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Showing results 1 - 10 of 31 for the search terms: factor zoo.

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Bringing Order to the Factor Zoo?

From a purely statistical perspective, how many factors are optimal for explaining both time series and cross-sectional variations in stock anomaly/stock returns, and how do these statistical factors relate to stock/firm characteristics? In their July 2018 paper entitled “Factors That Fit the Time Series and Cross-Section of Stock Returns”, Martin Lettau and Markus Pelger search for the optimal set of equity factors via a generalized Principal Component Analysis (PCA) that includes a penalty on return prediction errors returns. They apply this approach to three datasets:

  1. Monthly returns during July 1963 through December 2017 for two sets of 25 portfolios formed by double sorting into fifths (quintiles) first on size and then on either accruals or short-term reversal.
  2. Monthly returns during July 1963 through December 2017 for 370 portfolios formed by sorting into tenths (deciles) for each of 37 stock/firm characteristics.
  3. Monthly excess returns for 270 individual stocks that are at some time components of the S&P 500 Index during January 1972 through December 2014.

They compare performance of their generalized PCA to that of conventional PCA. Using the specified datasets, they find that: Keep Reading

Sifting the Factor Zoo

The body of U.S. stock market research offers hundreds of factors (the factor zoo) to explain and predict return differences across stocks. Is there a reduced set of factors that most accurately and consistently captures fundamental equity risks? In their March 2018 paper entitled “Searching the Factor Zoo”, Soosung Hwang and Alexandre Rubesam employ Bayesian inference to test all possible multi-factor linear models of stock returns and identify the best models. This approach enables testing of thousands of individual assets in combination with hundreds of candidate factors. They consider a universe of 83 candidate factors: the market return in excess of the risk-free rate, plus 82 factors measured as the difference in value-weighted average returns between extreme tenths (deciles) of stocks sorted on stock/firm characteristics. Their stock universe consists of all U.S. listed stocks excluding financial stocks, stocks with market capitalizations less than the NYSE 20th percentile (microcaps) and stocks priced less than $1. They test microcaps separately. They further test 20 sets of test portfolios (300 total portfolios). The overall sample period is January 1980 through December 2016. To assess factor model performance consistency, they break this sample period into three or five equal subperiods. Using the specified data as available over the 36-year sample period, they find that: Keep Reading

Emptying the Equity Factor Zoo?

As described in “Quantifying Snooping Bias in Published Anomalies”, anomalies published in leading journals offer substantial opportunities for exploitation on a gross basis. What profits are left after accounting for portfolio maintenance costs? In their November 2017 paper entitled “Accounting for the Anomaly Zoo: A Trading Cost Perspective”, Andrew Chen and Mihail Velikov examine the combined effects of post-publication return deterioration and portfolio reformation frictions on 135 cross-sectional stock return anomalies published in leading journals. Their proxy for trading frictions is modeled stock-level effective bid-ask spread based on daily returns, representing a lower bound on costs for investors using market orders. Their baseline tests employ hedge portfolios that are long (short) the equally weighted fifth, or quintile, of stocks with the highest (lowest) expected returns for each anomaly. They also consider capitalization weighting, sorts into tenths (deciles) rather than quintiles and portfolio constructions that apply cost-suppression techniques. Using data as specified in published articles for replication of 135 anomaly hedge portfolios, they find that:

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Taming the Factor Zoo?

How should researchers address the issue of aggregate/cumulative data snooping bias, which derives from many researchers exploring approximately the same data over time? In the October 2014 version of their paper entitled “. . . and the Cross-Section of Expected Returns”, Campbell Harvey, Yan Liu and Heqing Zhu examine this issue with respect to studies that discover factors explaining differences in future returns among U.S. stocks. They argue that aggregate/cumulative data snooping bias makes conventional statistical significance cutoffs (for example, a t-statistic of at least 2.0) too low. Researchers should view their respective analyses not as independent single tests, but rather as one of many within a multiple hypothesis testing framework. Such a framework raises the bar for significance according to the number of hypotheses tested, and the authors give guidance on how high the bar should be. They acknowledge that they considered only top journals and relative few working papers in discovering factors and do not (cannot) count past tests of factors falling short of conventional significance levels (and consequently not published). Using a body of 313 published and 63 near-published (working papers) encompassing 316 factors explaining the cross-section of future U.S. stock returns from the mid-1960s through 2012, they find that: Keep Reading

Equity Factor Census

Should investors trust academic equity factor research? In their February 2019 paper entitled “A Census of the Factor Zoo”, Campbell Harvey and Yan Liu announce a comprehensive database of hundreds of equity factors from top academic journals and working papers through January 2019, including a link to citation and download information. They distinguish among six types of common factors and five types of firm characteristic-based factors. They also explore incentives for factor discovery and reasons why many factors are lucky findings that exaggerate expectations and disappoint in live trading. Finally, they announce a project that allows researchers to add published and working papers to the database. Based on their census of published factors and analysis of implications, they conclude that: Keep Reading

Better Five-factor Model of Stock Returns?

Which factor models of stock returns are currently best? In their June 2018 paper entitled “q5,  Kewei Hou, Haitao Mo, Chen Xue and Lu Zhang, introduce the q5 model of stock returns, which adds a fifth factor (expected growth) to the previously developed q-factor model (market, size, asset growth, return on equity). They measure expected growth as 1-year, 2-year and 3-year ahead changes in investment-to-assets (this year total assets minus last year total assets, divided by last year total assets) as forecasted monthly via predictive regressions. They define an expected growth factor as average value-weighted returns for top 30% 1-year expected growth minus bottom 30% 1-year expected growth, calculated separately and further averaged for big and small stocks. They examine expected growth as a standalone factor and then conduct an empirical horse race of recently proposed 4-factor, 5-factor (including q5) and 6-factor models of stock returns based on their abilities to explain average return differences for value-weighted extreme tenth (decile) portfolios for 158 significant anomalies. Using monthly return and accounting data for a broad sample of non-financial U.S. common stocks during July 1963–December 2016, they find that:

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Perfect Factor Model of U.S. Stock Returns?

How many factors are optimal for modeling future returns of individual stocks? How do these factors relate to conventionally used factors (market, size, value, momentum, investment, profitability…)? In the June 2016 version of their paper entitled “Multifactor Models and the APT: Evidence from a Broad Cross-Section of Stock Returns”, Ilan Cooper, Paulo Maio and Dennis Philip derive mathematically an optimal set of factors for predicting returns of 278 stock portfolios created by sorting U.S. stocks into tenths (deciles) according to 28 market anomalies encompassing aspects of value, momentum, investment, profitability and intangibles. They apply asymptotic principal components analysis to these portfolios to identify the factors. They quantify the premium of each of these factors as the average return spread between extreme deciles of monthly sorts of the 278 source portfolios on the factor. They then examine interactions between this mathematical factor set and several widely used empirical multi-factor models: the Fama-French 3-factor model (market, size, book-to-market); a 4-factor model (adding momentum to the 3-factor model); a second 4-factor model (adding liquidity to the 3-factor-model); a third 4-factor model (market, size, investment, profitability); and, a 5-factor model (adding investment and profitability to the 3-factor model). Using monthly returns for the 278 source stock portfolios during January 1972 through December 2013, they find that: Keep Reading

Economic Uncertainty as a Stock Return Factor

Do specific stocks react differently to economic uncertainty? In their December 2016 paper entitled “Is Economic Uncertainty Priced in the Cross-Section of Stock Returns?”, Turan Bali, Stephen Brown and Yi Tang investigate the role of economic uncertainty in the cross-sectional pricing of individual stocks. They measure economic uncertainty monthly as an aggregation of the volatilities of the unpredictable components of a large number of economic indicators (see the chart below). They then calculate each stock’s sensitivity to economic uncertainty by regressing next-month returns versus economic uncertainty over rolling 60-month windows. Finally, sort stocks into tenths (deciles) by economic uncertainty regression betas and measure economic uncertainty factor returns as the difference in next-month average returns of stocks in extreme deciles. They test robustness via multiple factor models of stock returns and many control variables. Using monthly economic uncertain index data, monthly returns for a broad sample of U.S. stocks and monthly values of control variables during July 1972 through December 2014, they find that: Keep Reading

Bear Market Expectation Risk Factor

Is there a unique stock risk factor associated with expectations of a bear market? In the November 2016 version of their paper entitled “Bear Beta”, Zhongjin Lu and Scott Murray relate a put option-based indicator of the risk that the U.S. equity market will enter a bear state to individual stock returns. This indicator is based on two near-term out-of-the-money S&P 500 Index put options: a short position in a put option with strike price 1.5 standard deviations (based on S&P 500 implied volatility, VIX) below a zero excess (relative to the risk-free rate) index return; and, a long position in a put option 1.0 standard deviation below a zero excess index return. Using S&P 500 Index option prices, S&P 500 Index levels, VIX levels, risk-free rates, returns for a broad sample of U.S. stocks and various factor returns during January 1996 through August 2015, they find that: Keep Reading

Liquidity an Essential Equity Factor?

Is it possible to test factor models of stock returns directly on individual stocks rather than on portfolios of stocks sorted per preconceived notions of factor importance. In their November 2015 paper entitled “Tests of Alternative Asset Pricing Models Using Individual Security Returns and a New Multivariate F-Test”, Shafiqur Rahman, Matthew Schneider and Gary Antonacci apply a statistical method that allows testing of equity factor models directly on individual stocks. Results are therefore free from the information loss and data snooping bias associated with sorting stocks based on some factor into portfolios. They test several recently proposed multi-factor models based on five or six of market, size, value (different definitions), momentum, liquidity (based on turnover), profitability and investment factors. They compare alternative models via 100,000 Monte Carlo simulations each in terms of ability to eliminate average alpha and appraisal ratio (absolute alpha divided by residual variance) across individual stocks. Using monthly returns and stock/firm characteristics for the 407 Russell 3000 Index stocks with no missing monthly returns during January 1990 through December 2014 (300 months), they find that: Keep Reading