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Equity Premium

Governments are largely insulated from market forces. Companies are not. Investments in stocks therefore carry substantial risk in comparison with holdings of government bonds, notes or bills. The marketplace presumably rewards risk with extra return. How much of a return premium should investors in equities expect? These blog entries examine the equity risk premium as a return benchmark for equity investors.

Are Equity Momentum ETFs Working?

Are stock and sector momentum strategies, as implemented by exchange-traded funds (ETF), attractive? To investigate, we consider nine momentum-oriented equity ETFs, all currently available, in order of longest to shortest available histories:

We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). We assign broad market benchmark ETFs according to momentum fund descriptions. Using monthly dividend-adjusted returns for the nine momentum funds and respective benchmarks as available through April 2023, we find that: Keep Reading

Are IPO ETFs Working?

Are exchange-traded funds (ETF) focused on Initial Public Offerings of stocks (IPO) attractive? To investigate, we consider three of the largest IPO ETFs and one recent Special Purpose Acquisition Company (SPAC) ETF, all currently available with moderate trading volumes, in order of longest to shortest available histories:

We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). For all these ETFs, we use SPDR S&P 500 (SPY) as the benchmark. Using monthly returns for the IPO ETFs and SPY as available through April 2023, we find that:

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Shapes of U.S. Stock Market Bull and Bear States

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

Expert Estimates of 2023 Country Equity Risk Premiums and Risk-free Rates

What are current estimates of equity risk premiums (ERP) and risk-free rates around the world? In their April 2023 paper entitled “Survey: Market Risk Premium and Risk-Free Rate used for 80 countries in 2023”, Pablo Fernandez, Diego García de la Garza and Javier Acin summarize results of a March 2023 email survey of international economic professors, analysts and company managers “about the Risk-Free Rate and the Market Risk Premium (MRP) used to calculate the required return to equity in different countries.” Results are in local currencies. Based on 3,812 specific and credible premium estimates spanning 80 countries for which there are at least six estimates, they find that: Keep Reading

Best Equity Risk Premium

What are the different ways of estimating the equity risk premium, and which one is best? In the March 2023 update of his paper entitled “Equity Risk Premiums (ERP): Determinants, Estimation and Implications – The 2023 Edition”, Aswath Damodaran updates a comprehensive overview of equity risk premium estimation and application. He examines why different approaches to estimating the premium disagree and how to choose among them. Using data from multiple countries (but focusing on the U.S.) over long periods through the end of 2022, he concludes that: Keep Reading

Factor Zoo Shrinking?

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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Benefit of Complexity in Machine Learning Models

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

Suppressing Long-side Factor Premium Frictions

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

Constructing and Deconstructing ESG Performance

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 distanceprincipal 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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Performance of Defined Outcome ETFs

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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