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Basic U.S. Stock Market Return Statistics

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

The Decision Moose Asset Allocation Framework

A reader requested review of the Decision Moose asset allocation framework. Decision Moose is “an automated stock, bond, and gold momentum model developed in 1989. Index Moose uses technical analysis and exchange traded index funds (ETFs) to track global investment flows in the Americas, Europe and Asia, and to generate a market timing signal.” The trading system allocates 100% of funds to the index projected to perform best. The site includes a history of switch recommendations since the end of August 1996, with gross performance. To evaluate Decision Moose, we assume that switches and associated trading returns are as described (out of sample, not backtested) and compare the returns to those for dividend-adjusted SPDR S&P 500 (SPY) over the same intervals. Using Decision Moose signals/performance data and contemporaneous SPY prices during 8/30/96 through 10/19/18 (22+ years), we find that: Keep Reading

Weekly Summary of Research Findings: 10/29/18 – 11/2/18

Below is a weekly summary of our research findings for 10/29/18 through 11/2/18. These summaries give you a quick snapshot of our content the past week so that you can quickly decide what’s relevant to your investing needs.

Subscribers: To receive these weekly digests via email, click here to sign up for our mailing list. Keep Reading

Turn of the Year and Size in U.S. Equities

Is there a reliable and material market capitalization (size) effect among U.S. stocks around the turn-of-the-year (TOTY)? To check, we track cumulative returns from 20 trading days before through 20 trading days after the end of the calendar year for the Russell 2000 Index, the S&P 500 Index and the Dow Jones Industrial Average (DJIA) since the inception of the Russell 2000 Index. We also look at full-month December and January returns for these indexes. Using daily and monthly levels of all three indexes from December 1987 through January 2018 (31 December and 31 January observations), we find that: Keep Reading

Retirement Withdrawal Modeling with Actuarial Longevity and Stock Market Mean Reversion

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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SACEVS Input Risk Premiums and EFFR

The “Simple Asset Class ETF Value Strategy” (SACEVS) seeks diversification across a small set of asset class exchanged-traded funds (ETF), plus a monthly tactical edge from potential undervaluation of three risk premiums:

  1. Term – monthly difference between the 10-year Constant Maturity U.S. Treasury note (T-note) yield and the 3-month Constant Maturity U.S. Treasury bill (T-bill) yield.
  2. Credit – monthly difference between the Moody’s Seasoned Baa Corporate Bonds yield and the T-note yield.
  3. Equity – monthly difference between S&P 500 operating earnings yield and the T-note yield.

Premium valuations are relative to historical averages. How might this strategy react to increases in the Effective Federal Funds Rate (EFFR)? Using end-of-month values of the three risk premiums, EFFRtotal 12-month U.S. inflation and core 12-month U.S. inflation during March 1989 (limited by availability of operating earnings data) through September 2018, we find that: Keep Reading

Exploiting Consensus Mutual Fund Conviction Stock Picks

Does combining the wisdom of multiple stock-picking models via ensemble methods, as done in forecasting landfall of hurricanes, improve investment portfolio performance? In their September 2018 paper entitled “Ensemble Active Management”, Alexey Panchekha, Robert Tull and Matthew Bell test the application of ensemble methods to active portfolio management, looking for consensus or near-consensus among multiple, independent stock picking sources. Ensemble diversification tends to neutralize biases among individual sources when: (1) sources are independent; (2) sources employ different approaches; and, (3) most sources achieve at least 50% individual accuracies. As sources, they use the holdings and weights of 37 actively managed U.S. equity large-capitalization mutual funds, focusing on high-conviction stock selections (those with large mismatches with respect to market capitalization). Specifically, every two weeks they:

  • Reform 30,000 randomly generated clusters of 10 mutual funds.
  • For each cluster, reform a long-only Ensemble Active Management (EAM) portfolio consisting of the 50 stocks with the highest consensus overweights within the cluster.
  • Calculate total returns for EAM portfolios, their respective clusters and the S&P 500 Index.

They debit performance of each EAM portfolio by the average contemporaneous expense ratio of the 37 mutual funds (average 0.94% across all years). To aggregate results, they calculate rolling 1-year and 3-year performances of EAM portfolios, mutual fund clusters and the index. Using daily estimated stock holdings and weights for the 37 mutual funds and associated stock prices as available during July 2007 through December 2017, they find that:

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U.S. Stock Market Returns after Extreme Up and Down Days

What happens after extreme up days or extreme down days for the U.S. stock market? To investigate, we define extreme up or down days as those with daily returns at least X standard deviations above or below the mean (average) return over the past four years (the U.S. political cycle, about 1,000 trading days). This methodology allows identification of extreme days starting in January 1954. Focusing on three standard deviations, we then look at average returns and return variabilities over the next 63 trading days (three months). Using daily closes for the S&P 500 Index during January 1950 through late October 2018, we find that:

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Weekly Summary of Research Findings: 10/22/18 – 10/26/18

Below is a weekly summary of our research findings for 10/22/18 through 10/26/18. These summaries give you a quick snapshot of our content the past week so that you can quickly decide what’s relevant to your investing needs.

Subscribers: To receive these weekly digests via email, click here to sign up for our mailing list. Keep Reading

Stock Liquidity Premium Update

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

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