Equity Premium

What do basic U.S. stock market return statistics say about consistency of equity risks and predictability of returns? We define basic statistics as first through fourth moments of the return distribution: mean (average), standard deviation, skewness and kurtosis. For tractability, we calculate these four statistics month-by-month based on daily returns. Using daily closes of the Dow Jones Industrial Average (DJIA) since January 1930 and the S&P 500 Index since January 1950, both through September 2018, we find that: Keep Reading

How does use of actuarial estimates of retiree longevity and empirical mean reversion of stock market returns affect estimated retirement portfolio success rates? In the October 2018 revision of his paper entitled “Joint Effect of Random Years of Longevity and Mean Reversion in Equity Returns on the Safe Withdrawal Rate in Retirement”, Donald Rosenthal presents a model of safe inflation-adjusted retirement portfolio withdrawal rates that addresses: (1) uncertainty about the number of years of retirement (rather than the commonly assumed 30 years); and, (2) mean reversion in annual U.S. stock market returns (rather than a random walk). He estimates retirement longevity as a random input based on the Social Security Administration’s 2015 Actuarial Life Table. He estimates stock market real returns and measures their mean reversion using S&P 500 Index inflation-adjusted total annual returns during 1926 through 2017. He models real bond returns using 10-year U.S. Treasury note (T-note) total annual returns during 1928 through 2017. He applies Monte Carlo simulations (3,000 trials for each scenario) to assess retirement portfolio performance by:

• Assuming an initial retirement portfolio either 100% invested in stocks or 60%/40% in stocks/T-notes (rebalanced at each year-end).
• Debiting the portfolio each year-end by a fixed, inflation-adjusted percentage of the initial amount.
• Calculating percentage of simulation trials for which the portfolio is not exhausted before death (success) and average portfolio terminal balance for successful trials.

He considers two benchmarks: (1) no stock market mean reversion (random walk) and fixed 30-year retirement; and, (2) no stock market mean reversion and actuarial estimate of retirement duration. He also runs sensitivity tests to see how changes in assumptions affect success rate. Using the specified data, he finds that:

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Two major theories of asset pricing include: one based on asset risk (the market compensates inherent riskiness); and, another based on asset illiquidity (the market compensates illiquidity). In his July 2018 paper entitled “Illiquidity and Stock Returns: A Revisit”, Yakov Amihud presents cross-sectional and time series analyses of illiquidity and U.S. stock returns that extend the 1964-1997 sample period of his seminal illiquidity research. Specifically, he:

• Each year, sorts stocks by volatility (standard deviation of daily returns for the 12 months ending November) into three groups.
• Each year, sorts stocks within each volatility group into five illiquidity sub-groups, with illiquidity specified as the 12-month average of absolute daily return divided by same-day dollar volume traded over the same 12 months.
• Each month during the subsequent January through December, calculates the monthly return of each of the resulting 15 portfolios, weighting stocks based on their market capitalization weights at the end of the prior month.
• Each month, calculates an illiquid-minus-liquid factor (IML) as average return of the most illiquid portfolios across volatility groups minus average return of the least illiquid portfolios across volatility groups.

This process controls for interaction between volatility and illiquidity. He segments findings into replicating Period I (1964-1997) and new Period II (1998-2017). He screens source stocks by requiring for each year: price between $5 and $1000; over 200 days of valid returns and volumes; and, not in the top 1% of illiquidities (outliers). Using data for NYSE/AMEX common stocks that meet these criteria during 1964 through 2017, he finds that: Keep Reading

What are the implications of rapid global adoption of factor (smart beta) investing in single-factor, multi-factor and dynamic multi-factor strategies, most notably via equity exchange-traded funds (ETF). In their September 2018 paper entitled “Smart-Beta Herding and Its Economic Risks: Riding the Dragon?”, Eduard Krkoska and Klaus Schenk-Hoppé summarize the current state of smart beta investing, providing a concise overview of academic research, investment community reports and financial media coverage. They address evidence and implications of investor herding into smart beta vehicles. Based on the body of research and experience, they conclude that: Keep Reading

Quantitative investing involves disciplined rule-based approaches to help investors structure optimal portfolios that balance return and risk. How has such investing evolved? In their June 2018 paper entitled “The Current State of Quantitative Equity Investing”, Ying Becker and Marc Reinganum summarize key developments in the history of quantitative equity investing. Based on the body of research, they conclude that: Keep Reading

A subscriber proposed four alternative ways of timing the U.S. stock market based on simple moving averages (SMA) of the market price-earnings ratio (P/E), as follows:

1. 5-Year Binary – hold stocks (cash) when P/E is below (above) its 5-year SMA.
2. 10-Year Binary – hold stocks (cash) when P/E is below (above) its 10-year SMA.
3. 15-Year Binary – hold stocks (cash) when P/E is below (above) its 15-year SMA.
4. 5-Year Scaled – hold 100% stocks (cash) when P/E is five or more units below (above) its 5-year SMA. Between these levels, scale allocations linearly.

To obtain a sample long enough for testing these rules, we use the monthly U.S. data of Robert Shiller. While offering a very long history, this source has the disadvantage of blurring monthly data as averages of daily values. How well do these alternative timing strategies work for this dataset? Using monthly data for the S&P Composite Index, annual dividends, annual P/E and 10-year government bond yield since January 1871 and monthly 3-month U.S. Treasury bill (T-bill) yield as return on cash since January 1934, all through August 2018, we find that: Keep Reading

Is there a best way for investors to measure firm profitability for global stock selection? In their August 2018 paper entitled “Constructing a Powerful Profitability Factor: International Evidence”, Matthias Hanauer and Daniel Huber investigate which measure of firm profitability best predicts associated stock returns. They consider six measures: return on equity; gross profitability; operating profitability calculated in two ways; cash-based operating profitability (excluding accruals); and, cash-based gross profitability (also excluding accruals). They construct a long-short profitability factor for each measure and test its power to predict stock returns both standalone and in combination with other kinds of factors (market, size, book-to-market, momentum, investment and accruals) and the other profitability factors. Using monthly returns and annual accounting data for non-financial common stocks in 49 countries (excluding the U.S.) during July 1989 through June 2016, they find that: Keep Reading

How, and how well, do institutional equity traders manage global stock trading frictions? In the April 2018 draft of their paper entitled “Trading Costs”, Andrea Frazzini, Ronen Israel and Tobias Moskowitz examine the real-world trading frictions of a large trader. They define trading frictions as the difference in results between a theoretical portfolio with zero frictions and a practical tracking portfolio with frictions. They account for all components of trading frictions: broker commissions, bid-ask spreads and price impacts of trading. They record market price at trade initiation, volume traded and execution price for each share traded, as well as type of trade (buy long, buy-to-cover, sell long or sell short). They describe how frictions vary by trade type, stock characteristics, trade size, time and exchange. Based on preliminary findings, they devise and test out-of-sample a price impact model based on market conditions, stock characteristics and trade size calibrated to actual U.S. and international trades. Using $1.7 trillion of orders and trade execution data from a large institutional money manager spanning 21 developed equity markets during August 1998 through June 2016, they find that: Keep Reading

Do stock dividends exhibit exploitable risk premiums? In their July 2018 paper entitled “A Model-Free Term Structure of U.S. Dividend Premiums”, Maxim Ulrich, Stephan Florig and Christian Wuchte construct a term structure of the dividend risk premium and test strategies to time this premium at specific horizons. They specify dividend risk premium as the spread between:

• Expected dividend growth rate based on analyst 1-year and 2-year S&P 500 dividend forecasts, extended by analyst 5-year earnings growth estimates assuming constant future payout ratio.
• Expected dividend growth rate derived from equity index put and call option prices across different maturities.

They model an S&P 500 dividend capture portfolio for a given horizon as: long an S&P 500 Index put option of maturity matching the horizon; short an index call option of same maturity and strike price; long the index; and, short the money market in an amount matched to the option strike price. They test two strategies for capturing this premium at a 12-month horizon: (1) each month (last trading day) reform and hold the dividend capture portfolio; or, (2) each month reform and hold the dividend capture portfolio only when the dividend risk premium is positive (analyst-estimated dividends are higher than options-implied dividends). They model the risk-free rate/money market rate across horizons using the U.S. Dollar Overnight Index Swap rate for one day to 10 years. For the S&P 500 Index, they assume annual expense ratio 0.07% and 0.01% average bid-ask spread. For options, they estimate trading frictions with actual bid-ask spreads. Using S&P 500 Index/options and analyst forecast data as specified during January 2004 through October 2017, they find that:

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From a purely statistical perspective, how many factors are optimal for explaining both time series and cross-sectional variations in stock anomaly/stock returns, and how do these statistical factors relate to stock/firm characteristics? In their July 2018 paper entitled “Factors That Fit the Time Series and Cross-Section of Stock Returns”, Martin Lettau and Markus Pelger search for the optimal set of equity factors via a generalized Principal Component Analysis (PCA) that includes a penalty on return prediction errors returns. They apply this approach to three datasets:

1. Monthly returns during July 1963 through December 2017 for two sets of 25 portfolios formed by double sorting into fifths (quintiles) first on size and then on either accruals or short-term reversal.
2. Monthly returns during July 1963 through December 2017 for 370 portfolios formed by sorting into tenths (deciles) for each of 37 stock/firm characteristics.
3. Monthly excess returns for 270 individual stocks that are at some time components of the S&P 500 Index during January 1972 through December 2014.

They compare performance of their generalized PCA to that of conventional PCA. Using the specified datasets, they find that: Keep Reading