factor investing - QuantPedia

Equity Momentum in Years 1820-1930

June 10, 2019

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 profitable – 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 profitable factor – with an average annual return close to 9% – and the most volatile – with 20% annual standard deviation.

Momentum in years 1820-1930

Dissecting momentum returns. Recent literature debates whether momentum is long or short term. In our sample, UMD profits 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 confirms 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 profitable 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. Specically, 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 significant 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, significant at the 1%. However, introducing DIV momentum reduces the alpha to 2.9%, and the alpha is insignificantly 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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Skewness / Lottery Effect in Commodities

May 30, 2019

We at Quantpedia are continually building a database of ideas for quantitative trading strategies derived out of the academic research papers. Motivated by the recent fall of the S&P500 index at the end of 2018, we have added a new filtering field into our Screener, which you can use to find strategies that can be utilized as a hedge/diversification to equity market risk factor during bear markets. We would like to present one strategy that is profitable itself, but with an added value of negative correlation with the equity market, to be able to perform in the desired way also during the " bad" times.

The strategy we would be talking about can be found in our database under the name #281 – Skewness Effect in Commodities and is built on a research paper written by Fernandez-Perez, Frijns, Fuertes and Miffre – The Skewness of Commodity Futures Returns. Guys at AlphaArchitect have been really generous and they have provided a space for us to write a short article in which we 1) briefly discuss the lottery effect, 2) we discuss the research on this topic in the context of commodities, and 3) we conduct an independent replication effort of the commodity lottery effect identified in academic research.

Authors: Vojtko, Padysak

Title: Skewness Effect in Commodities

Link: https://alphaarchitect.com/2019/05/30/skewness-effect-in-commodities/

Shortly:

"Economies and markets have their seasonalities and cyclicality, where bull markets alternate with bear markets. Bull markets are connected with particularly good performance of the stocks and profiting investors. However on the other hand, during the bear markets, investors tend to lose in the falling equity market. Therefore, during these stressful times, it might be better for practitioners to invest in a portfolio that is negatively correlated with the equity market to gain profit instead of counting loses.

There is strong evidence that investors have a preference for lottery-like assets (the assets that have a relatively small probability of a large payoff or in other words, big skewness). Therefore, it should be profitable to not play the lottery, but rather be “the lottery ticket issuer“ by shorting the commodities with high skewness and going long commodities with low skewness. Additionally, commodities as an asset class are quite distinct from equities and therefore they can often be used as a diversifier to equities.

Lottery strategy in commodites

Clearly, the strategy is profitable, a dollar invested in 1991 would result in more than 9 dollars by 2019, which results in a yearly performance of nearly 8,5%. Moreover, the risk of the strategy is relatively low, with the maximal drawdown of around 16 %, which results in a return to a drawdown ratio of slightly more than 0,5.

Our research suggests that the performance of the equity market represented by the S&P500 index is negatively correlated with the performance of the skewness strategy. Therefore, if the equity market performs badly, our strategy should be still profitable.

What is more important, if we would look upon the worst months of S&P500 index (blue bars) and compare it with the performance of the strategy (orange bars), we would see the performance of the suggested strategy is at most times positive and therefore the investor would be able to hedge his equity portfolio.

Worst equity month performance vs. commodity strategy

To sum it up, the lottery anomaly in commodities is alive and performs in a desirable way also in the recent period. Moreover, the profitable strategy based on this anomaly could also serve as a hedge against equities and offer a profitable possibility to invest during times when equities are in bear markets.

Authors:
Radovan Vojtko, CEO, Quantpedia.com
Matus Padysak, Analyst, Quantpedia.com

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Transaction Costs of Factor Strategies

May 25, 2019

A very important research papers related to all equity factor strategies …

Authors: Li, Chow, Pickard, Garg

Title: Transaction Costs of Factor Investing Strategies

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3359947

Abstract:

Although hidden, implicit market impact costs of factor investing strategies may substantially erode the strategies' expected excess returns. The authors explain these market impacts costs and model them using rebalancing data of a suite of large and longstanding factor investing indices. They introduce a framework to assess the costs of rebalancing activities, and attribute these costs to characteristics such as rate of turnover and the concentration of turnover, which intuitively describe the strategies' demands on liquidity. The authors evaluate a number of popular factor-investing strategy implementations and identify how index construction methods, when thoughtfully designed, can reduce market impact costs.

Notable quotations from the academic research paper:

"Factor investing strategies have become increasingly popular. According to data from Morningstar Direct, assets under management (AUM) in factor investing ETFs and mutual funds across global markets increased from just below US$75 billion in 2005 to more than US$800 billion by the end of 2016.

In practice, when a provider rebalances an index, most managers tracking it execute the necessary transactions near the close of the rebalancing day in order to minimize their portfolio’s tracking error. The fund managers may appear to be perfectly tracking the index; in another words, minimizing implementation shortfall, which is the aggregate difference between the average traded price and the closing price of each of the index's underlying securities on the rebalancing day. Thus, the total implementation cost of an index fund could be perceived as merely the sum of the explicit costs associated with trading, such as commissions, taxes, ticker charges, and so forth. This notion misses the propagating market impact that trading has on the index’s value. The large volume of buy and sell orders for the same securities, executed at the same time, can result in securities prices moving against the managers, producing losses for both the index and the fund investors. This implicit cost is often overlooked because it is not visible when comparing a fund’s net asset value (NAV) and the index’s value; it can, however, be overwhelmingly large relative to the explicit costs for strategies with massive AUM. This article focuses on unmasking the market impact costs that arise from synchronous buying and selling.

We analyze the behavior of stocks that were traded during the rebalancing of 49 FTSE RAFI™ Indices (henceforth, “the indices”). We find significant evidence of market impact on the rebalancing day and a subsequent price reversal over the next four days. We find that the magnitude of price impact is predictable, because it is directly related to the security’s liquidity and the size of the trade.

Specifically, we identify that a fund incurs approximately 30 basis points (bps) of trading costs due to market impact for every 10% of a stock’s average daily volume (ADV) traded in aggregate by the factor investing index–tracking funds.

Market Impact

Our simple relationship of market impact versus the security’s liquidity and the size of the trade can be used to estimate the implicit transaction costs of rebalancing trades. We apply our model and evaluate the costs of an extended list of popular strategies with various turnover rates, trade sizes, levels of security liquidity, and number of rebalances. We find that, at a modest level of AUM, and assuming all rebalancing trades occur near the end of
the rebalancing date, the expected transaction costs can significantly erode the expected alpha as indicated by long-term historical backtests. Specifically, with as little as $10 billion in AUM, momentum indexing strategies can have trading costs of 200 bps or more. At the same level of assets, income strategies’ costs are in the 60–80 bps range, and quality strategies’ costs fall below 40 bps. We report the capacities, defined as AUM when expected costs reach a high and fixed level (50 bps a year), of these strategies. We also present an attribution model to relate costs to strategy characteristics and explain in detail how certain styles of investing—for instance, those that trade frequently and those that trade completely in and out of a few illiquid positions—require higher costs than others.

Liquidity characteristics

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The Impact of Crowding on Alternative Risk Premiums

May 17, 2019

Related to all factor strategies …

Author: Baltas

Title: The Impact of Crowding in Alternative Risk Premia Investing

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3360350

Abstract:

Crowding is a major concern for investors in the alternative risk premia space. By focusing on the distinct mechanics of various systematic strategies, we contribute to the discussion with a framework that provides insights on the implications of crowding on subsequent strategy performance. Understanding such implications is key for strategy design, portfolio construction, and performance assessment. Our analysis shows that divergence premia, like momentum, are more likely to underperform following crowded periods. Conversely, convergence premia, like value, show signs of outperformance as they transition into phases of larger investor flows.

Notable quotations from the academic research paper:

"Crowding risk is listed as one of the most important impediments for investing in alternative risk premia. We contribute to this industry debate by exploring the mechanics of the various ARP in the event of investor flows, and study the implications of crowdedness on subsequent performance.

The cornerstone of our methodology is the classification of the ARP strategies into divergence and convergence premia. Divergence premia, like momentum, lack a fundamental anchor and inherently embed a self-reinforcing mechanism (e.g. in momentum, buying outperforming assets, and selling underperforming ones). This lack of a fundamental anchor creates the coordination problem that Stein (2009) describes, which can ultimately have a destabilising effect.

Divergence factor

Conversely, convergence premia, like value, embed a natural anchor (e.g. the valuation spread between undervalued and overvalued assets) that acts as an self-correction mechanism (as undervalued assets are no longer undervalued if overbought). Extending Stein’s (2009) views, such dynamics suggest that investor flows are actually likely to have a stabilising effect for convergence premia.

Convergence premia

In order to test these hypotheses we use the pairwise correlation of factor-adjusted returns of assets in the same peer group (outperforming assets, undervalued assets and so on so forth) as a metric for crowding.

We provide empirical evidence in line with these hypotheses. Divergence premia within equity, commodity and currency markets are more likely to underperform following crowded periods.

All divergence premias

Whereas convergence premia show signs of outperformance as they transition into phases of higher investor flows.

All convergence premias "

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News Implied VIX Since The Year 1890

May 9, 2019

We present an interesting academic paper with a methodology that allows estimating VIX (volatility risk) since the year 1890 …

Authors: Manela, Moreira

Title: News Implied Volatility and Disaster Concerns

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2382197

Abstract:

We construct a text-based measure of uncertainty starting in 1890 using front-page articles of the Wall Street Journal. News implied volatility (NVIX) peaks during stock market crashes, times of policy-related uncertainty, world wars and financial crises. In US post-war data, periods when NVIX is high are followed by periods of above average stock returns, even after controlling for contemporaneous and forward-looking measures of stock market volatility. News coverage related to wars and government policy explains most of the time variation in risk premia our measure identifies. Over the longer 1890-2009 sample that includes the Great Depression and two world wars, high NVIX predicts high future returns in normal times, and rises just before transitions into economic disasters. The evidence is consistent with recent theories emphasizing time variation in rare disaster risk as a source of aggregate asset prices fluctuations.

Notable quotations from the academic research paper:

"This paper aims to quantify this “spirit of the times”, which after the dust settles is forgotten, and only hard data remains to describe the period. Specifically, our goal is to measure people’s perception of uncertainty about the future, and to use this measurement to investigate what types of uncertainty drive aggregate stock market risk premia.

We start from the idea that time-variation in the topics covered by the business press is a good proxy for the evolution of investors’ concerns regarding these topics.

We estimate a news-based measure of uncertainty based on the co-movement between the front-page coverage of the Wall Street Journal and options-implied volatility (VIX). We call this measure News Implied Volatility, or NVIX for short. NVIX has two useful features that allow us to further our understanding of the relationship between uncertainty and expected returns:

(i) it has a long time-series, extending back to the last decade of the nineteen century, covering periods of large economic turmoil, wars, government policy changes, and crises of various sorts;

(ii) its variation is interpretable and provides insight into the origins of risk variation.

The first feature enables us to study how compensation for risks reflected in newspaper coverage has fluctuated over time, and the second feature allows us to identify which kinds of risk were important to investors.

We rely on machine learning techniques to uncover information from this rich and unique text dataset. Specifically, we estimate the relationship between option prices and the frequency of words using Support Vector Regression. The key advantage of this method over Ordinary Least Squares is its ability to deal with a large feature space. We find that NVIX predicts VIX well out-of-sample, with a root mean squared error of 7.48 percentage points (R2 = 0.19). When we replicate our methodology with realized volatility instead of VIX, we find that it works well even as we go decades back in time, suggesting newspaper word-choice is fairly stable over this period.

News Based VIX Index

We study whether fluctuations in NVIX encode information about equity risk premia. We begin by focusing on the post-war period commonly studied in the literature for which high-quality stock market data is available. We find strong evidence that times of greater investor uncertainty are followed by times of above average stock market returns. A one standard deviation increase in NVIX predicts annualized excess returns higher by 3.3 percentage points over the next year and 2.9 percentage points annually over the next two years.

Interpretability, a key feature of the text-based approach, enables us to investigate what type of news drive the ability of NVIX to predict returns. We decompose the text into five categories plausibly related (to a varying degree) to disaster concerns: war, financial intermediation, government policy, stock markets, and natural disasters. We find that a large part of the variation in risk premia is related to wars (53%) and government policy (27%). A substantial part of the time-series variation in risk premia NVIX identifies is driven by concerns tightly related to the type of events discussed in the rare disasters literature."

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An Analysis of PIMCO’s Bill Gross’ Alpha

May 4, 2019

Bill Gross is probably the most known fixed income fund manager. A new academic paper sheds more light on his track record and sources of his stellar performance …

Authors: Dewey, Brown

Title: Bill Gross' Alpha: The King Versus the Oracle

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3345604

Abstract:

We set out to investigate whether ''Bond King" Bill Gross demonstrated alpha (excess average return after adjusting for market exposures) over his career, in the spirit of earlier papers asking the same question of ''Oracle of Omaha," Warren Buffett. The journey turned out to be more interesting than the destination. We do find, contrary to previous research, that Gross demonstrated alpha at conventional levels of statistical significance. But we also find that result depends less on the historical record than on whether we take the perspective of academics interested in market efficiency, investors picking a fund or someone (say a potential employer) asking whether a manager has skill or is throwing darts to pick positions. These are often thought to be overlapping or even identical questions. That's not completely unreasonable in equity markets, but in fixed income these are distinct. We also find quantitative differences, mainly that fixed-income securities have much higher correlations with each other than equities, make alpha 4.5 times as hard to measure for Gross than Buffett. We don't think our results will have much practical effect on attitudes toward Gross as an investor, but we hope they will advance understanding of what alpha means and appropriate ways to estimate it.

Notable quotations from the academic research paper:

"Superstar bond portfolio manager Bill Gross announced his retirement last week. From 1987 to 2014, his PIMCO Total Return fund generated 1.33% per year of alpha versus the Barclays US Credit index, with a t-statistic of 3.76. For many years his fund was the largest bond fund in the world, and was generally considered to be the most successful. This track record inspired us to take a closer quantitative look along the lines of Frazzini, Kabiller and Pedersen's Buffett's Alpha (FKP). Gross, like Buffett, often publicly discussed what he perceives as the drivers of his returns. At the Morningstar Conference in 2014 and in a 2005 paper titled "Consistent Alpha Generation Through Structure" Gross highlighted three factors behind his returns: more credit risk than his benchmark, more 5-year and less 30-year exposure, and long mortgages and other securities with negative convexity.

We present five main findings:

1. We confirm that those three factors, plus one for the general level of interest rates, explain 89% of the variance in Gross' monthly return over the 27-year period. We further estimate that Gross outperformed a passive factor portfolio by 0.84% per year, which is significant at the 5% level. Gross' compounded annual return over the period was 7.52%, versus 6.44% for the Barclay's Aggregate US Index. So we find that most of his 1.08% annual outperformance of the index was alpha.

Bill Gross' Alpha

2. The FKP paper mentioned above considered one of the best-known track records in the equity asset class, Warren Buffett's. We compliment this work by examining one of the best-known track records in the fixed-income asset class. Fixed-income investing offers a dierent set of challenges and opportunities than equity. We offer a novel discussion on the concept of manager alpha including important qualitative and quantitative differences in the concept of alpha with Gross versus Buffett.

3. The main qualitative difference is that Gross exploited well known sources of risk and potentially excess return in the fixed-income market, exposures that investors rationally demand additional yield to accept. Buffett's performance, for the most part, correlates with factors uncovered long after he began investing and were still not accepted as fully as factors like credit risk or mortgage prepayment risk. Moreover Buffett's factors probably result from behavioral biases and institutional constraints rather than rational investor preferences.

4. The main statistical difference is the much higher r2 value in Gross' regression versus Buffett's (about 0.9 versus 0.3) makes the alpha significance estimate 4.5 times as sensitive to the observed returns on the factor portfolios. Since it is nearly impossible to estimate expected returns – there is considerable debate about the level of the equity premium even with 150 years or more of data – this makes it important to select factors that conform as closely as possible to what Gross actually did, rather than factors that merely have a high return correlation to Gross' results. The closer the factors conform to Gross' practice, the better the chance that any deviations in factor performance from expectation over the period are reflected equally in both Gross' actual results and the factor portfolio results.

5. Gross earned essentially all of his alpha in favorable markets for his factors and had a significantly negative timing ability in the sense that his factor exposures were greater in months the factor had negative returns than in months the factor had positive return. This latter feature could be unfortunate timing decisions or negative convexity in the factor exposures. We discuss whether this can shed light on the source of Gross' alpha, specifically whether it relates to preferential access to new issues and leverage."

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Tax Management is Extremely Important for Equity Factor Strategies

February 7, 2019

Benjamin Franklin once said "… in this world nothing can be said to be certain, except death and taxes." and we completely agree with that quote. Traders and portfolio managers often strongly concentrate on a process of building the strategy which delivers the highest outperformance. But a lot of them forget to include taxes into that building process. And this can be a significant mistake as the following research paper shows:

Authors: Goldberg, Hand, Cai

Title: Tax-Managed Factor Strategies

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3309974

Abstract:

We examine the tax efficiency of an indexing strategy and six factor tilts. Between June 1995 and March 2018, average value added by tax management exceeded 1.4% per year at a 10- year horizon for all the strategies we considered. Tax-managed factor tilts that are beta 1 to the market generated average tax alpha between 1.6% and 1.9% per year, while average tax alpha for the tax-managed indexing strategy was 2.3% per year. These remarkable results depend on the availability of short-term capital gains to offset. To a great extent, they can be attributed to loss harvesting and the tax rate differential.

Notable quotations from the academic research paper:

"In 1993, Rob Jeffrey and Rob Arnott asked a provocative question: Is an investor’s alpha big enough to cover its taxes? Arnott and Jeffrey pointed out that alpha generation typically requires high turnover, which erodes pre-tax alpha by increasing taxes, but this important fact tended to be overlooked by investors and researchers. Twenty-five years later, the situation has not changed too much.

Some principles of tax-aware investing, such as locating high-tax investments in tax-deferred accounts or using tax-free municipal bonds (instead of their taxable counterparts) as investments and benchmarks, are no more than common sense. Other principles of taxaware investing may rely on more sophisticated mathematics and economics, as well as more detailed knowledge of the complex and ever-changing US tax code. An example of the latter would be loss harvesting, which is a tax-aware option that combines delayed realization of capital gains with immediate realization of capital losses. A second timing option, which depends on the tax rate differential, involves the realization of long-term gains in order to facilitate the harvesting of short-term losses.

In the present study, we document the performance of after-tax return and risk profiles of an indexing strategy and six factor tilts over the period June 1995 to March 2018.7 We focus on active return, and our results rely on a number of methodological innovations. We mitigate the substantial impact of period dependence on results by launching each strategy at regular intervals over a long horizon, generating ranges of outcomes obtained in different market climates. We construct each portfolio with a one-step optimization that balances the competing imperatives of constraining factor exposures, harvesting losses, and minimizing tracking error (TE) to a diversified benchmark. We develop an after-tax performance attribution scheme that decomposes estate/donation and liquidation active returns into factor alpha, tax alpha, and tracking return. We measure the impact of the tax rate differential that affects tax-managed factor tilts.

Our results span several dimensions. First, we compare after-tax performance of tax-managed versions to tax-indifferent versions of each strategy. In back-tests, average value added by tax management during the period studied exceeded 1.50% per year at 10-year horizon for all the strategies we considered. This finding illustrates the potential power of loss harvesting and lets us move on to the more nuanced topic of the loss-harvesting capacities of different strategies.

tax-managed factor strategies

Figure 1 presents the average after-tax active return of the tax-managed versions of the strategies graphically. Overall, the best average performance was delivered by the Small Value strategy, but more than half the after-tax active return was due to factor alpha. On the basis of tax alpha, the strategies divide into the three groups. The highest average tax alpha was delivered by the indexing strategy. Each of the four beta-1 strategies captured at least 70% of the tax alpha in the indexing strategy, but the two lower-risk strategies captured less than 35%. The division is marked in the performance charts."

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Biased Betting Against Beta?

January 17, 2019

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.

BAB equally weighted portfolio

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 with costs

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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The Size Effect Has a Lottery-Style Payoff

January 11, 2019

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 diversification but leaves an under-diversified 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-diversified size investors aiming to exploit the so-called size premium. under-diversified 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 fit the conditional logit model to each industry separately. We apply the conditional logit model at an industry-specific 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 specific 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.

size lottery

Our empirical findings also highlight the role of industry momentum in determining the relationship between market capitalization and portfolio performance. Specifically, market capitalization has significantly 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-specific 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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Quantpedia’s Solution for Bear Markets

January 6, 2019

Dear readers,

Equity markets have once again entered a high volatility regime at the end of the year 2018. Risk of an economic slowdown increases and investors and traders are looking for trading strategies which can perform well in such uncertain times.

We at Quantpedia can help with that!

I am really excited to give you an opportunity to work with a new filtering field in our Screener, which you can use to find strategies that can be utilized as a hedge/diversification to equity market risk factor during bear markets.

Come and find your new hedge!

Team of Quantpedia.com