Equity Premium

Can investors safely use leverage to squeeze incremental return from low-volatility/factor-tilted stocks, thereby avoiding underperformance of these stocks during bull markets? In their October 2024 paper entitled “Low-Risk Alpha Without Low Beta”, David Blitz, Clint Howard, Danny Huang and Maarten Jansen exploit the low-volatility anomaly by leveraging multifactor, low-risk, global stock portfolios to a beta of 1.0 while controlling tracking error relative to a capitalization-weighted benchmark. Their portfolio formation rules are:

• The portfolio is long only and fully invested in liquid (large-capitalization) stocks.
• Maximum individual stock weight is the lower of 1.5% or 20 times its benchmark weight.
• Exposure to countries, regions and sectors may deviate at most 10% from benchmark weights.
• Portfolio beta (portfolio-weighted sum of historical stock betas for the last 156 weekly returns) must be less than 0.8 relative to the benchmark.
• Portfolio optimization involves trading off expected returns, benchmark tracking error and turnover. Expected stock returns derive from a multifactor score with 50% for low-risk (equal-weighted combination of past 260-day volatility, 156-week volatility, 260-day beta and 156-week beta), 16.67% for value (net payout yield), 16.67% for quality (gross profits to assets) and 16.67% for momentum (return from 12 months ago to one month ago).
• Use synthetic positions (for example, via equity options) to achieve leverage, with no cash collateral and financing costs equal to the risk-free rate.
• Rebalance at the end of each month but ignore slight deviations from target weights.

They separately discuss impacts of portfolio rebalancing frictions and additional leverage costs/penalties. They focus on developed markets but also look at an emerging markets sample and North American, European and Asia Pacific subsamples. Using daily and monthly data for developed market stocks since December 1985 and emerging market stocks since December 1995, all through December 2023, along with contemporaneous spreads and interest/Treasury bill rates, they find that: Keep Reading

A reader requested a test of the following hypothesis from the article “Gold’s Bluff – Is a 30 Percent Drop Next?” [no longer available]: “Ironically, gold is more than just a hedge against market turmoil. Gold is actually one of the most accurate indicators of the stock market’s long-term direction. The Dow Jones measured in gold is a forward looking indicator.” To test this assertion, we examine relationships between the spot price of gold and the level of the Dow Jones Industrial Average (DJIA). Using monthly data for the spot price of gold in dollars per ounce and DJIA over the period January 1971 through October 2024, we find that: Keep Reading

Can investors reasonably anticipate the signals (stock rankings) for stock anomalies that are based on firm financial information. In their August 2024 paper entitled “Predicting Anomalies”, Boone Bowles, Adam Reed, Matthew Ringgenberg and Jake Thornock investigate whether: (1) stock returns follow predictable patterns before availability of anomaly trading signals; and, (2) anomaly trading signals are themselves predictable. They focus on a set 28 published anomalies that are entirely based on publicly available information in quarterly financial statements. They each quarter for each anomaly reform a hedge portfolio that is long (short) the tenth of stocks with the highest (lowest) expected returns. They consider four models to predict stock rankings for each anomaly: (1) a first-order autoregression that projects strength of signals; (2) a first-order autoregression that projects stock rankings; (3) a machine learning model that uses past anomaly signals and rankings; and, (4) a (martingale) model that assumes anomaly portfolio rankings for next quarter will be the same as current rankings. Using as-published specifications for each of the 28 anomalies plus daily returns and quarterly/annual financial reports for a broad sample of U.S. stocks during January 1990 through December 2019, they find that: Keep Reading

Can market efficiency be falling despite ubiquitous data, computing and networking? In his August 2024 paper entitled “The Less-Efficient Market Hypothesis”, Clifford Asness argues that markets have become less efficient in the relative pricing of common stocks over recent decades. To make his argument, he relies on the ratio of expensive stock valuations to cheap stock valuations (the value spread). He considers two versions of this spread, one based on the conventional price-to-book ratio to measure value and the other based on five industry-neutral value metrics. He discusses three potential reasons why the value spread is rising. He closes with advice for value investors. Reflecting on 35 years of research experience, he concludes that:

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Why have stock return anomalies generally degraded over recent decades? In their August 2024 paper entitled “What Drives Anomaly Decay?”, Jonathan Brogaard, Huong Nguyen, Tālis Putniņš and Yuchen Zhang examine why stock return anomalies decay by:

• Decomposing returns into market-wide, public firm-specific and private firm-specific elements.
• Separating cash flow and discount rate effects within each of these three components.
• Accounting for noise.

This breakdown lets them determine whether changes in anomaly returns over time derive from anomaly publication, identifiable liquidity shocks (such as stock price decimalization) or a more general increase market efficiency. They apply this approach to daily returns of long-short (hedge) portfolios, reformed monthly, for 204 stock return anomalies from Open Source Asset Pricing. Using the required firm characteristics and daily prices for all NYSE/AMEX/NASDAQ common stocks during 1956 through 2021 (an average 4,029 firms per year and a total of 16,966 firms), they find that:

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Do changes in the Effective Federal Funds Rate (EFFR), the actual cost of short-term liquidity derived from a combination of market demand and Federal Reserve open market operations designed to maintain the Federal Funds Rate (FFR) target, predictably influence the U.S. stock market over horizons up to a few months? To investigate, we relate smoothed (volume-weighted median) monthly levels of EFFR to monthly U.S. stock market returns (S&P 500 Index or Russell 2000 Index) over available sample periods. Using monthly data as specified since July 1954 for EFFR and the S&P 500 Index (limited by EFFR) and since September 1987 for the Russell 2000 Index, all through August 2024, we find that: Keep Reading

Can machine learning exploit interactions between many equity factors and many potential factor return predictors to create an attractive factor timing strategy? In their August 2024 paper entitled “Optimal Factor Timing in a High-Dimensional Setting”, Robert Lehnherr, Manan Mehta and Stefan Nagel apply machine learning with mean-variance optimization to time equity factors when the numbers of factors and potential factor return predictors are large. They consider both a small set of four (size, book-to-market, profitability and investment) and a much larger set of 131 factors. They focus on a small set of 11 potential predictors (five economic variables and six specific to the small set of factors) but consider also a much larger set augmenting those 11 with many other factor specific variables. They simplify outputs by suppressing the weakest signals. Their machine learning process each year uses an expanding window of at least 20 years for training, one year for validation and one year for testing. They focus on Sharpe ratio as the essential performance metric. Their benchmarks are annually rebalanced: (1) equal weighting of factors; and, (2) straightforward mean-variance optimization of factors that ignores interactions between factors and potential predictors. To estimate net performance, they apply 0.1% portfolio reformation frictions at the portfolio of factors (not factor) level. Using monthly factor portfolio returns and economic variable values during January 1965 through December 2022, with 1986 the first year of portfolio testing, they find that: Keep Reading

How has the immediate price impact associated with a stock entering or leaving the S&P 500 evolved? In the March 2024 revision of their paper entitled “The Disappearing Index Effect”, Robin Greenwood and Marco Sammon revisit abnormal returns during the trading day after S&P 500 additions and deletions and investigate four potential drivers of findings. Using announcement dates, implementation dates and daily returns for 732 S&P 500 additions and 726 S&P 500 deletions, and holdings of large U.S. equity funds, during 1980 through 2020, they find that:

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Do stock markets following predictable long boom and bust periods? In the August 2024 draft of their paper entitled “The Anatomy of Lost Stock Market Decades”, Todd Feldman and Brian Yang examine the regularity/frequency of bull periods (strong gains) and lost periods (no gains) of at least 10 years. They also test two metrics to identify when the S&P 500 Index is in a bull or lost period: (1) the ratio of the S&P 500 Index level to a dividend discount model (DDM) valuation of the index; and, (2) an exponential cumulative loss metric calibrated via a 20-year moving average (weighting recent losses more than older losses to sharpen regime shift detection). Using monthly stock market levels from Global Financial Data for the U.S., Canada, Japan, Australia, Germany and France and Robert Schiller’s data for the S&P Composite Index from the 1800s through 2023, they find that:

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How does the performance of the global multi-class market look when evaluated at a monthly frequency? In their August 2024 paper entitled “The Risk and Reward of Investing”, Ronald Doeswijk and Laurens Swinkels assess global investing rewards and risks via an exhaustive $150 trillion portfolio of investable global assets priced at a monthly frequency, enabling greater granularity of risk estimates than does the annual frequency used in prior research. They consider five asset classes: equities, real estate, non-government bonds, government bonds and commodities. For these classes and the multi-class market, they examine stability of Sharpe ratios and severity, frequency and duration of drawdowns. Their default base currency is the U.S. dollar, but they measure effects of choosing one of nine other currencies on global market portfolio performance. They calculate excess investment returns generally relative to government bill yields as a proxy for return on savings. Using monthly returns for all investable global assets with reinvested dividends during 1970 through 2022, they find that:

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