Momentum Investing

A subscriber asked about extending “Simple Momentum Strategy Applied to TSP Funds” back in time to 1988. That test employs the following five funds, all available to U.S. federal government employees via the Thrift Savings Plan (TSP) as of January 2001:

G Fund: Government Securities Investment Fund (G)
F Fund: Fixed Income Index Investment Fund (F)
C Fund: Common Stock Index Investment Fund (C)
S Fund: Small Cap Stock Index Investment Fund (S)
I Fund: International Stock Index Investment Fund (I)

S Fund and I Fund data limit the combined sample period. To extend the test back to first availability of G Fund, F Fund and C Fund data in February 1988, we use Vanguard Small Cap Index Investors Fund (NAESX) as a proxy for the S Fund and Vanguard International Value Investors Fund (VTRIX) as a proxy for the I Fund prior to 2001. We first perform a sensitivity test of fund ranking (lookback) intervals ranging from one to 12 months on the following monthly reformed portfolios: the winner fund (Top 1); an equally weighting of the top two funds (EW top 2); an equally weighting of the Top 3 funds (EW Top 3); and, an equal weighting of all five funds (EW All). We then perform detailed tests using a representative lookback interval. Using monthly returns for the five TSP funds as available during February 1988 through June 2017 (351 months) and monthly returns for NAESX and VTRIX during February 1988 through December 2000, we find that:

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Does an asset class breadth rule work better than a class-by-class exclusion rule for momentum strategy crash protection? In their July 2017 paper entitled “Breadth Momentum and Vigilant Asset Allocation (VAA): Winning More by Losing Less”, Wouter Keller and Jan Keuning introduce VAA as a dual momentum asset class strategy aiming at returns above 10% with drawdowns less than -20% deep. They specify momentum as the average of annualized total returns over the past 1, 3, 6 and 12 months. This specification gives greater weight to short lookback intervals than a simple average of past returns over these intervals. Specifically, they:

1. Each month rank asset class proxies based on momentum.
2. Each month select a “cash” holding as the one of short-term U.S. Treasury, intermediate-term U.S. Treasury and investment grade corporate bond funds with the highest momentum. 
3. Set (via backtest) a breadth protection threshold (B). When the number of asset class proxies with negative momentum (b) is equal to or greater than B, the allocation to “cash” is 100%. When b is less than B, the base allocation to “cash” is b/B.
4. Set (via backtest) the number of top-performing asset class proxies to hold (T) in equal weights. When the base allocation to “cash” is less than 100% (so when b<B), allocate the balance to the top (1-b/B)T asset class proxies with highest momentum (irrespective of sign).
5. Mitigate portfolio rebalancing intensity (when B and T are different) by rounding fractions b/B to multiples of 1/T.

They construct four test universes from: a short sample of 17 (mostly simulated) exchange traded fund (ETF)-like global asset class proxies spanning December 1969 through December 2016; and, a long sample of 21 index-like U.S. asset classes spanning December 1925 through December 2016. After reserving the first year for initial momentum calculations, they segment each sample into halves for in-sample optimization of B and T and out-of-sample testing. For all cases, they apply 0.1% one-way trading frictions for portfolio changes. Their key portfolio performance metrics are compound annual growth rate (CAGR), maximum drawdown (MaxDD) and a composite of the two. Using monthly returns for the selected ETF-like and index-like assets over respective sample periods, they find that:

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A subscriber asked for augmentation of “SACEMS at Weekly and Biweekly Frequencies” to determine whether bimonthly (every two months) measurement of asset class momentum works better than monthly measurement as used in “Simple Asset Class ETF Momentum Strategy” (SACEMS). To investigate, we apply a bimonthly strategy to 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)

We use the same lookback interval as for basic SACEMS and consider portfolios of past ETF winners based on Top 1 and on equally weighted (EW) Top 2 and Top 3. Since a bimonthly lookback interval uses every other set of monthly signals, we consider two variations: (1) start at the end of July 2006, when signals are first available for the entire set of ETFs, and end with May 2017; and, (2) start at the end of August 2006 and end with June 2017. We consider as benchmarks an equally weighted portfolio of all ETFs, rebalanced monthly (EW All) and basic monthly SACEMS. We focus on gross compound annual growth rates (CAGR), annual returns and maximum drawdowns (MaxDD) as performance metrics. Using monthly dividend-adjusted closing prices for the asset class proxies and the yield for Cash during February 2006 (when all ETFs are first available) through June 2017 (137 months), we find that: Keep Reading

Does time series (intrinsic or absolute) return momentum work everywhere all the time? In their June 2017 paper entitled “A Century of Evidence on Trend-Following Investing”, Brian Hurst, Yao Ooi and Lasse Pedersen investigate the robustness of intrinsic momentum across 67 assets over 137 years. Robustness tests address subperiods, market return/volatility states and economic conditions. They rely mostly on futures prices series but use cash index returns financed at local short-term interest rates when futures data is not available. They consider lookback intervals of one, three and 12 months for momentum measurement. Specifically, they each month:

• Measure for each asset 1-month, 3-month and 12-month past excess returns (relative to the risk-free rate).
• For each lookback interval, take a long (short) position for each asset with a positive (negative) past excess return, scaled to target equal volatility.
• Combine positions across the three lookback intervals and scale the aggregate portfolio to 10% expected annualized volatility (based on rolling 3-year historical windows) for comparability over time.
• Subtract portfolio reformation frictions (based on current and historical estimates) and fees (2% annually plus 20% performance fee above a high-water mark).

Using monthly returns for 67 assets from four classes (29 commodities, 11 equity indexes, 15 bond indexes and 12 currency pairs), along with equity market and economic data used in robustness tests, as available during 1880 through 2016, they find that:

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Is recent Fama-French 5-factor alpha (accounting for market, size, book-to-market, profitability and investment risks) a useful predictor of U.S. equity sector performance? In other words, is there an alpha momentum anomaly at the sector level? In their June 2017 paper entitled “US Sector Rotation with Five-Factor Fama-French Alphas”, Golam Sarwar, Cesario Mateus and Natasa Todorovic examine 5-factor alphas of U.S. equity sectors and test both long-only and long-short sector rotation strategies based on 36-month alpha ranking. They conduct long-sample conceptual tests on 10 Fama-French U.S. sector (or industry) portfolios and short-sample tests on S&P Select Sector SPDR exchange-traded funds (ETF). Specifically, they each month measure rolling alpha for each sector based on the last 36 months of returns, and:

• Long-only strategy – Each month take equal positions in sectors with positive alphas at the end of the prior month.
• Long-short strategy – Each month take equal long (short) positions in sectors with positive (negative) alphas at the end of the prior month.
• Alternative long-only strategy – (1) each month during U.S. economic expansions (per NBER), take equal positions in sectors with positive alphas at the end of the prior month; and, (2) each month during U.S. economic contractions, hold 1-month U.S. Treasury bills (T-bills).

They also compare effectiveness of Fama-French 3-factor model versus 5-factor model for analysis of sector returns. Using monthly returns for Fama-French sectors and factor models, monthly returns for the S&P 500 Index and T-bill yields since January 1964, and monthly returns for sector ETFs since January 1999, all through December 2014, they find that:

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Do stock return momentum and reversal strategies work better when focused on certain intraday intervals rather than close-to-close, according to whether trades are primarily exploiting information or supplying liquidity? In his April 2017 paper entitled “Reversal, Momentum and Intraday Returns”, Haoyu Xu examines intraday versions of momentum and reversal anomalies, with focus on the first two hours and the last two hours of the normal U.S. trading day. He hypothesizes that information-driven trades drive momentum profitability early in the day, and liquidity-driven trades drive reversal profitability late in the day. His anomaly measures are:

• Momentum – (1) sort stocks into tenths (deciles) by cumulative close-to-close or first 2-hour returns over a 6-month ranking interval; (1) skip one month or six months (echo momentum); and, (3) form a portfolio that is long (short) the equally weighted decile with the highest (lowest) past returns; and, (4) hold for one month or six months.
• Reversal – (1) sort stocks into deciles by cumulative close-to-close, first 2-hour or last 2-hour returns over the past month; (2) form a portfolio that is long (short) the equally weighted decile with the lowest (highest) returns; and, (3) hold for one month.

His principal performance metrics are average gross raw monthly return, gross monthly 3-factor alpha (adjusting for market, size and book-to-market), gross monthly 4-factor alpha (adding momentum) and gross monthly 5-factor alpha (adding short-term reversal ). Using daily and intraday prices for a broad sample of U.S. common stocks with prices at least $5 and in the top 90% of NYSE capitalizations during January 1993 through December 2014, he finds that:

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What is the most effective way to hedge against equity market crashes? In their June 2017 paper entitled “The Best Strategies for the Worst Crises”, Michael Cook, Edward Hoyle, Matthew Sargaison, Dan Taylor and Otto Van Hemert examine active and passive strategies with potential to generate positive returns during the worst crises. They test these strategies across the seven S&P 500 Index drawdowns of more than 15% during 1985 through 2016. They focus on two active strategies:

1. Time-series (intrinsic or absolute) momentum long-short portfolio comprised of 50 liquid futures and forwards series spanning currencies, equity indexes, bonds, agricultural products, energy and metals. They consider return lookback intervals of 1, 3 and 12 months. They apply risk adjustments, risk allocations by class and finally a scale factor targeting 10% annualized portfolio volatility. They consider three extensions of the strategy that preclude or restrict positive exposure to equity market beta.
2. Quality factor long-short portfolios comprised of intermediate and large capitalization U.S. stocks. These portfolios ares long (short) the highest-ranked (lowest-ranked) stocks, as selected based on one of 18 metrics representing profitability, growth in profitability, safety and payout. Rankings are risk-adjusted and portfolios are equity market beta-neutral. They again apply a scale factor targeting 10% annualized portfolio volatility. They also consider several composite factor portfolios by averaging individual factor rankings and weighting for dollar neutrality, beta neutrality, sector neutrality and/or volatility balancing.

Using daily data for all indicated assets during 1985 through 2016, they find that: Keep Reading

Does a dual momentum selection/weighting approach applied to the U.S. Treasuries term structure identify a safe haven superior to any one duration? In his February 2015 paper entitled “The Search for Crisis Alpha: Weathering the Storm Using Relative Momentum”, Nathan Faber tests a dual momentum safe haven based on U.S. Treasuries of different durations as proxied by either constant maturity indexes or exchange-traded funds (ETFs). He constructs constant maturity indexes from 1-year, 3-year, 5-year, 7-year, 10-year and 20-year constant maturity U.S. Treasuries yields by each month accruing a coupon and repricing at the new yield. For ETFs, he uses total returns for five iShares U.S. Treasuries ETFs: SHY (1-3 years), IEI (3-5 years), IEF (7-10 years), TLH (10-20 years) and TLT (20+ years). The dual momentum approach consists of the following steps:

1. Calculate the return from 10 months ago to one month ago for each duration.
2. Subtract from the return of each duration that of 1-year U.S. Treasuries (SHY) if using constant maturity indexes (ETFs) to calculate an excess return as a measure of intrinsic (absolute or time series) momentum.
3. Discard any durations with negative excess returns.
4. Rank remaining durations based on risk-adjusted excess returns, with variances used to indicate risk, as a measure of relative momentum and assign weights to these durations based on their ranks. If no durations have positive excess returns, assign 100% weight to 1-year U.S. Treasuries (or SHY if using ETFs).

He then investigates the performance of this dual momentum strategy as a safe haven during S&P 500 crises defined in two ways: (1) drawdowns of at least 20% peak to trough; or, (2) monthly declines of at least 5%. He further tests a specific strategy that is long the S&P 500 Index (or SPY if using ETFs) when above its 10-month SMA (SMA10) and in either the dual momentum safe haven portfolio or in a fixed duration (1-year or 20+ years) when below its SMA10. Using data for the yields/indexes/funds specified above since 1962 for constant maturity index tests and since 2003 for ETF tests, all through 2014, he finds that: Keep Reading

Does average sign of recent returns work as well as recent cumulative return as a momentum metric? In their May 2017 paper entitled “Returns Signal Momentum”, Fotis Papailias, Jiadong Liu and Dimitrios Thomakos introduce and test a momentum strategy (RSM) based on the equally weighted average signs (1 for positive and 0 for negative) of past returns over a given lookback interval. This metric employs each of the past returns during the lookback interval, not a single cumulative return as in times series (intrinsic or absolute) momentum. It considers only signs of past returns, not their magnitudes as in conventional relative momentum. They focus on monthly returns over a lookback interval of 12 months. They test RSM on a universe of 55 of the most liquid futures/forwards: 24 commodities; 9 currency exchange rates versus the U.S. dollar; 9 developed country equity indexes; and, 13 government bonds of various maturities from six developed countries. Their strategy is each month long (short) a contract series when average sign of its last 12 monthly returns is above (below) a threshold. They consider two types of thresholds: (1) fixed over the test period, with the featured optimal value selected by experimentation; and, (2) time-varying, each month choosing the best-performing value (from among 0.2, 0.3, 0.4, 0.5, 0.6, 0.7 and 0.8) over the prior 24 months. Using returns for the 55 futures/forwards series as available to support a strategy test period of January 1985 through March 2015, they find that:
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How well do time series (intrinsic) and cross-sectional (relative) momentum work for different types of currency exchange rates? In their April 2017 paper entitled “Momentum in Traditional and Cryptocurrencies Made Simple”, Janick Rohrbach, Silvan Suremann and Joerg Osterrieder compare the effectiveness of time series and cross-sectional momentum as applied to three groups of currency exchange rates: G10 currencies; non-G10 conventional currencies; and, cryptocurrencies. To measure momentum they employ three pairs (one fast and one slow) of exponential moving averages (EMA) spanning short, intermediate and long horizons. When the fast EMA of a pair is above (below) the slow EMA, the trend is positive (negative). They extract a momentum signal for each exchange rate from these three EMA pairs by:

1. For each EMA pair, taking the difference between the fast and slow EMA.
2. For each EMA pair, dividing the output of step 1 by the standard deviation of the exchange rate over the last three months to scale currency fluctuations to the same magnitude.
3. For each EMA pair, dividing the output of step 2 by its own standard deviation over the last year to suppress series volatility.
4. For each EMA pair, mapping all outputs of step 3 to signals between -1 and 1.
5. Averaging the signals across the three EMA pairs to produce an overall momentum signal.

The time series portfolio holds all currencies weighted each day according to their respective prior-day overall momentum signals.  The cross-sectional portfolio is each day long (short) the three currencies with the highest (lowest) overall momentum signals. Key performance metrics are annualized average gross return, annualized standard deviation of returns, annualized gross Sharpe ratio (assuming risk-free rate 0%) and maximum drawdown. Using daily foreign currency exchange rates for 23 conventional currencies and seven cryptocurrencies versus the U.S. dollar as available through late March 2017, they find that: Keep Reading