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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.

Equity Factor Timing from Deep Neural Networks

Can enhanced machine learning models accurately time popular equity factors? In their January 2024 paper entitled “Multi-Factor Timing with Deep Learning”, Paul Cotturo, Fred Liu and Robert Proner explore equity factor timing via a multi-task neural network model (MT) to capture the commonalities across factors and a dynamic multi-task neural network model (DMT) to extract financial and macroeconomic states. They attempt to time six well-known factors: (1) excess market return, size, value, profitability, investment and momentum. They employ 272 model inputs (123 macroeconomic and 149 financial) to predict each month:

  1. The sign of next-month return for each factor.
  2. The return for an equal-weighted portfolio that holds the factors (the risk-free asset) for factors with positive (negative) predicted returns.

The compare performances of MT and DMT with those of seven simpler off-the-shelf machine learning models: logistic regression (LR), penalized logistic regression (EN), random forest (RF), extremely randomized trees (XRF), gradient boosted trees (GBT), support vector machine (SVM) and feed-forward neural network (NN). For all models, they use the first 20 years of their sample period for training, the next five years for validation and the remaining years for out-of-sample testing. Their benchmark is an equal-weighted portfolio of all six factors. Using monthly data for the 272 model inputs and monthly returns for the six factors during January 1965 through December 2021, with out-of-sample testing starting January 1990, they find that: Keep Reading

Profitable Machine Learning Stock Picking Strategies?

Can machine learning models pick stocks that unequivocally generate alpha out-of-sample? In their November 2023 paper entitled “The Expected Returns on Machine-Learning Strategies”, Vitor Azevedo, Christopher Hoegner and Mihail Velikov assess expected net returns and alphas of machine learning-based anomaly trading strategies. They use nine machine learning models to predict next-month stock returns based on inputs for up to 320 published anomalies, added to the mix according to respective publication dates:

They train the models using an expanding window, with the last seven years reserved for six years of validation and one year of out-of-sample-testing. During the test year, they each month reform a portfolio that is long (short) the value-weighted tenth, or decile, of stocks with the highest (lowest) predicted next-month returns. They then calculate actual next-month gross returns and 6-factor (market, size, value, profitability, investment and momentum) alphas during the test year. To calculate net returns and alphas, they multiply trading frictions estimated from historical bid-ask spreads times monthly portfolio turnovers. Using returns and firm characteristics for a broad sample of U.S. common stocks having data covering at least 20% of the 320 anomalies during March 1957 through December 2021, with out-of-sample tests starting January 2005, they find that:

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Understandable AI Stock Pricing?

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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Causal Discovery Applications in Stock Investing

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

Party in Power and Stock Returns

Past research relating U.S. stock market returns to the party holding the Presidency mostly concludes that Democratic presidents are better for the stock market than Republican presidents. However, Presidents share power conferred by the electorate with Congress. Does historical data confirm that Democratic control of Congress is also better for stock market returns than Republican control of Congress? Is control of the smaller Senate more decisive than control of the House of Representatives? To check, we relate annual U.S. stock market (S&P 500 Index) returns to various combinations of party control of the Presidency, the Senate and the House of Representatives. Using party in power data and annual levels of the S&P 500 Index for December 1927 through December 2023 (96 years), we find that: Keep Reading

FFR Actions, Stock Market Returns and Bond Yields

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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U.S. Academic Research Extinguishing Global Stock Anomalies?

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

How Are Robotics-AI ETFs Doing?

How do exchange-traded-funds (ETF) focused on development of robotics-artificial intelligence (AI), an arguably hot area of technology, perform? To investigate, we consider five of the largest such ETFs, all currently available, as follows:

We use Invesco QQQ Trust (QQQ) as a benchmark, assuming investors look at robotics-AI stocks as a way to beat other technology stocks. We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly total returns for the five robotics-AI ETFs and QQQ as available through December 2023, we find that: Keep Reading

Focus on Global Factors?

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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Volatility-adjusted Retirement Income Streams

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

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