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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.

One, Three, Five or Seven Stock Return Factors?

How many, and which, factors should investors include when constructing multi-factor smart beta portfolios? In their August 2017 paper entitled “How Many Factors? Does Adding Momentum and Volatility Improve Performance”, Mohammed Elgammal, Fatma Ahmed, David McMillan and Ali Al-Amari examine whether adding momentum and low-volatility factors enhances the Fama-French 5-factor (market, size, book-to-market, profitability, investment) model of stock returns. They consider statistical significance, economic sense and investment import. Specifically, they:

  • Determine whether factor regression coefficient signs and values distinguish between several pairs of high-risk and low-risk style portfolios (assuming stock style portfolio performance differences derive from differences in firm economic risk).
  • Relate time-varying factor betas across style portfolios to variation in economic and market risks as proxied by changes in U.S. industrial production and S&P 500 Index implied volatility (VIX), respectively.
  • Test an out-of-sample trading rule based on extrapolation of factor betas from 5-year historical rolling windows to predict next-month return for five sets (book-to-market, profitability, investment, momentum, quality) of four style portfolios (by double-sorting with size) and picking the portfolio within a set with the highest predicted returns.

Using monthly factor return data during January 1990 through October 2016, they find that: Keep Reading

FundX Upgrader Funds of Funds Performance

A subscriber requested review of FUNDX momentum-oriented funds of funds. We focus on three funds: FundX Upgrader (FUNDX)FundX Aggressive Upgrader (HOTFX); and, FundX Conservative Upgrader (RELAX). The offeror describes the upgrading process as follows: “…we sort funds and ETFs by risk, separating more speculative sector and single-country funds from more diversified funds, and we rank these funds each month based on relative performance. We buy highly ranked funds and ETFs and sell these funds when they fall in our ranks. By continually following this active process of buying leaders and selling laggards, the Upgrading strategy seeks to align the FundX Upgrader Funds portfolios with current market leadership and change the Fund portfolios as market leadership changes.” Strategy details are proprietary. As benchmarks and competition, we consider SPDR S&P 500 (SPY) for large-capitalization stocks, iShares Russell 2000 (IWM) for small-capitalization stocks and Simple Asset Class ETF Momentum Stategy (SACEMS) Top 1 and equal-weighted (EW) Top 3 variations. Using monthly total returns for FUNDX, HOTFX, RELAX, SPY and IWM since July 2002 (limited by HOTFX and RELAX), SACEMS Top 1 since January 2003 and SACEMS EW Top 3 since August 2006, all through July 2017, we find that: Keep Reading

Stock Factor/Anomaly Momentum

Do stock factors/anomalies exhibit performance streaks exploitable via intrinsic (absolute, or time series) and relative (cross-sectional) momentum? In his July 2017 paper entitled “Factor Momentum and the Momentum Factor”, Sina Ehsani investigates stock factor/anomaly monthly time series (TS) and cross-sectional (XS) momentum. He considers 15 anomalies for U.S. stocks (accruals, betting against beta, investments, cash flow-to-price, earnings-to-price, book-to-market, long-term reversal, liquidity, net share issue, quality minus junk, profitability, residual variance relative to the 3-factor model, market capitalization, short-term reversal and momentum) and global stock versions of seven of these anomalies. He considers the following baseline strategies:

  • Time series momentum:
    1. TS Winners –  each month hold equally weighted anomaly hedge portfolios with a positive average monthly return over the past 12 months.
    2. TS Losers – each month hold equally weighted anomaly hedge portfolios with a negative average monthly return over the past 12 months.
    3. TS – each month buy TS Winners and sell TS Losers.
  • Cross-sectional momentum:
    1. XS Winners –  each month hold equally weighted anomaly hedge portfolios with an above-average monthly return over the past 12 months.
    2. XS Losers – each month hold equally weighted anomaly hedge portfolios with a below-average monthly return over the past 12 months.
    3. XS – each month buy XS Winners and sell XS Losers.
  • Benchmark – each month hold an equally weighted combination of all anomaly hedge portfolios.

He tests different lookback and holding intervals for these strategies. He also tests interaction of factor/anomaly momentum with investor sentiment. Using monthly returns as available for the 15 U.S. stock anomalies since July 1963 and seven of these anomalies applied to global stocks since July 1990, all through December 2015 (mostly Kenneth French data), he finds that: Keep Reading

Acceleration Stock Momentum Strategy

Does incorporation of stock price acceleration boost the performance of a conventional momentum strategy? In their July 2017 paper entitled “Evolution of Historical Prices in Momentum Investing”, Li-Wen Chen, Hsin-Yi Yu and Wen-Kai Wang examine whether stock price acceleration adds value to a conventional momentum strategy among U.S. stocks by identifying the best winners and the worst losers. They focus on a stock ranking interval of 12 months and a portfolio holding interval of six months, with a skip-month between. Specifically, they each month:

  • Rank stocks into fifths (quintiles) based on past 12-month returns. The top (bottom) quintile holds winners (losers).
  • Fit daily time series prices over the same past 12 months for each stock to a quadratic equation and re-rank stocks within past return quintiles by the coefficient of the quadratic term, resulting in 25 portfolios sorted by past return and quadratic coefficient. A positive (negative) coefficient means that price is accelerating up (down).
  • Skip one month.
  • Compare three value-weighted hedge portfolios held over the next six months to highlight the incremental effect of the quadratic coefficient on conventional momentum:
    1. Conventional: buy winners and sell losers.
    2. Acceleration: buy accelerating winners and sell accelerating losers.
    3. Deceleration: buy decelerating winners and sell decelerating losers.

The monthly return for each strategy is the average return for its six overlapping portfolios. Using daily and monthly returns, characteristics and accounting data for a broad sample of U.S. common stocks with price at least $5 during January 1962 through December 2014, they find that:

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Stock Momentum Strategy Risk Management with and without Leverage

What aspect of momentum strategy volatility is best for risk management? In his July 2017 paper entitled “Risk-Managed Momentum: The Effect of Leverage Constraints”, Federico Nucera examines stock momentum strategy risk management via different aspects of realized strategy variance with and without latitude for leverage. Specifically, he considers the following stock momentum strategy variations:

  1. Conventional – each month long (short) the value-weighted tenth, or decile, of stocks that are the biggest winners (losers) last month per Kenneth French’s specifications.
  2. Full Variance Weighting – each month weighting the conventional momentum portfolio by 1.44% (12% annual volatility) divided by the full variance of daily conventional momentum strategy returns over the past six months.
  3. Positive Semi-variance Weighting – each month weighting the conventional momentum portfolio by 0.68% divided by the semi-variance of positive daily conventional momentum strategy returns over the past six months.
  4. Negative Semi-variance Weighting – each month weighting the conventional momentum portfolio by 0.76% divided by the semi-variance of negative daily conventional momentum strategy returns over the past six months.

For each variation, he considers full weights (leverage), weights limited to 1.5X leverage and weights limited to 1.0X (no leverage). He focuses on gross annualized Sharpe ratio as the key performance metric. Using daily and monthly value-weighted momentum decile portfolio returns for a broad sample of U.S. stocks during November 1926 through December 2016, he finds that: Keep Reading

Extended Simple Momentum Strategy Test of TSP Funds/Proxies

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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Conservative Breadth Rule for Asset Class Momentum Crash Protection

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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SACEMS-SACEVS Diversification with Mutual Funds

“SACEMS-SACEVS Mutual Diversification” finds that the “Simple Asset Class ETF Value Strategy” (SACEVS) and the “Simple Asset Class ETF Momentum Strategy” (SACEMS) are mutually diversifying. Do the longer samples available from “SACEVS Applied to Mutual Funds” and “SACEMS Applied to Mutual Funds” confirm this finding? 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).

Using monthly gross returns for SACEVS and SACEMS mutual fund portfolios during September 1997 through June 2017, we find that:

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SACEMS at a Bimonthly Frequency

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

Trend Following with Intrinsic Momentum over the Very Long Run

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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