Equity Premium

Can explainable artificial intelligence (AI) bridge the gap between complex machine learning predictions and economically meaningful interpretations? In their December 2023 paper entitled “Empirical Asset Pricing Using Explainable Artificial Intelligence”, Umit Demirbaga and Yue Xu apply explainable artificial intelligence to extract the drivers of stock return predictions made by four machine learning models: XGBoost, decision tree, K-nearest neighbors and neural networks. They use 209 firm/stock-level characteristics and stock returns, all measured monthly, as machine learning inputs. They use 70% of their data for model training, 15% for validation and 15% for out-of-sample testing. They consider two explainable AI methods:

1. Local Interpretable Model-agnostic Explanations (LIME) – explains model predictions by approximating the complex model locally with a simpler, more interpretable model.
2. SHapley Additive exPlanations (SHAP) – uses game theory to determine which stock-level characteristics are most important for predicting returns.

They present a variety of visualizations to help investors understand explainable AI outputs. Using monthly data as described for all listed U.S stocks during March 1957 through December 2022, they find that:

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Can causal discovery algorithms (which look beyond simple statistical association, and instead consider all available data and allow for lead-lag relationships) make economically meaningful contributions to equity investing? In their December 2023 paper entitled “Causal Network Representations in Factor Investing”, Clint Howard, Harald Lohre and Sebastiaan Mudde assess the economic value of a representative score-based causal discovery algorithm via causal network representations of S&P 500 stocks for three investment applications:

1. Generate causality-based peer groups (e.g., to account for characteristic concentrations) to neutralize potentially confounding effects in long-short equity strategies across a variety of firm/stock characteristics.
2. Create a centrality factor represented by returns to a portfolio that is each month long (short) peripheral (central) stocks.
3. Devise a monthly network topology density market timing indicator.

Using daily and monthly data for S&P 500 stocks and monthly returns for widely used equity factors during January 1993 through December 2022, they find that: Keep Reading

Do Federal Funds Rate (FFR) actions taken by the Federal Reserve open market operations committee reliably predict stock market and U.S. Treasuries yield reactions? To investigate, we use the S&P 500 Index (SP500) as a proxy for the stock market and the yield for the 10-Year U.S. Constant Maturity Treasury note (T-note). We look at index returns and changes in T-note yield during the one and two months after FFR actions, separately for FFR increases and FFR decreases. Using data for the three series during January 1990 through December 2023, we find that:

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Does publication of academic studies on stock return anomalies in the U.S. tend to extinguish these anomalies in global markets? In their November 2023 paper entitled “Does U.S. Academic Research Destroy the Predictability of Global Stock Returns?”, Guohao Tang, Yuwei Xie and Lin Zhu compare out-of-sample (post-research sample) and post-publication global returns to research-sample global returns for 87 factors described in U.S. journals. The global sample includes 38 country markets (22 developed and 16 developing). The 87 factors include those based on momentum, value, investment, profitability, intangibles and trading frictions. For each factor each month, they reform a portfolio that is long (short) the fifth of stocks expected to have the highest (lowest) next-month returns. They weight stocks in each portfolio either equally or by market capitalization according to the approach used in the associated published paper. Using data required to compute monthly returns for 87 anomalies across 38 countries with research sample end dates after 2000 during January 1990 through December 2020, they find that: Keep Reading

Should investors focus on global equity factors or local (country) equity factors when trying to predict their local market returns? In their November 2023 paper entitled “How Global is Predictability? The Power of Financial Transfer Learning”, Oliver Hellum, Lasse Heje Pedersen and Anders Rønn-Nielsen compare the importance of global factors versus local factors for predicting local stock market returns in 35 countries. They generate optimal local and global factor models using the generalized elastic net usually trained in an early subsample and tested in a later subsample. They perform an array of tests:

• For each country, they compare predictive powers of local and global factor models optimized pre-2000 and tested during 2000-2021.
• For each country, they compare predictive powers of local and U.S. factor models optimized pre-2000 and tested during 2000-2021.
• They check the predictive power of a non-U.S. factor model optimized during 1982-2021 and tested in the U.S. during 1926-1981.

Using trimmed monthly returns in U.S. dollars and most of the 153 firm characteristics (inputs) used in prior research for broad samples of firms/stocks since 1926 for the U.S. and since 1982 as available for 34 other countries, all through 2021, they find that:

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Should investors consider portfolio volatility when choosing allocations to stocks and bonds in their retirement accounts? In his October 2023 paper entitled “Retirement Planning: The Volatility-Adjusted Coverage Ratio”, Javier Estrada introduces volatility-adjusted coverage ratio (VAC) as an alternative retirement portfolio metric. He defines this metric as coverage ratio (C, number of years of withdrawals supported relative to retirement period length) divided by annual portfolio volatility during retirement. He compares optimal stocks-bonds allocations for different fixed real annual withdrawal rates across 22 country markets and the world market using either C of VAC. For all markets and withdrawal rates, he uses historical returns for stocks and bonds with annual portfolio rebalancing and 30-year retirement periods. Using annual returns for stocks and bonds and annual inflation rates in the U.S. during 1872 through 2022 (Shiller data) and in 21 other countries during 1900 through 2019 (Dimson-Marsh-Staunton data), he finds that: Keep Reading

Is there a clearly superior multi-factor model of next-month stock returns? In the November 2023 revision of their paper entitled “A Quantum Leap in Asset Pricing: Explaining Anomalous Returns”, James Kolari, Jianhua Huang, Wei Liu and Huiling Liao compare abilities of the following eight multi-factor models of stock returns to explain 133 stubbornly persistent stock return anomalies via out-of-sample (one-month-ahead) cross-sectional regression tests:

1. Capital Asset Pricing Model (CAPM, 1-factor)
2. Fama-French 3-factor model (FF3, adding size and book-to-market)
3. Carhart 4-factor model (adding momentum to FF3)
4. Fama-French 5-factor model (FF5, adding profitability and investment to FF3)
5. Fama-French 6-factor model (FF6, adding momentum to FF5)
6. Hou-Xue-Zhang 4-factor model (market, size, profitability, investment)
7. Stambaugh-Yuan 4-factor model (market, size, management, performance)
8. Kolari-Liu-Huang ZCAPM (market, return dispersion)

They specify return dispersion as the standard deviation of daily returns across all stocks aggregated over the past year. They call dependence of each stock’s return on this metric the stock’s zeta (analogous to beta for the interaction of a stock’s return with the market return). The goal of the study is to identify the model that best account for those pricing anomalies that are historically most difficult to explain. Using publicly available daily return data for 133 stock return anomalies and for the factors used in the above multi-factor models as available during July 1972 through December 2021, they find that: Keep Reading

Can investors reliably time the market, size, value and profitability long-short equity factor premiums? In their October 2023 paper entitled “Another Look at Timing the Equity Premiums”, Wei Dai and Audrey Dong test strategies that time these four premiums in U.S., developed ex-U.S. and emerging equity markets. They define the premiums as:

1. Market – the capitalization-weighted market return minus the U.S. Treasury bill yield.
2. Size – average return on small-capitalization stocks minus average return on large-capitalization stocks.
3. Value – average return on value stocks minus average return on growth stocks.
4. Profitability – average return on stocks of high-profitability firms minus average return on stocks of low-profitability firms.

They time each premium separately based on each of:

1. Valuation ratio – When the difference in aggregate price-to-book ratio between the long and short sides of a premium becomes high (low) relative to its historical distribution, switch to the short (long) side.
2. Mean reversion – When the premium itself becomes high (low) relative to its historical distribution, switch to the short (long) side  of the premium.
3. Momentum – When the premium over the last year becomes relatively high (low), switch to the long (short) side of the premium.

To measure historical premium distributions, they consider an expanding window of initial length 10 years or a rolling 10-year window. For switching to the short side of premiums, they consider historical distribution thresholds of top 10%, 20% or 50% (bottom 10%, 20% or 50%) for valuation ratio and mean reversion (momentum). For switching to the long side of premiums, they consider thresholds of bottom 10%, 20% or 50% (top 50%) for valuation ratio and mean reversion (momentum). They consider  monthly or annual portfolio rebalancing. The number of timing strategies tested is thus 720. For the U.S. sample, monthly returns start in July 1963 for profitability and July 1927 for the other three premiums. For the developed ex-U.S. (emerging markets) sample, premium returns start in July 1990 (July 1994). Benchmarks are returns to strategies that continuously hold just the long side of each premium portfolio. Using monthly data as specified through December 2022, they find that: Keep Reading

The number of published factors significantly explaining variation in individual stock returns has grown steadily over time into the hundreds, inviting the term “factor zoo.” Are all these factors important when applied in combination? In their October 2023 paper entitled “Factor Zoo”, Alexander Swade, Matthias Hanauer, Harald Lohre and David Blitz assess compressibility of the factor zoo by starting with the market factor and then adding one-at-a-time via iterative regressions the factor explaining the largest amount of residual (unexplained) alpha, until the incremental alpha explained by adding a factor is no longer significant. For each factor in their main analysis, they each month calculate its return by: (1) sorting stocks based on the factor; (2) forming a portfolio that is long (short) the third of stocks with the the highest (lowest) expected returns; and, (3) holding the portfolio for one month. They weight stocks in these portfolios based on market valuation capped at the 80th percentile of NYSE valuations (but consider simple value-weighted and equal-weighted portfolios in robustness tests). Using monthly returns for 153 known U.S. equity factors during November 1971 through December 2021, they find that:

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Do conventional market capitalization-weighted stock indexes suffer from a long-term buy-high/sell-low performance drag when adding and deleting stocks? In their October 2023 paper entitled “Reimagining Index Funds”, Robert Arnott, Chris Brightman, Xi Liu and Que Nguyen construct alternative indexes that select stocks based on fundamental measures of underlying firm size and then weight them by market capitalization (Fundamental-selection Cap-weighted, FS-CW). Specifically, the each March:

• For each firm, calculate four fundamental measures of firm size as percentages of aggregate values for all U.S. firms:
  1. Current book value adjusted for intangibles.
  2. 5-year trailing average sales adjusted for the equity-to-asset ratio.
  3. 5-year trailing average cash flow plus R&D expenses.
  4. 5-year trailing average dividend plus share repurchases.
• For each firm, average these four measures.
• Rank stocks of these firms based on their respective averages.
• Reform equal-weighted indexes of the top 500 (FS-CW 500) or the top 1000 (FS-CW 1000) stocks.

For perspective, they also reform at the end of each June a portfolio of the top 500 stocks selected purely based on market capitalization (True CW 500). They then compare returns and 4-factor (adjusting for market, size, book-to-market and momentum) alphas of the Russell 1000, True CW 500, FS-CW 500 and FS-CW 1000 measured relative to the S&P 500. Using monthly data as described above for all publicly traded U.S. stocks, S&P 500, Russell 1000 and the four stock factors to support backtesting from July 1991 through December 2022, they find that: Keep Reading