Momentum Investing

Do prices of commodity futures contract series reliably exhibit reversal and/or momentum? In their October 2018 paper entitled “Do Momentum and Reversal Strategies Work in Commodity Futures? A Comprehensive Study”, Andrew Urquhart and Hanxiong Zhang investigate the performance of four momentum/reversal trading strategies as applied to excess return indexes for 29 commodity futures contract series. Excess return indexes invest continuously in nearest S&P GSCI futures, rolling forward during the fifth to ninth business day of each month. The four strategies are:

1. Pairs reversal trading – At the end of each formation interval, identify the five pairs of indexes (with equal capital commitments) that track most closely based on sum of squared deviations of normalized price differences. During the ensuing trading interval, when the normalized prices of any pairs diverge by at least two standard deviations of formation period differences, go long (short) the member of the pair that is undervalued (overvalued). Close all pair trades when prices re-converge at a daily close or at the end of the trading interval.
2. Pairs momentum trading – The inverse of pairs reversal trading, wherein the long (short) position is the pair member exhibiting relative strength (weakness) during the trading interval.
3. Conventional momentum – At the end of each month, rank all indexes by cumulative return over the formation interval. Go long (short) the equal-weighted 30% of assets with the highest (lowest) past returns during the ensuing holding interval.
4. Nearness to high momentum – At the end of each month, rank all indexes based on nearness to respective formation interval highs. Go long (short) the equal-weighted 30% of assets that are nearest/at (farthest below) past highs during the ensuing holding interval.

They consider nine formation intervals (1, 3, 6, 9, 12, 24, 36, 48 and 60 months) and 21 holding intervals (1, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57 and 60 months).They assume that long-short strategies are about 50% collateralized, with capital therefore available to handle holding interval margin calls. They also test effects of 0.69% per year (0.06% per month) transaction costs. Using daily levels of six energy, 10 metal and 13 agriculture and live stock commodity futures excess return indexes during January 1979 through October 2017, they find that:

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Do exchange-traded funds (ETF) exhibit statistically reliable short-term reversal and intermediate-term momentum? In their October 2018 paper entitled “Momentum Strategies for the ETF-Based Portfolios”, Daniel Nadler and Anatoly Schmidt look for reversal and momentum in next-month performance of past winners and past losers for the following 13 universes:

• U.S. Equity ETFs: 28 US equity ETFs with returns available at the beginning of 2006.
• Multi-Asset Class ETFs: U.S. Equity ETFs plus one gold ETF, five international equity ETFs and five bond ETFs, also with returns available at the beginning of 2006.
• 11 U.S. Equity ETF Proxies: formed separately from the stock holdings as of January 2018 of each of SPDR S&P 500 (SPY), PowerShares NASDAQ 100 (QQQ) or one of the nine Select Sector SPDRs.

Every day for each universe, they reform overlapping winner (loser) portfolios consisting of the equally weighted tenth (decile) of assets with the highest (lowest) total returns over the past 21, 63, 126 or 252 trading days and hold for 21 trading days. They consider two test periods: 2007 through 2017, and 2011 through 2007. They use equal-weighted portfolios of all assets in each universe as the benchmark for that universe. They conclude that one portfolio beats another when the difference between average 21-day future returns is statistically significant with p-value less than 0.10. Using daily returns for the specified assets during 2006 through 2017, they find that: Keep Reading

What is the best way to construct equity multifactor portfolios? In the November 2018 revision of their paper entitled “Equity Multi-Factor Approaches: Sum of Factors vs. Multi-Factor Ranking”, Farouk Jivraj, David Haefliger, Zein Khan and Benedict Redmond compare two approaches for forming long-only equity multifactor portfolios. They first specify ranking rules for four equity factors: value, momentum, low volatility and quality. They then, each month:

• Sum of factor portfolios (SoF): For each factor, rank all stocks and form a factor portfolio of the equally weighted top 50 stocks (adjusted to prevent more than 20% exposure to any sector). Then form a multifactor portfolio by equally weighting the four factor portfolios.
• Multifactor ranking (MFR): Rank all stocks by each factor, average the ranks for each stock and form an equally weighted portfolio of those stocks with the highest average ranks, equal in number of stocks to the SoF portfolio (again adjusted to prevent more than 20% exposure to any sector).

They consider variations in number of stocks selected for individual factor portfolios from 25 to 200, with comparable adjustments to the MFR portfolio. They assume trading frictions of 0.05% of turnover. Using monthly data required to rank the specified factors for a broad sample of U.S. common stocks and monthly returns for those stocks and the S&P 500 Total Return Index (S&P 500 TR) during January 2003 through July 2016, they find that: Keep Reading

Is the U.S. equity turn-of-the-month (TOTM) effect exploitable as a diversifier of other assets? In their October 2018 paper entitled “A Seasonality Factor in Asset Allocation”, Frank McGroarty, Emmanouil Platanakis, Athanasios Sakkas and Andrew Urquhart test U.S. asset allocation strategies that include a TOTM portfolio as an asset. The TOTM portfolio buys each stock at the open on the last trading day of each month and sells at the close on the third trading day of the following month, earning zero return the rest of the time. They consider four asset universes with and without the TOTM portfolio:

1. A conventional stocks-bonds mix.
2. The equity market portfolio.
3. The equity market portfolio, a small size portfolio and a value portfolio.
4. The equity market portfolio, a small size portfolio, a value portfolio and a momentum winners portfolio.

They consider six sophisticated asset allocation methods:

1. Mean-variance optimization.
2. Optimization with higher moments and Constant Relative Risk Aversion.
3. Bayes-Stein shrinkage of estimated returns.
4. Bayesian diffuse-prior.
5. Black-Litterman.
6. A combination of allocation methods.

They consider three risk aversion settings and either a 60-month or a 120-month lookback interval for input parameter measurement. To assess exploitability, they set trading frictions at 0.50% of traded value for equities and 0.17% for bonds. Using monthly data as specified above during July 1961 through December 2015, they find that:

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Which economic and market variables are most effective in predicting U.S. stock market returns? In his October 2018 paper entitled “Forecasting US Stock Returns”, David McMillan tests 10-year rolling and recursive (inception-to-date) one-quarter-ahead forecasts of S&P 500 Index capital gains and total returns using 18 economic and market variables, as follows: dividend-price ratio; price-earnings ratio; cyclically adjusted price-earnings ratio; payout ratio; Fed model; size premium; value premium; momentum premium; quarterly change in GDP, consumption, investment and CPI; 10-year Treasury note yield minus 3-month Treasury bill yield (term structure); Tobin’s q-ratio; purchasing managers index (PMI); equity allocation; federal government consumption and investment; and, a short moving average. He tests individual variables, four multivariate combinations and and six equal-weighted combinations of individual variable forecasts. He employs both conventional linear statistics and non-linear economic measures of accuracy based on sign and magnitude of forecast errors. He uses the historical mean return as a forecast benchmark. Using quarterly S&P 500 Index returns and data for the above-listed variables during January 1960 through February 2017, he finds that: Keep Reading

How does a large sample of stock return anomalies fare in recent replication testing? In their October 2018 paper entitled “Replicating Anomalies”, Kewei Hou, Chen Xue and Lu Zhang attempt to replicate 452 published U.S. stock return anomalies, including 57, 69, 38, 79, 103, and 106 anomalies 57 momentum, 69 value-growth, 38 investment, 79 profitability, 103 intangibles and 106 trading frictions (trading volume, liquidity, market microstructure) anomalies. Compared to the original papers, they use the same sample populations, original (as early as January 1967) and extended (through 2016) sample periods and similar methods/variable definitions. They test limiting influence of microcaps (stocks in the lowest 20% of market capitalizations) by using NYSE (not NYSE-Amex-NASDAQ) size breakpoints and value-weighted returns. They consider an anomaly replication successful if average high-minus-low tenth (decile) return is significant at the 5% level, translating to t-statistic at least 1.96 for pure standalone tests and at least 2.78 assuming multiple testing (accounting for aggregate data snooping bias). Using required anomaly data and monthly returns for U.S. non-financial stocks during January 1967 through December 2016, they find that:

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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

Brian Livingston introduces his 2018 book, Muscular Portfolios: The Investing Revolution for Superior Returns with Lower Risk, as follows: “What we laughingly call the financial ‘services’ industry is a cesspool filled with sharks intent on siphoning your money away and making it their own. The good news is that it is absolutely possible to grow your savings with no fear of financial sharks or stock market crashes. In the past few years, we’ve seen an explosion of low-cost index funds, along with serious mathematical breakthroughs in how to combine these funds into low-risk portfolios. …This book shows you how.  …You can start with just a little money and make it grow.” Based on research from multiple sources and extensions of that research, he concludes that: Keep Reading

A subscriber asked whether applying a filter that restricts monthly asset selections of the “Simple Asset Class ETF Momentum Strategy” (SACEMS) to those currently at an intermediate-term high improves performance. This strategy each month reforms a portfolio of winners from the following universe based on total return over a specified lookback interval:

PowerShares DB Commodity Index Tracking (DBC)
iShares MSCI Emerging Markets Index (EEM)
iShares MSCI EAFE Index (EFA)
SPDR Gold Shares (GLD)
iShares Russell 2000 Index (IWM)
SPDR S&P 500 (SPY)
iShares Barclays 20+ Year Treasury Bond (TLT)
Vanguard REIT ETF (VNQ)
3-month Treasury bills (Cash)

To investigate, we focus on the equally weighted (EW) Top 3 SACEMS portfolio and replace any selection not at an intermediate-term high with Cash. We define intermediate-term high based on monthly closes over a specified past interval ranging from one month to six months. We consider all gross performance metrics used for base SACEMS. Using monthly dividend adjusted closing prices for the asset class proxies and the yield for Cash over the period February 2006 (the earliest all ETFs are available) through July 2018 (150 months), we find that: Keep Reading

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