Equity Premium

Which equity factor model is best among non-U.S. global stock markets? In other words, what market/accounting variables are most important to investors screening non-U.S. stocks? In his February 2020 paper entitled “A Comparison of Global Factor Models”, Matthias Hanauer compares eight widely used equity factor models on a common dataset spanning stocks from 47 non-U.S. developed and emerging markets based on gross Sharpe ratio. The models are:

1. The Capital Asset Pricing Model (CAPM) – market.
2. FF3 (3-factor) – market, size, book-to-market.
3. FF5 (5-factor) – adds profitability based on operating profits-to-book equity and investment to FF3.
4. FF6 (6-factor) – adds momentum to FF5.
5. FF6_CP (6-factor) – substitutes cash-based operating profits-to-assets for the profitability factor used in FF6.
6. HXZ4, or q-factor (4-factor) – market, size, profitability based on return-on-equity (ROE), investment.
7. SY4, or Mispricing (4-factor) – market, size, management, performance.
8. FF6_CP,m (6-factor) – substitutes a monthly value factor for the annual value factor in FF6_CP.

He employs annual accounting data because quarterly data are unavailable in many countries at the beginning of my sample period. Using factor input and return data for 56,171 stocks across developed and emerging markets during 1990 through 2018, he finds that: Keep Reading

Has 24-hour trading of equity index futures created a reliable pattern in hour-by-hour returns? In their February 2020 preliminary paper entitled “The Overnight Drift”, Nina Boyarchenko, Lars Larsen and Paul Whelan study round-the-clock U.S. stock market performance decomposing S&P 500 Index futures returns by hour, with focus on dealer inventory management. Using 24-hour high-frequency trades and quotes for S&P 500 futures contracts during January 1998 through December 2018, they find that: Keep Reading

Does success in the U.S. equity market depend on an ever- shrinking percentage of outperforming stocks? In his February 2020 paper entitled “Wealth Creation in the U.S. Public Stock Markets 1926 to 2019”, Hendrik Bessembinder updates his analysis of wealth creation in excess of 1-month U.S. Treasury bills (T-bills) across U.S. stocks since 1926 by adding 2017-2019. Wealth creation differs from market capitalization by accounting for all cash flows to and from shareholders via new share issuances, share repurchases and dividends not reinvested in stocks. Using price, share issuance/repurchase and dividend data for 26,168 U.S. stocks and the T-bill yield during 1926 through 2019, he finds that:

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Why does the coincident relationship between U.S. aggregate corporate earnings growth and stock market return change from negative in older research to positive in recent research? In their January 2020 paper entitled “Assessing the Structural Change in the Aggregate Earnings-Returns Relation”, Asher Curtis, Chang‐Jin Kim and Hyung Il Oh examine when the change in the aggregate earnings growth-market returns relationship occurs. They then examine factors explaining the change based on asset pricing theory (expected cash flow and expected discount rate). They calculate aggregate earnings growth as the value-weighted average of year-over-year change in firm quarterly earnings scaled by beginning-of-quarter stock price. They consider only U.S. firms with accounting years ending in March, June, September or December, and they exclude firms with stock prices less than $1 and firms in the top and bottom 0.5% of quarterly earnings growth. They calculate corresponding quarterly stock market returns from one month prior to two months after fiscal quarter ends to capture earnings announcement effects. Using quarterly earnings and returns data as specified for a broad sample of U.S. public firms from the first quarter of 1970 through the fourth quarter of 2016, they find that:

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How does execution delay affect the performance of the Best Value and Weighted versions of the “Simple Asset Class ETF Value Strategy” (SACEVS)? These strategies each month allocate funds to the following asset class exchange-traded funds (ETF) according to valuations of term, credit and equity risk premiums, or to cash if no premiums are undervalued:

3-month Treasury bills (Cash)
iShares 20+ Year Treasury Bond (TLT)
iShares iBoxx $ Investment Grade Corporate Bond (LQD)
SPDR S&P 500 (SPY)

To investigate, we compare 22 variations of each strategy with execution days ranging from end-of-month (EOM) per the baseline strategy to 21 trading days after EOM (EOM+21). For example, an EOM+5 variation computes allocations based on EOM but delays execution until the close five trading days after EOM. We include a benchmark that each month allocates 60% to SPY and 40% to TLT (60-40) to see whether variations are unique to SACEVS. We focus on gross compound annual growth rate (CAGR), maximum drawdown (MaxDD) and annual Sharpe ratio as key performance statistics. Using daily dividend-adjusted closes for the above ETFs from the end of July 2002 through January 2020, we find that:

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A subscriber requested verification of findings in “Smart Money Indicator for Stocks vs. Bonds”, where the Smart Money Indicator (SMI) is a complicated variable that exploits differences in futures and options positions in the S&P 500 Index, U.S. Treasury bonds and 10-year U.S. Treasury notes between institutional investors (smart money) and retail investors (dumb money). To verify, we simplify somewhat the approach for calculating and testing SMI, as follows:

• Use a “modern” sample of weekly Traders in Financial Futures; Futures-and-Options Combined Reports from CFTC, starting in mid-June 2006 and extending into early February 2020.
• For each asset, take Asset Manager/Institutional positions as the smart money and Non-reporting positions as the dumb money.
• For each asset, calculate weekly net positions of smart money and dumb money as longs minus shorts. 
• For each asset, use a 52-week lookback interval to calculate weekly z-scores of smart and dumb money net positions (how unusual current net positions are). This interval should dampen any seasonality.
• For each asset, calculate weekly relative sentiment as the difference between smart money and dumb money z-scores.
• For each asset, use a 13-week lookback interval to calculate recent maximum/minimum relative sentiments between smart money and dumb money for all three inputs. The original study reports that short intervals work better than long ones, and 13 weeks is a quarterly earnings interval.
• Use a 13-week lookback interval to calculate final SMI as described in “Smart Money Indicator for Stocks vs. Bonds”.

We perform three kinds of tests to verify original study findings, using dividend-adjusted SPDR S&P 500 (SPY) as a proxy for a stock market total return index, 3-month Treasury bill (T-bill) yield as return on cash (Cash) and dividend-adjusted iShares 20+ Year Treasury Bond (TLT) as a proxy for government bonds. We calculate asset returns based on Friday closes (or Monday closes when Friday is a holiday) because source report releases are normally the Friday after the Tuesday report date, just before the stock market close. 

1. Calculate full sample correlations between weekly final SMI and both SPY and TLT total returns for lags of 0 to 13 weeks.
2. Calculate over the full sample average weekly SPY and TLT total returns by ranked tenth (decile) of SMI for each of the next three weeks after SMI ranking.
3. Test a market timing strategy that is in SPY (cash or TLT) when SMI is positive (zero or negative), with 0.1% (0.2%) switching frictions when the alternative asset is cash (TLT). We try execution at the same Friday close as report release date and for lags of one week (as in the original study) and two weeks. We focus on compound annual growth rate (CAGR) and maximum drawdown (MaxDD) as key performance metrics. Buying and holding SPY is the benchmark.

Using inputs as specified above for 6/16/06 through 2/7/20, we find that: Keep Reading

Are there any seasonal, technical or fundamental strategies that reliably time the U.S. stock market as proxied by the S&P 500 Total Return Index? In the February 2018 version of his paper entitled “Investing In The S&P 500 Index: Can Anything Beat the Buy-And-Hold Strategy?”, Hubert Dichtl compares excess returns (relative to the U.S. Treasury bill [T-bill] yield) and Sharpe ratios for investment strategies that time the S&P 500 Index monthly based on each of:

• 4,096 seasonality strategies.
• 24 technical strategies (10 slow-fast moving average crossover rules; 8 intrinsic [time series or absolute] momentum rules; and, 6 on-balance volume rules).
• 18 fundamental variable strategies based on a rolling 180-month regression, with 1950-1965 used to generate initial predictions.

In all cases, when not in stocks, the strategies hold T-bills as a proxy for cash. His main out-of-sample test period is 1966-2014, with emphasis on a “crisis” subsample of 2000-2014. He includes extended tests on seasonality and some technical strategies using 1931-2014. He assumes constant stock index-cash switching frictions of 0.25%. He addresses data snooping bias from testing multiple strategies on the same sample by applying Hansen’s test for superior predictive ability. Using monthly S&P 500 Index levels/total returns and U.S. Treasury bill yields since 1931 and values of fundamental variables since January 1950, all through December 2014, he finds that:

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Is the conventional linear factor model comprised of a few presumably independent predictors the best, or even a good, way to model differences in returns across assets? In the December 2019 update of their paper entitled “The Cross-Section of Returns: A Non-Parametric Approach”, Enoch Cheng and Clemens Struck compare predictive powers of conventional linear models and less presumptive tree-based methods. The latter accommodate multivariate interactions and non-linearities across all predictors. They consider two linear and two tree-based methods with parameter settings commonly used in other studies:

1a. Logit – a linear regression model including all factors.

1b. LASSO – a linear regression model with a shrinkage term that sets betas to zero for (discards) predictors that do not add information, and thereby acts as a variable selection tool.

2a. Bagged regression trees – bootstrapping to create different samples from the original data, growing an individual tree on each and combining predictions of individual trees by a simple majority vote.

2b. Boosted regression trees – a modification to bagging whereby bagging and growing trees takes place sequentially with bootstrapping subsequently adjusted to improve prediction accuracy for the forest with each new tree.

Specifically, they measure relationships between 59 predictor variables and next-month (4-week) return for a universe of 28 liquid commodity futures series. This asset universe has low trading costs and avoids survivorship bias. They use nearest, second and third month contracts, the latter two only to construct signals and the first for trading. They generally roll contracts 10 days before the last trade date. The 59 predictors include time series (intrinsic or absolute) momentum variants, moving average variants, volatility variants, value metrics, miscellaneous variables, dummies for calendar months and dummies for each of the 28 commodity contract series. They consider long-short portfolios based on top half-bottom half, top five-bottom five and top three-bottom three assets in terms of expected returns. Their break point for in-sample and out-of-sample testing is the end of 2013. Using monthly data for the 28 commodity contract series and the 59 predictors during January 1987 through October 2019, they find that: Keep Reading

Does combining an economic growth variable trend with an asset price trend improve the power to predict stock market return? What is the best way to use such a combination signal? In his December 2019 paper entitled “Growth-Trend Timing and 60-40 Variations: Lethargic Asset Allocation (LAA)”, Wouter Keller investigates variations in a basic Growth-Trend timing strategy (GT) that is bullish and holds the broad U.S. stock market unless both: (1) the U.S. unemployment rate is below its 12-month simple moving average (SMA12); and, (2) the S&P 500 Index is below its SMA10. When both SMAs trend downward, GT is bearish and holds cash. Specifically, he looks at:

• Basic GT versus a traditional 60-40 stocks-bonds portfolio, rebalanced monthly, with stocks proxied by actual/modeled SPY and bonds/cash proxied by actual/modeled IEF.
• Improving basic GT, especially maximum drawdown (MaxDD), by replacing assets with equal-weighted, monthly rebalanced portfolios with various component selections. His ultimate portfolio is the Lethargic Asset Allocation (LAA), optimized in-sample based on Ulcer Performance Index (UPI) during February 1949 through June 1981 (mostly rising interest rates) and tested out-of-sample during July 1981 through October 2019 (mostly falling interest rates).

He considers two additional benchmarks: GT applied to the Permanent portfolio (25% allocations to each of SPY, GLD, BIL and TLT) and GT applied to the Golden Butterfly portfolio (20% to each of SPY, IWN, GLD, SHY and TLT). He applies 0.1% one-way trading frictions in all tests. Using monthly unemployment rate since January 1948 and actual/modeled monthly returns for ETFs as specified since February 1949, all through October 2019, he finds that: Keep Reading

Which equity factors truly explain stock returns, and what group of them constitute the best model? In their November 2019 paper entitled “Bayesian Solutions for the Factor Zoo: We Just Ran Two Quadrillion Models”, Svetlana Bryzgalova, Jiantao Huang and Christian Julliard present a Bayesian estimation and model selection method for pricing of stock portfolios that allows simultaneous examination of the entire zoo of equity factors. They apply the method to 51 factors described in past papers, yielding a total of 2.25 quadrillion factor models of U.S. stock returns. They test abilities of these factors and models to price 25 portfolios of stocks sorted by market capitalization (size) and book-to-market ratio (value) and 30 industry portfolios. Using returns for factors available monthly during January 1970 through December 2017 and for factors available only quarterly during first quarter 1952 through third quarter 2017, and contemporaneous test portfolio returns, they find that: Keep Reading