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Momentum Investing

Do financial market prices reliably exhibit momentum? If so, why, and how can traders best exploit it? These blog entries relate to momentum investing/trading.

Robustness of SACEMS Based on Sharpe Ratio

Subscribers have asked whether risk-adjusted returns might work better than raw returns for ranking Simple Asset Class ETF Momentum Strategy (SACEMS) assets. In fact, “Alternative Momentum Metrics for SACEMS?” supports belief that Sharpe ratio beats raw returns. Is this finding strong enough to justify changing the strategy, which each month selects the best performers over a specified lookback interval from among the following eight asset class exchange-traded funds (ETF), plus cash:

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 update the basic comparison and conduct three robustness tests:

  1. Does Sharpe ratio beat raw returns consistently across Top 1, equally weighted (EW) Top 2, EW Top 3 and EW Top 4 portfolios, and the 50%-50% SACEMS EW Top 3-Simple Asset Class ETF Value Strategy (SACEVS) Best Value portfolio?
  2. Does Sharpe ratio beat raw returns consistently across different lookback intervals?
  3. For multi-asset portfolios, does weighting by Sharp ratio rank beat equal weighting? In other words, do future returns behave systematically across ranks?

To calculate Sharpe ratios, we each month for each asset subtract the risk-free rate (Cash yield) from raw monthly total returns to generate monthly total excess returns over a specified lookback interval. We then calculate Sharpe ratio as average monthly excess return divided by standard deviation of monthly excess returns over the lookback interval. We set Sharpe ratio for Cash at zero (though it is actually zero divided by zero). Using monthly dividend-adjusted closing prices for asset class proxies and the yield for Cash during February 2006 (when all ETFs are first available) through December 2018, we find that: Keep Reading

Does Active Stock Factor Timing/Tilting Work?

Does active stock factor exposure management boost overall portfolio performance? In their November 2018 paper entitled “Optimal Timing and Tilting of Equity Factors”, Hubert Dichtl, Wolfgang Drobetz, Harald Lohre, Carsten Rother and Patrick Vosskamp explore benefits for global stock portfolios of two types of active factor allocation:

  1. Factor timing – exploit factor premium time series predictability based on economic indicators and factor-specific technical indicators.
  2. Factor tilting – exploit cross-sectional (relative) attractiveness of factor premiums.

They consider 20 factors spanning value, momentum, quality and size. For each factor each month, they reform a hedge portfolio that is long (short) the equal-weighted fifth, or quintile, of stocks with the highest (lowest) expected returns for that factor. For implementation of factor timing, they consider: 14 economic indicators standardized by subtracting respective past averages and dividing by standard deviations; and, 16 technical indicators related to time series momentum, moving averages and volatilities. They suppress redundancy and noise in these indicators via principal component analysis separately for economic and technical groups, focusing on the first principal component of each group. They translate any predictive power embedded in principal components into optimal factor portfolio weights using augmented mean-variance optimization. For implementation of factor tilting, they overweight (underweight) factors that are relatively attractive (unattractive) based on valuations of factor top and bottom quintile stocks, top-bottom quintile factor variable spreads, prior-month factor returns (momentum) and volatilities of past monthly factor returns. Their benchmark portfolio is the equal-weighted combination of all factor hedge portfolios. For all portfolios, they assume: monthly portfolio reformation costs of 0.75% (1.15%) of turnover value for the long (short) side; and, annual 0.96% cost for an equity swap to ensure a balanced portfolio of factor portfolios. For monthly factor timing and tilting portfolios only, they assume an additional cost of 0.20% of associated turnover. Using monthly data for a broad sample of global stocks from major equity indexes and for specified economic indicators during January 1997 through December 2016 (4,500 stocks at the beginning and 5,000 stocks at the end), they find that: Keep Reading

Momentum and Stock Return Dispersion

Is stock price momentum an imperfect proxy for sensitivity of individual stocks to past dispersion of returns across stocks (zeta risk, or return dispersion)? In their November 2018 paper entitled “Market Risk and the Momentum Mystery”, James Kolari and Wei Liu investigate relationships between momentum and return dispersion as predictors of individual U.S. stock returns. They employ both portfolio comparisons and regression tests. For the former, their momentum portfolio is long (short) the equally weighted top (bottom) tenth, or decile, of stocks ranked on past 12-month minus one skip-week returns, reformed monthly. Their main return dispersion portfolio is long (short) the equally weighted decile of stocks with the most positive (negative) sensitivities to the dispersion of all individual daily stock returns over the past 12 months minus one skip-week, reformed monthly. Using daily and monthly returns for a broad sample of U.S. stocks priced over $5 since January 1964, and contemporaneous 1-month U.S. Treasury bill yields and monthly returns of selected stock return model factors since January 1965, all through December 2017, they find that:

Keep Reading

SACEMS with SMA Filter

A subscriber asked whether applying a simple moving average (SMA) filter to  “Simple Asset Class ETF Momentum Strategy” (SACEMS) winners improves strategy performance. SACEMS each months picks winners from among the following asset class exchange-traded fund (ETF) proxies based on past returns over a specified 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)

Since many technical traders use a 10-month SMA (SMA10), we test effectiveness of requiring that each winner pass an SMA10 filter by comparing performances for three scenarios:

  1. Baseline – SACEMS as presented at “Momentum Strategy”.
  2. With SMA10 Filter – Run Baseline SACEMS and then apply SMA10 filters to dividend-adjusted prices of winners. If a winner is above (below) its SMA10, hold the winner (Cash). This rule is inapplicable to Cash as a winner.
  3. With Half SMA10 Filter – Same as scenario 2, but, if a winner is above (below) its SMA10, hold the winner (half the winner and half cash at the T-bill yield).

We focus on compound annual growth rates (CAGR) and maximum drawdowns (MaxDD) of SACEMS Top 1, equally weighted (EW) Top 2 and EW Top 3 portfolios. 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 November 2018, we find that: Keep Reading

Commodity Futures Momentum and Reversal

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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Testing ETF Momentum/Reversal Strategies

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

SACEMS-SACEVS Mutual Diversification

Are the “Simple Asset Class ETF Value Strategy” (SACEVS) and the “Simple Asset Class ETF Momentum Strategy” (SACEMS) mutually diversifying. To check, we look at the following three equal-weighted (50-50) combinations of the two strategies, rebalanced monthly:

  1. SACEVS Best Value paired with SACEMS Top 1 (aggressive value and aggressive momentum).
  2. SACEVS Best Value paired with SACEMS Equally Weighted (EW) Top 3 (aggressive value and diversified momentum).
  3. SACEVS Weighted paired with SACEMS EW Top 3 (diversified value and diversified momentum).

We also test sensitivity of results to deviating from equal SACEVS-SACEMS weights. Using monthly gross returns for SACEVS and SACEMS portfolios since January 2003 for the first strategy and since July 2006 for the latter two, all through October 2018, we find that: Keep Reading

Separate vs. Integrated Equity Factor Portfolios

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

U.S. Equity Turn-of-the-Month as a Diversifying Portfolio

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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Most Effective U.S. Stock Market Return Predictors

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

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