Equity Premium

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

Is the the conventional retirement portfolio glidepath as recommended by many financial advisors, away from stocks and toward bonds over time, really optimal? In their October 2023 paper entitled “Beyond the Status Quo: A Critical Assessment of Lifecycle Investment Advice”, Aizhan Anarkulova, Scott Cederburg and Michael O’Doherty present a lifecycle income/wealth model using stationary block bootstrap simulations (average block length 120 months to preserve long-term behaviors) with labor income uncertainty, Social Security income, longevity uncertainty and historical monthly returns for stock indexes, government bonds and government bills across developed countries. They apply this model to estimate outcomes for several age-dependent, monthly rebalanced portfolios of stocks and bonds, including a representative target-date fund (TDF), as well as some fixed-percentage allocation strategies. They focus on a U.S. couple (a female and a male) who save during working years starting at age 25 and consume Social Security income and savings starting at age 65 with constant real 4% annual withdrawals. They evaluate four outcomes: (1) wealth at retirement; (2) retirement income; (3) conservation of savings; and, (4) bequest at death. Using monthly (local) real returns for domestic stock indexes, international stock indexes, government bonds and government bills as available for 38 developed countries during 1890 through 2019, they find that:

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The “Simple Asset Class ETF Value Strategy” (SACEVS) seeks diversification across a small set of asset class exchanged-traded funds (ETF), plus a monthly tactical edge from potential undervaluation of three risk premiums:

1. Term – monthly difference between the 10-year Constant Maturity U.S. Treasury note (T-note) yield and the 3-month Constant Maturity U.S. Treasury bill (T-bill) yield.
2. Credit – monthly difference between the Moody’s Seasoned Baa Corporate Bonds yield and the T-note yield.
3. Equity – monthly difference between S&P 500 operating earnings yield and the T-note yield.

Premium valuations are relative to historical averages. How might this strategy react to changes in the Effective Federal Funds Rate (EFFR)? Using end-of-month values of the three risk premiums, EFFR, total 12-month U.S. inflation and core 12-month U.S. inflation during March 1989 (limited by availability of operating earnings data) through September 2023, we find that: Keep Reading

Prior research indicates that stocks of firms with high direct and indirect carbon dioxide emissions tend to beat the market (offer a carbon premium). Does high-emissions stock outperformance derive from surprisingly high earnings? In their September 2023 paper entitled “Does the Carbon Premium Reflect Risk or Mispricing?”, Yigit Atilgan, Ozgur Demirtas, Alex Edmans and Doruk Gunaydin examine relationships between firm carbon dioxide emissions and future earnings surprises. They consider three levels of emissions from S&P Global Trucost: Scope 1 directly from firm operations; Scope 2 from firm consumption of purchased heat/electricity/steam; and, Scope 3 from upstream supply chain operations. They consider level of emissions (natural logarithm of emissions measured in tons) and annual change in level of emissions, with the latter winsorized at the 2.5% level. They consider several measures of earnings surprises, all comparing analyst forecasts to actual earnings. They calculate market reactions to earnings announcements as 3-day cumulative abnormal returns (CAR) relative to a 3-factor (market, size, book-to-market) model the day before through the day after earnings announcements. Using carbon dioxide emissions data, stock returns, market valuations, book values and analyst earnings forecasts for a broad sample of U.S. stocks during 2002 through 2021, they find that: Keep Reading

Are concentrated stock portfolios inherently disadvantaged by lack of diversification? In his June 2023 paper entitled “Underperformance of Concentrated Stock Positions”, Antti Petajisto analyzes rolling future returns for individual U.S. stocks relative to the broad U.S. stock market (market-adjusted) as a way to assess implications of concentrated stock portfolios. He focuses on median return as most representative of investor experience. He considers monthly rolling investment horizons of five, 10 and 20 years because concentrated stock positions are typically long-term holdings. He looks also at the relationship between 5-year past returns and future returns for individual stocks. Using monthly returns for individual U.S. common stocks from an evolving sample similar to the Russell 3000 (no microcaps) and for the overall capitalization-weighted U.S. stock market during January 1926 through December 2022, he finds that:

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Are new machine learning portfolio strategies practically better than old stock factor ways? In their August 2023 paper entitled “Predicting Returns with Machine Learning Across Horizons, Firms Size, and Time”, Nusret Cakici, Christian Fieberg, Daniel Metko and Adam Zaremba examine the ability of various machine learning models to predict stock returns for: (1) monthly and annual return forecast horizons; (2) three ranges of firm size; and, (3) two subperiods. They apply eight machine learning models (including simple and penalized linear regressions, dimension reduction techniques, regression trees and neural networks) to 153 firm/stock characteristics following approaches typical in the finance literature. For each model, they employ rolling 11-year intervals, with:

• Model training using the first seven years.
• Model validation using the next three years.
• Out-of-sample testing the last year using hedge portfolios that are long (short) the value-weighted fifth, or quintile, of stocks with the highest (lowest) predicted returns, reformed either monthly or annually depending forecast horizon.

They focus on gross 6-factor (market, size, book-to-market, profitability, investment, momentum) alpha to assess machine learning effectiveness. Using data for the selected 153 firm/stock characteristics and associated stock returns, measured monthly, for all listed U.S. stocks during January 1972 through December 2020, they find that: Keep Reading

The conventional approach to measuring equity factor returns is via hedge portfolios that are long (short) the equal-weighted or value-weighted extreme highest (lowest) fifth or tenth of stocks sorted by some firm/stock characteristic. Is there a better way? In their August 2023 paper entitled “Power Sorting”, Anastasios Kagkadis, Harald Lohre, Ingmar Nolte, Sandra Nolte and Nikolaos Vasilas construct equity factor portfolios based on power sorting, which: (1) models the firm characteristic-future stock return relationship using a power series; and, (2) uses the power series to set factor portfolio weights. This approach requires no arbitrary quantile break points, instead allocating some weight to all stocks and tilting toward/away stocks with extreme characteristics as a compromise between conventional sorts and machine learning methods. Power sorting employs separate parameters for the long and short sides of the factor portfolio. Higher parameter values generate portfolios that concentrate more in stocks with characteristic extremes, while lower values spread weights more evenly across stocks. Differences between the two parameters allow differently weighted long and short sides of a factor portfolio. Additionally, they set an upper limit on the allocation to any one stock (2% in their main analysis) to ensure factor portfolio diversification. Using monthly factor data and associated stock returns for 85 widely accepted factor characteristics during March 1980 through December 2021, they find that:

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Should investors trust artificial intelligence (AI) models such as ChatGPT to pick stocks? In their August 2023 paper entitled “ChatGPT-based Investment Portfolio Selection”, Oleksandr Romanko, Akhilesh Narayan and Roy Kwon explore use of ChatGPT to recommend 15, 30 or 45 S&P 500 stocks, with portfolio weights, based on textual sentiment as available to Chat GPT via web content up to September 2021. For robustness, they ask ChatGPT to repeat recommendations for each portfolios 30 times and select the 15, 30 or 45 most frequently recommended stocks for respective portfolios. They then test out-of-sample performance of the following five implementations of each portfolio during September 2021 to July 2023, mid-March 2023 to July 2023, and May 2023 to July 2023:

1. ChatGPT picks and ChatGPT weights.
2. ChatGPT picks weighted equally.
3. ChatGPT picks weighted based on minimum variance (Min Var) weights from a 5-year rolling weekly history.
4. ChatGPT picks weighted based on maximum return (Max Ret) weights from a 5-year rolling weekly history.
5. ChatGPT picks weighted based on maximum Sharpe ratio (Max Sharpe) weights from a 5-year rolling weekly history.

For benchmarking, they consider:

• Long-only portfolios that incorporate all possible combinations of 15, 30 or 45 S&P 500 stocks weighted as above for Min Var, Vax Ret or Max Sharpe.
• The S&P 500 Index, Dow Jones Industrial Average and the NASDAQ Index.
• Average performance of 13 popular equity funds.

Using weekly data as specified up to September 2021 for training and subsequent weekly data through June 2023 for out-of-sample testing, they find that:

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