Equity Premium

Is there a way to restore/enhance the relevance to investors of the Fed model, which is based on a putative investor-driven positive relationship between stock market earnings yield (equity earnings-to-price ratio) and U.S. Treasury bond (10-year) yield? In his February 2023 paper entitled “The Fed Model: Is it Still With Us?”, David McMillan re-examines the predictive power of this relationship with the addition of regime shifts that may expose predictive power not persistent across the full sample. He considers three versions of the Fed model:

1. Fed1 – ratio of earnings yield to bond yield (yield ratio).
2. Fed2 – simple difference between earnings yield and bond yield (yield gap).
3. Fed3 – logarithmic version of Fed2 (log yield gap).

He tests the power of each model variation to predict stock market returns at horizons of 1, 3 and 12 months, either including or excluding earnings yield and the interest rate term structure (U.S. Treasury 10-year yield minus 3-month yield) as control variables. He considers two ways to detect regime shifts in each model variation: (1) regressing each series on a constant term and looking for a break in its value; and, (2) a Markov-switching approach. Using monthly S&P Composite index level and earnings, and 10-year and 3-month U.S. Treasury yields during January 1959 through December 2021, he finds that:

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A subscriber requested measurement of a “premium” associated with U.S. stocks relative to those of other developed markets by looking at the difference in returns between the following two exchange-traded funds (ETF):

• SPDR S&P 500 (SPY)
• iShares MSCI EAFE Index Fund (EFA)

Using monthly dividend-adjusted closing prices for these ETFs during August 2001 (limited by EFA) through January 2023, we find that: Keep Reading

How can researchers assess the true value and robustness of new stock return anomalies (predictors) in consideration for addition to the factor zoo? In their January 2023 paper entitled “Assaying Anomalies”, Robert Novy-Marx and Mihail Velikov present a protocol/tool set for dissecting and understanding newly proposed cross-sectional stock return predictors. The tools address the most important issues involved in testing asset pricing strategies, including some machine learning techniques. They pay particular attention to implementation costs that prevent exploitation of predictors with good gross returns (as with high turnover and/or overweighting small stocks). The tool set, including automated report generator, is available as a free web application and a public github repository. Key aspects of reports generated by this tool set are:

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Does aggregate insider stock buying and selling offer clues about future stock market returns? In their January 2023 paper entitled “Aggregate Insider Trading in the S&P 500 and the Predictability of International Equity Premia”, Andre Guettler, Patrick Hable, Patrick Launhardt and Felix Miebs investigate relationships between net aggregate insider trading and future stock market excess returns at horizons from one month to one year. They define net aggregate insider trading as unscheduled open market insider purchases minus sales, divided by purchases plus sales. They focus on S&P 500 firm insider trading and S&P 500 Index excess returns (relative to the U.S. Treasury bill yield). They also consider U.S. non-S&P 500 insider trading. They further look at insider trading and stock market excess returns within Canada, France, Germany, Great Britain and Italy. Using monthly aggregations of the specified insider trading data from 2iQ and monthly stock market index returns during January 2004 through December 2018, they find that:

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Can investors exploit information about business credit tightening/loosening as reported since 1990 in the Federal Reserve’s quarterly Senior Loan Officer Survey to time the U.S. stock market? In the January 2023 draft of his paper entitled “Profitable Timing of the Stock Market with the Senior Loan Officer Survey”, Linus Wilson examines the power of “Net Percentage of Domestic Banks Tightening Standards for Commercial and Industrial Loans to Large and Middle-Market Firms” to predict S&P 500 Index next-quarter returns. A positive (negative) reading means that credit conditions are tightening (loosening) for large and medium-sized firms. Specifically, he relates January survey results to subsequent April-June stock market returns, May survey results to July-September returns, August survey results to October-December returns and November survey results to January-March returns. He considers the full sample of 32 years, two subperiods of 15 years and three subperiods of 10 years. For portfolio tests, he uses the first 15-year subperiod to model allocation decisions to the S&P 500 Index/3-month U.S. Treasury bills (either long-short the stock index or long-only the index) and applies the model to a July 2005 through March 2022 test period. Using quarterly survey results, monthly S&P 500 Index levels and monthly estimated S&P 500 dividends (from Shiller’s data) during April 1990 through March 2022, he finds that: Keep Reading

A subscriber requested confirmation that a strategy of holding SPDR S&P 500 ETF Trust (SPY) at all times except options expiration week beats holding SPY all the time. To investigate, we look at holding SPY at all times except from the close on the second Friday of each month to the close on the third Friday of each month (Strategy). When the market is closed on Friday, we use the Thursday or next earliest close. We focus on compound annual growth rate (CAGR) and maximum drawdown (MaxDD) as essential performance statistics. We apply round-trip trading frictions of 0.1% for SPY-cash switches. Given settlement/cash-sweep delays, we assume zero return on cash. Using daily dividend-adjusted closes of SPY from inception in January 1993 through December 2022, we find that: Keep Reading

A subscriber asked about an assertion that bitcoin (BTC) price trend/return predicts return of the S&P 500 Index (SP500). To investigate, we relate BTC returns to SP500 returns at daily, weekly and monthly frequencies. We rationalize the different trading schedules for these two series by excluding BTC trading dates that are not also SP500 trading days. Most results are conceptual, but we test three versions of an SP500 timing strategy based on prior BTC returns focused on compound annual growth rate (CAGR) and maximum drawdown (MaxDD). Using daily SP500 levels and (pruned) BTC prices during 9/17/2014 (limited by the BTC series) through 12/21/2022, we find that:

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A subscriber requested evaluation of a strategy that seeks to exploit U.S stock market reversion after dips by temporarily applying margin. Specifically, the strategy:

• At all times holds the U.S. stock market.
• When the stock market closes down more than 7% from its high over the past year, augments stock market holdings by applying 50% margin.
• Closes each margin position after two months.

To investigate, we assume:

• The S&P 500 Index represents the U.S. stock market for calculating drawdown over the past year (252 trading days).
• SPDR S&P 500 (SPY) represents the market from a portfolio perspective.
• We start a margin augmentation at the same daily close as the drawdown signal by slightly anticipating the drawdown at the close.
• 50% margin is set at the opening of each augmentation and there is no rebalancing to maintain 50% margin during the two months (42 trading days) it is open.
• If S&P 500 Index drawdown over the past year is still greater than 7% after ending a margin augmentation, we start a new margin augmentation at the next close.
• Baseline margin interest is U.S. Treasury bill (T-bill) yield plus 1%, debited daily.
• Baseline one-way trading frictions for starting and ending margin augmentations are 0.1% of margin account value.
• There are no tax implications of trading.

We use buying and holding SPY without margin augmentation as a benchmark. Using daily levels of the S&P 500 Index, daily dividend-adjusted SPY prices and daily T-bill yields from the end of January 1993 (limited by SPY) through November 2022, we find that: Keep Reading

A subscriber asked whether currency exchange rates exhibit reliable seasonality that may be used to time equities (with a stronger currency implying lower asset prices). To investigate, we look for reliable calendar month effects for the U.S. dollar (USD)-euro exchange rate and for Invesco DB US Dollar Index Bullish Fund (UUP). We further look at how monthly returns for these variables relate to those for SPDR S&P 500 ETF Trust (SPY) as a proxy for the U.S. stock market. Using monthly data for the USD-euro exchange rate since January 1999 and for UUP since March 2007, and corresponding data for SPY, all through November 2022, we find that: Keep Reading

Are models based on advanced machine learning adept at predicting returns for individual emerging market stocks? In the November 2022 version of their paper entitled “Machine Learning and the Cross-section of Emerging Market Stock Returns”, Matthias Hanauer and Tobias Kalsbach compare abilities of machine learning models to predict emerging market stock returns. They consider nine alternatives: two traditional linear models (ordinary least squares and elastic net); two tree-based models (gradient boosted regression trees and random forest); and, five neural networks (one to five layers). Tree-based methods and neural networks identify non-linearities and variable interactions. They further consider a combination of the five neural networks and a combination of all tree-based plus neural network methods. For each model at the end of each month, they rank stocks into country-neutral fifths, or quintiles, based on next-month expected returns and reform a portfolio that is long (short) the quintile with the highest (lowest) expected returns. For tests of long-only net performance, they assume 1-way trading frictions are half the estimated bid-ask spread and apply trading cost mitigation rules. Using returns and 36 accounting/trading variables for 15,152 unique stocks from 32 emerging market countries as included in the MSCI Emerging Markets Index during July 1995 through December 2021 (with out-of-sample testing starting January 2002), they find that:

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