribution of monthly momentum returns is left skewed and displays excess kurtosis. Within the five largest EW (VW) momentum crashes, investors lost 18% (26%) on average. The difference between the beta of the winners and that of the losers has been -2.4 (-3.5), on average, and the losses stemmed mostly from the performance of the losers, which averaged at 24% (21%) monthly return. We find little action in the winners portfolio, which returned on average 2% (-6%).

Predictability and dynamic hedging. Dynamic hedging consists in levering the portfolio when its realized volatility has been low and/or the market has been under-performing, and de-levering otherwise. We begin our analysis by looking at whether set of variables helps predicting momentum returns in our sample, and we find that it does not. Probably, this is because the crashes in our sample are more heterogeneous both in terms of origins and in terms of length. In particular, they do not necessarily occur when the market rebounds after a long downturn, and they tend to last for shorter periods of time. As a consequence, our out-of-sample test of the dynamic hedged UMD strategy shows that either it underperforms static momentum, or it does not improve its returns.

"

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Despite the fact that the economic theory states that financial markets are efficient and investors are rational, a large amount of research is about anomalies, where the result is different from the theoretical expectation. At Quantpedia, we deal with anomalies in the financial markets and we have identified more than 500 attractive trading systems together with hundreds of related academic papers.

This article should be a case study of some strategies that are listed in our Screener, with an aim to present a possible usage of strategies in our database. Moreover, we have extended the backtesting period and we show that the strategies are still working and have not diminished. This blog also should serve as a case study how to use the Quantpedia’s database itself; therefore the choice of strategies was not obviously random and strategies were filtered by given criteria, however, every strategy is listed in the “free“ section, and therefore no subscription is needed.

Academic research has documented several hundreds of factors that explain expected stock returns. Now, question is: Are all this factors product of data mining? Recent paper by Andrew Chen runs a numerical simulation that shows that it is implausible, that abudance of equity factors can be explained solely by p-hacking …

Author: Chen

Title: The Limits of P-Hacking: A Thought Experiment

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3358905

Abstract:

Suppose that asset pricing factors are just p-hacked noise. How much p-hacking is required to produce the 300 factors documented by academics? I show that, if 10,000 academics generate 1 factor every minute, it takes 15 million years of p-hacking. This absurd conclusion comes from applying the p-hacking theory to published data. To fit the fat right tail of published t-stats, the p-hacking theory requires that the probability of publishing t-stats < 6.0 is infinitesimal. Thus it takes a ridiculous amount of p-hacking to publish a single t-stat. These results show that p-hacking alone cannot explain the factor zoo.

Notable quotations from the academic research paper:

"Academics have documented more than 300 factors that explain expected stock returns. This enormous set of factors begs for an economic explanation, yet there is little consensus on their origin. A p-hacking (a.k.a. data snooping, data-mining) offers a neat and plausible solution. This cynical explanation begins by noting that the cross-sectional literature uses statistical tests that are only valid under the assumptions of classical single hypothesis testing. These assumptions are clearly violated in practice, as each published factor is drawn from multiple unpublished tests. In this well-known explanation, the factor zoo consists of factors that performed well by pure chance.

In this short paper, I follow the p-hacking explanation to its logical conclusion. To rigorously pursue the p-hacking theory, I write down a statistical model in which factors have no explanatory power, but published t-stats are large because the probability of publishing a t-stat ti follows an increasing function p(ti). I estimate p(ti ) by fitting the model to the distribution of published t-stats inHarvey, Liu, and Zhu (2016) and Chen and Zimmermann (2018). The p-hacking story is powerful: The model fits either dataset very well.

Though p-hacking fits the data, following its logic further leads to absurd conclusions. In particular, the pure p-hacking model predicts that the ratio of unpublished factors to published factors is ridiculously large, at about 100 trillion to 1. To put this number in perspective, suppose that 10,000 economists mine the data for 8 hours per day, 365 days per year. And suppose that each economist finds 1 predictor every minute. Even with this intense p-hacking, it would take 15 million years to find the 316 factors in theHarvey, Liu, and Zhu (2016) dataset.

This thought experiment demonstrates that assigning the entire factor zoo to p-hacking is wrong. Though the p-hacking story appears logical, following its logic rigorously leads to implausible conclusions, disproving the theory by contradiction. Thus, my thought experiment supports the idea that publication bias in the cross-section of stock returns is relatively minor."

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A new research paper related mainly to:

#26 – Value (Book-to-Market) Anomaly

Authors: Zhou

Title: Can Cash-Flow Beta Explain the Value Premium?

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3244791

Abstract:

It is well documented that the cash flow beta can partly explain the source of the value premium. This paper presents an empirical test that cast doubt on this widely accepted belief. We double sort the stocks with their value and quality dimension and obtain four corner portfolios: (A) expensive quality, (B) cheap junk, (C) cheap quality and (D) expensive junk stocks. Prior research has shown that the value premium concentrates on cheap quality minus expensive junk (i.e. undervalued minus overvalued) but is not significant in cheap junk minus expensive quality stocks. If cash-flow beta is the source of the value premium, we would expect a larger cash-flow beta difference between the cheap quality and expensive junk portfolio. However, our empirical test shows that β_CF ((B) cheap junk) – β_CF ((A) expensive quality) >>β_CF ((C) cheap quality)-β_CF ((D) expensive junk). In other words, B minus A does not contribute to the profit of the value premium but contribute most to the difference of the cash flow beta between value and growth portfolios. Therefore, our result may serve as evidence that the cash flow beta may only spuriously explain the value premium. Or, at least, the cash-flow risk premium estimated in the portfolio regression approach is biased.

Notable quotations from the academic research paper:

"The value premium is one of the most important anomalies in the field of asset pricing. It is well known that the market beta fails to explain the value premium in the dataset after 1963.

Campbell and Vuolteenaho (2004) first proposed a “good beta, bad beta” model to solve this dilemma. They decompose the traditional market beta into two components: A good beta is the beta that measures a stock’s covariance with the temporary market movement or discount rate news, which is usually induced by changing market sentiment and varying risk aversion; A bad beta measures a stock’s comovement with market-wide fundamental cash-flow news. Campbell and Vuolteenaho (2004) and Cohen, Polk, Vuolteenaho(2009) argue that investors will regard wealth decrease induced by discount rate news as less significant because it tends to be temporary and the investors will be compensated by better future investment opportunity in an increased discount rate environment. A rational investor will demand higher return for the bad beta than the good beta.

Together with Campbell and Vuolteenaho (2004), Cohen, Polk, Vuolteenaho(2009), Campbell, Polk and Vuolteenaho (2010) and Da and Warachka (2009) among others, use different proxy for the cash-flow news and find that value stocks have a higher cash-flow beta than growth stocks. They conclude that cash-flow beta is one of the sources of the value premium. In this paper, we present an empirical test that question this widely accepted belief.

Our test double-sorts the stocks by value and quality dimension. In a conceptual simplified picture, Figure 1 illustrates four groups of stocks: (A) high quality, high price (expensive quality), (B) low quality, low price (cheap junk), (C) high quality, low price (cheap quality), and (D) low quality, high price (expensive junk). The price of portfolio A and B is thought to be “right” as their price is more aligned with the quality. Portfolio C (D) is the undervalued (overvalued) stocks.

High price portfolio A and D are growth stocks, and low price portfolio B and C are value stocks. The value premium is the return of ( + ) − ( + ) = ( − ) + ( − ) . ( − ) and ( − ) are represented respectively by the light blue and dark blue arrow in Figure 1.

When the price is “right”, the value premium is not significant. The value premium is concentrated on ( − ), but not on ( − ). The return of the four portfolio have the relationship: R > R ≈ R > R .

If the cash flow beta is the source of the value premium and the value premium is concentrated on ( − ), one would naturally expect that f( ) − f( ) ≫ f( ) − f( ), in which, f is the cash flow beta. However, in our
test, we find the opposite results: f( ) − f( ) ≫ f( ) − f( ). ( − ) does not contribute to the profit of the value premium while f( ) − f( ) contribute the most to the cash-flow beta difference between the value and growth portfolio.

If the cash-flow beta represents a risk, we take most of the risk in the value-junk minus growth quality portfolio, but we earn no profit or even negative profit. We take very little or negative risk in the value-quality minus growth-junk portfolio, but we earn most of the profit of the value premium. We need to find a plausible explanation to this phenomena before we conclude that the cash-flow risk is the source of the value premium. A fundamental reason of our result is that, on the value dimension, higher return links to a higher cash-flow beta, while on the quality dimension, higher return links to a lower cash-flow beta."

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A new research paper related mainly to:

#77 – Beta Factor in Stocks

Authors: Novy-Marx, Velikov

Title: Betting Against Betting Against Beta

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3300965

Abstract:

Frazzini and Pedersen’s (2014) Betting Against Beta (BAB) factor is based on the same basic idea as Black’s (1972) beta-arbitrage, but its astonishing performance has generated academic interest and made it highly influential with practitioners. This performance is driven by non-standard procedures used in its construction that effectively, but non-transparently, equal weight stock returns. For each dollar invested in BAB, the strategy commits on average $1.05 to stocks in the bottom 1% of total market capitalization. BAB earns positive returns after accounting for transaction costs, but earns these by tilting toward profitability and investment, exposures for which it is fairly compensated. Predictable biases resulting from the paper’s non-standard beta estimation procedure drive results presented as evidence supporting its underlying theory.

Notable quotations from the academic research paper:

" Frazzini and Pedersen’s (FP) Betting Against Beta (BAB, 2014) is an unmitigated academic success. Despite being widely read, and based on a fairly simple idea, BAB is not well understood. This is because the authors use three unconventional procedures to construct their factor. All three departures from standard factor construction contribute to the paper’s strong empirical results. None is important for understanding the underlying economics, and each obscures the mechanisms driving reported effects.

Two of these non-standard procedures drive BAB’s astonishing “paper” performance, which cannot be achieved in practice, while the other drives results FP present as evidence supporting their theory. The two responsible for driving performance can be summarized as follows:

Non-standard procedure #1, rank-weighted portfolio construction: Instead of simply sorting stocks when constructing the beta portfolios underlying BAB, FP use a “rank-weighting” procedure that assigns each stock to either the “high” portfolio or the “low” portfolio with a weight proportional to the cross-sectional deviation of the stock’s estimated beta rank from the median rank.

Non-standard procedure #2, hedging by leveraging: Instead of hedging the low beta-minus-high beta strategy underlying BAB by buying the market in proportion to the underlying strategy’s observed short market tilt, FP attempt to achieve market-neutrality by leveraging the low beta portfolio and deleveraging the high beta portfolio using these portfolios’ predicted betas, with the intention that the scaled portfolios’ betas are each equal to one and thus net to zero in the long/short strategy.

FP’s first of these non-standard procedures, rank-weighting, drives BAB’s performance not by what it does, i.e., put more weight on stocks with extreme betas, but by what it does not do, i.e., weight stocks in proportion to their market capitalizations, as is standard in asset pricing. The procedure creates portfolios that are almost indistinguishable from simple, equal-weighted portfolios. Their second non-standard procedure, hedging with leverage, uses these same portfolios to hedge the low beta-minus-high beta strategy underlying BAB. That is, the rank-weighting procedure is a backdoor to equal-weighting the underlying beta portfolios, and the leveraging procedure is a backdoor to using equal-weighted portfolios for hedging.

BAB achieves its high Sharpe ratio, and large, highly significant alpha relative to the common factor models, by hugely overweighting micro- and nano-cap stocks. For each dollar invested in BAB, the strategy commits on average $1.05 to stocks in the bottom 1% of total market capitalization. These stocks have limited capacity and are expensive to trade. As a result, while BAB’s “paper” performance is impressive, it is not something an investor can actually realize. Accounting for transaction costs reduces BAB’s profitability by almost 60%. While it still earns significant positive returns, it earns these by tilting toward profitability and investment, exposures for which it is fairly compensated."

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A new research paper related mainly to:

#25 – SIze Premium

Authors: McGee, Olmo

Title: The Size Premium As a Lottery

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3279645

Abstract:

We investigate empirically the dependence of the size effect on the top performing stocks in a cross-section of risky assets separated by industry. We propose a test for a lottery-style factor payoff based on a stochastic utility model for an under-diversified investor. The associated conditional logit model is used to rank different investment portfolios based on size and we assess the robustness of the ranking to the inclusion/exclusion of the best performing stocks in the cross-section. Our results show that the size effect has a lottery-style payoff and is spurious for most industries once we remove the single best returning stock in an industry from the sample each month. Analysis in an asset pricing framework shows that standard asset pricing models fail to correctly specify the size premium on risky assets when industry winners are excluded from the construction of the size factor. Our findings have implications for stock picking, investment management and risk factor analysis.

Notable quotations from the academic research paper:

" Firms with small market capitalization tend to outperform larger companies. Investors are attracted to lottery-like assets with positively skewed returns because they offer a very large payoff with a small probability, which the investors overweight. This demand makes positively skewed securities overpriced and likely to earn low returns. In this article we test whether the size/market capitalization attribute, and associated factor-mimicking portfolios, receive a lottery-like payoff. The implications of this are that most small stocks do not payoff and the returns to a size strategy are driven by a small number of winners. This type of payoff can be captured through diversification but leaves an under-diversified investor exposed. The risk being that they will not include winning stocks and their resulting return expectation is negative.

To investigate the effect of winning stocks on the performance of investment portfolios based on the size we propose a conditional logit model for ranking different investment portfolios based on size and assess the robustness of the ranking to the inclusion/exclusion of the best performing stocks in the cross-section. This parametric choice is embedded within a stochastic utility model for explaining the investment decisions of under-diversified size investors aiming to exploit the so-called size premium. under-diversified individuals maximize their expected utility in each period by choosing the stock that is predicted to yield the highest return (highest positive skew). This choice is driven by market capitalization of the portfolio and modeled parametrically using the conditional logit model.

In order to obtain cross-sectional variation on the relationship between the size effect and portfolio performance we split the whole cross-section of stocks into different industries and fit the conditional logit model to each industry separately. We apply the conditional logit model at an industry-specific level across three ranked sorted portfolios based on market capitalization: a small, mid-size and big portfolio created from the stocks in each tercile of the cross-section of assets in a specific industry ranked by asset size. This exercise is repeated for 20 industries over the period January 1970 to November 2015. Our results reveal that the size effect vanishes once the top performing stocks in an industry are removed from the sample.

Our empirical findings also highlight the role of industry momentum in determining the relationship between market capitalization and portfolio performance. Specifically, market capitalization has significantly better predictive ability for portfolio return performance in the months following a positive return in an industry than in the months following a negative industry return.

Given these findings, we investigate further the influence of the winning stocks in industry-specific size portfolios. In particular, we propose an alternative size portfolio that we denominate as the winner-weighted index, based on the forecast rank probabilities of stocks provided by the conditional logit model. Intuitively, those stocks that are predicted to be winners in the next period receive a larger allocation of wealth than those stocks that have a low probability of becoming winners. More formally, the allocation of wealth to each asset in the portfolio is determined by the forecast winning probabilities obtained from the conditional logit model and driven by asset size. The performance of this portfolio is compared against a cap-weighted index benchmark portfolio. The weights in the latter portfolio are also driven by market capitalization, however, in contrast to our winner-weighted index portfolio, smaller stocks within an industry receive a smaller allocation of wealth. We consider statistical and economic measures such as the Sharpe ratio, Sortino ratio, the certainty equivalent return of a mean-variance investor and portfolio turnover. We observe the existence of two regimes in portfolio performance. During positive industry momentum periods, the winner-weighted index outperforms the cap-weighted portfolio for 19 out of 20 industries, the exception being the utilities industry. This result is, however, reversed in periods of negative industry momentum for which the cap-weighted index outperforms the winner-weighted index in 18 out of 20 industries.

Our second objective is to explore the influence of winning stocks on the size portfolio pricing factor widely used in the empirical asset pricing literature. Our empirical results for both a top-minus-bottom trading portfolio and a long-only portfolio show that standard asset pricing models are not able to adequately capture the contribution of the size premium to the overall risk premium when the winning stocks are removed from the size factor portfolio. In contrast, we note that the factor loadings (Beta's) associated to the size portfolio pricing factor in standard models are robust to the inclusion/exclusion of the winning stocks. The removal of winning stocks is affecting the risk premium rather than the covariance of portfolios with the risk factor."

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