Equity Premium

How does the U.S. stock return factor zoo, corrected for data snooping bias, change over time? In their March 2023 draft paper entitled “Useful Factors Are Fewer Than You Think”, Bin Chen, Qiyang Yu and Guofu Zhou tackle this question by asking:

• How many of 207 published factors remain significant after controlling for false discovery rate? In general, returns for each factor are for a portfolio that is each month long (short) subsamples stocks sorted on the factor with the highest (lowest) expected returns. 
• How does the number of significant factors in rolling 20-year subsamples change over time? 
• Taking into account factor redundancies, how many clusters of similar factors based on high return correlations (risk sources) are there?

In a supporting test, they compare pre-publication and post-publication factor performance. Using monthly returns for 207 published long-short factors applied to U.S. stocks during 1967 through 2021, they find that:

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Is model complexity (large number of parameters) more an analytical benefit in predicting asset returns, or more an avenue to discover in-sample luck? In their March 2023 paper entitled “Complexity in Factor Pricing Models”, Antoine Didisheim, Shikun Ke, Bryan Kelly and Semyon Malamud examine the theoretical relationship between input complexity and output accuracy for machine learning asset pricing models. They focus on a complexity wedge, the combination of overfitting (data snooping) and limits to learning that causes in-sample performance of a trained model to exceed out-of-sample performance. They apply ridge shrinkage (controlled by a regularization parameter that sets the strength of an overfitting penalty) to suppress data snooping bias and improve the limits to learning. They assess model performance by out-of-sample Sharpe ratio and out-of-sample pricing errors of optimal portfolios. They test theoretical conclusions on a broad sample of publicly traded U.S. stocks and a set of 110 monthly stock return factors, the latter augmented by a random feature generator that expands the 110 raw factors to any desired number of derivative factors. Using monthly data for the 110 stock return predictors and monthly U.S. stock returns during February 1963 through December 2019, they find that: Keep Reading

Are their practical ways to suppress the sometimes large reduction in academic (gross) equity factor premiums due to trading frictions and other implementation obstacles? In their March 2023 paper entitled “Smart Rebalancing”, Robert Arnott, Feifei Li and Juhani Linnainmaa first examine the performance and related turnover of seven long-only factor premiums: annually reformed (end of June) value, profitability, investment, and a composite of the three; and, monthly reformed value and momentum, and a composite of the two. Their long-only factor portfolios hold market-weighted stocks in the top fourth of factor signals. They reinvest any dividends in all stocks in the portfolios, such that dividends do not affect portfolio weights. They test three ways to suppress periodic turnover via a turnover limit:

1. Proportional Rebalancing – trade all stocks proportionally to meet the turnover limit.
2. Priority Best – buy stocks with the strongest factor signals and sell stocks with the weakest, until reaching the turnover limit.
3. Priority Worst – buy stocks that only marginally qualify for the factor portfolio and sell those that just barely fall out (with the strongest buy and sell signals last), until reaching the turnover limit.

They also apply these three turnover suppression tactics to non-calendar reformation, triggered when the difference between the current and target portfolios exceeds a specified threshold. They ignore the 100% initial formation turnover common to all portfolios. Using  accounting data and common stock returns for all U.S. publicly listed firms during July 1963 through December 2020, with portfolio tests commencing July 1964, they find that: Keep Reading

Do good firm environmental, social and governance (ESG) ratings signal attractive stock returns? If so, what is the best way to exploit the signals? In their February 2023 paper entitled “Quantifying the Returns of ESG Investing: An Empirical Analysis with Six ESG Metrics”, Florian Berg, Andrew Lo, Roberto Rigobon, Manish Singh and Ruixun Zhang test performance of long-short ESG portfolios of U.S., European and Japanese stocks based on proprietary ESG scores from six major rating sources. They consider ESG scores from individual sources and apply several statistical and voting-based methods to aggregate ESG ratings across sources, including: simple average, Mahalanobis distance, principal component analysis, average voting and singular transferable voting. They consider equal-weighted and ESG score-weighted portfolios. They consider different percentile thresholds for long and short holdings. They assess ESG portfolio alpha with respect to widely used 1-factor (market), 3-factor (plus size and value) and 5-factor (plus investment and profitability) models of stock returns. They further test long-short portfolios from aggregations of E, S and G scores separately across sources. Using proprietary ESG ratings, monthly returns of associated stocks and monthly factor model returns during 2014 through 2020, they find that:

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Defined outcome Exchange-Traded Funds (ETF) use complex options strategies that buffer against loss but cap gain to generate a defined outcome for investors over a predefined period. Are they attractive? In their February 2023 paper entitled “The Dynamics of Defined Outcome Exchange Traded Funds”, Luis García-Feijóo and Brian Silverstein analyze average performance of the Innovator Defined Outcome ETF Buffer Series from 2019 through 2021. They also model the performance of the underlying strategy and simulate average outcome during January 2013 through August 2022. They consider three benchmarks: SPDR S&P 500 ETF Trust (SPY); 50% allocation to SPY and 50% allocation to iShares Core US Aggregate Bond ETF (AGG); and, iShares MSCI USA Min Vol Factor ETF (USMV). Using actual and simulated returns for the selected defined outcome ETFs/benchmarks as described, they find that:

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Can machine learning perfect equity sector rotation? In the January 2023 version of their paper entitled “Deep Sector Rotation Swing Trading”, flagged by a subscriber, Joel Bock and Akhilesh Maewal present a sector rotation strategy guided by multiple-input, multiple output deep learning model. The strategy chooses weekly from among 11 U.S. sectors using exchange-traded fund (ETF) proxies. Specifically, each week during each year, they:

• Train the machine learning model on the last two years of weekly (Friday close) historical sector ETF prices and volumes and sometimes auxiliary economic data (10-year U.S. Treasury yield, USD currency index, crude oil proxy and stock market volatility) to predict next-week opening and closing prices for each ETF.
• Compare the predicted return estimate for each ETF to a dynamically updated threshold return to screen for potential buys.
• Apply additional filters to screen out potential buys with unusual past losses to accommodate investor loss aversion.
• At the next-week open, allocate available capital to surviving sector ETFs based on respective past win rate (profitable trade) and respective past sector trade momentum.
• Liquidate all positions just prior to the next-week close.

Their benchmark is buying and holding the S&P 500 Index with reinvested dividends. Using weekly inputs as described during January 2012 through December 2022, they find that:

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Is there a way to restore/enhance the relevance to investors of the Fed model, which is based on a putative investor-driven positive relationship between stock market earnings yield (equity earnings-to-price ratio) and U.S. Treasury bond (10-year) yield? In his February 2023 paper entitled “The Fed Model: Is it Still With Us?”, David McMillan re-examines the predictive power of this relationship with the addition of regime shifts that may expose predictive power not persistent across the full sample. He considers three versions of the Fed model:

1. Fed1 – ratio of earnings yield to bond yield (yield ratio).
2. Fed2 – simple difference between earnings yield and bond yield (yield gap).
3. Fed3 – logarithmic version of Fed2 (log yield gap).

He tests the power of each model variation to predict stock market returns at horizons of 1, 3 and 12 months, either including or excluding earnings yield and the interest rate term structure (U.S. Treasury 10-year yield minus 3-month yield) as control variables. He considers two ways to detect regime shifts in each model variation: (1) regressing each series on a constant term and looking for a break in its value; and, (2) a Markov-switching approach. Using monthly S&P Composite index level and earnings, and 10-year and 3-month U.S. Treasury yields during January 1959 through December 2021, he finds that:

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A subscriber requested measurement of a “premium” associated with U.S. stocks relative to those of other developed markets by looking at the difference in returns between the following two exchange-traded funds (ETF):

• SPDR S&P 500 (SPY)
• iShares MSCI EAFE Index Fund (EFA)

Using monthly dividend-adjusted closing prices for these ETFs during August 2001 (limited by EFA) through January 2023, we find that: Keep Reading

How can researchers assess the true value and robustness of new stock return anomalies (predictors) in consideration for addition to the factor zoo? In their January 2023 paper entitled “Assaying Anomalies”, Robert Novy-Marx and Mihail Velikov present a protocol/tool set for dissecting and understanding newly proposed cross-sectional stock return predictors. The tools address the most important issues involved in testing asset pricing strategies, including some machine learning techniques. They pay particular attention to implementation costs that prevent exploitation of predictors with good gross returns (as with high turnover and/or overweighting small stocks). The tool set, including automated report generator, is available as a free web application and a public github repository. Key aspects of reports generated by this tool set are:

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Does aggregate insider stock buying and selling offer clues about future stock market returns? In their January 2023 paper entitled “Aggregate Insider Trading in the S&P 500 and the Predictability of International Equity Premia”, Andre Guettler, Patrick Hable, Patrick Launhardt and Felix Miebs investigate relationships between net aggregate insider trading and future stock market excess returns at horizons from one month to one year. They define net aggregate insider trading as unscheduled open market insider purchases minus sales, divided by purchases plus sales. They focus on S&P 500 firm insider trading and S&P 500 Index excess returns (relative to the U.S. Treasury bill yield). They also consider U.S. non-S&P 500 insider trading. They further look at insider trading and stock market excess returns within Canada, France, Germany, Great Britain and Italy. Using monthly aggregations of the specified insider trading data from 2iQ and monthly stock market index returns during January 2004 through December 2018, they find that:

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