Equity Premium

With monthly market state specified as positive (negative) when prior-month market excess return relative to U.S. Treasury bill (T-bill) yield is positive (negative), “Equity Factor Performance Following Positive and Negative Market Returns” reports that average monthly market excess return is 0.83% (10.0% annualized) positive market states and 0.05% (0.6% annualized) for negative states during August 1965 through January 2017. Is this finding reliable and easily exploitable? To check, we look at SPDR S&P 500 ETF Trust (SPY) monthly total returns after prior-month total returns are positive or negative out-of-sample with respect to the cited study. We also consider SPY excess returns according to whether its prior-month excess total returns are positive or negative. Using end-of-month SPY dividend-adjusted prices and monthly 3-month T-bill yield during January 2017 through June 2023, we find that:

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Do stock return anomalies perform differently after positive and negative monthly market returns? In their July 2023 paper entitled “The Market State, Mispricing and Asset Pricing Anomalies”, Michael Di Carlo and Ilias Tsiakas examine the role of the overall market state in estimating returns for stock return anomalies, specifying the market state as positive (negative) for a month when the market excess return relative to U.S. Treasury bill yield is positive (negative) the prior month. They then measure returns during each of the two states for 14 stock return anomalies, including: market beta, size, book-to-market, operating profitability, asset growth, momentum, short-term reversal, volatility, idiosyncratic volatility, correlation with the market, maximum return over the last month, maximum return over the past year, illiquidity and 1% value-at-risk. For each anomaly, they measure returns via a hedge portfolio that is each month long (short) the fifth, or quintile, of stocks with the highest (lowest) expected returns based on the relevant anomaly characteristic. Using the required monthly data for U.S. common stocks priced over $5 during August 1965 through January 2017, they find that: Keep Reading

Is the ability of the VIX percentile threshold rule described in “Using VIX and Investor Sentiment to Explain Stock Market Returns” to explain future stock market excess return in-sample readily exploitable out-of-sample? To investigate, we test a strategy (VIX Percentile Strategy) that each month holds SPDR S&P 500 ETF Trust (SPY) or 3-month U.S. Treasury bills (T-bills) according to whether a recent end-of-month level of the CBOE Volatility Index (VIX) is above or below a specified inception-to-date (not full sample) percentage threshold. To test sensitivities of the strategy to settings for its two main features, we consider:

• Each of 70th, 75th, 80th, 85th or 90th percentiles as the VIX threshold for switching between T-bills and SPY.
• Each of 0, 1, 2 or 3 skip months between VIX measurement and strategy response.

We focus on compound annual growth rate (CAGR) and maximum drawdown (MaxDD) as essential performance metrics and use buy-and-hold SPY as a benchmark. We do not quantify frictions due to switching between SPY and T-bills for the VIX Percentile Strategy. Using end-of-month VIX levels since January 1990 and dividend-adjusted SPY prices and T-bill yields since January 1993 (SPY inception), all through May 2023, we find that: Keep Reading

What characteristics of U.S. equity factor return series are most relevant to respective factor performance? In his May 2023 paper entitled “The Cross-Section of Factor Returns” David Blitz explores long-term average returns and market alphas, 60-month market betas and factor performance cyclicality for U.S. equity factors. He also assesses potentials of three factor rotation strategies: low-beta, seasonal and return momentum. Using monthly returns for 153 published U.S. equity market factors, classified statistically into 13 groups, during July 1963 through December 2021, he finds that:

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Do the stocks that dominate shareholder wealth-building (accounting for share price changes, dividends, repurchases/new share issuances and investor money flows) increasing concentrate within a small pool? In his May 2023 paper entitled “Shareholder Wealth Enhancement”, Hendrik Bessembinder identifies the stocks with the largest increases and largest decreases in shareholder wealth since 1926. He examines the degree to which increases in shareholder wealth concentrate among stocks over time. Using monthly data (including delisting returns) for 28,114 publicly traded U.S. common stocks and contemporaneous 1-month U.S. Treasury bill yield as a benchmark during 1926 through 2022, he finds that:

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What kind of return patterns are typical of beginnings and ends of equity bull and bear markets? In his April 2023 paper entitled “Investor Overreaction: Evidence From Bull and Bear Markets”, Valeriy Zakamulin examines return patterns of U.S. stock market bull and bear states as a way to decide when investors tend to overreact. He uses the S&P 500 Index as a proxy for the U.S. stock market. He applies a pattern recognition algorithm to: (1) identify index peaks and troughs; and, (2) ensure that a full bear-bull cycle lasts at least 16 months and bear or bull states last at least 5 months, unless the index rises or falls by more than 20%. He then standardizes the duration of each market state to 10 intervals and assumes that the bull or bear return evolves quadratically with state age. Because the available sample is relatively small, he applies bootstrapping to enhance reliability of findings. Using monthly S&P 500 Index returns (excluding dividends) during January 1926 through December 2022, he finds that: Keep Reading

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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