Momentum Investing

How sensitive in a recent sample are outcomes from simple trend following rules to the length of the measurement interval used to detect a trend. To investigate, we consider two simple types of trend following rules as applied to the U.S. market:

1. Hold a risky asset when its price is above its x-month simple moving average (SMAx) and cash when below, with x ranging from two to 12.
2. Hold a risky asset when its x-month return, absolute or intrinsic momentum (IMx), is positive and cash when negative, with x ranging from one to 12.

Specifically, we apply these 23 rule variations to time the S&P 500 Index since the inception of SPDR S&P 500 (SPY) as an easy and flexible way to trade the index over the available sample period and two subperiods, the decade of the 2000s and the last five years. We use the yield on 3-month U.S. Treasury bills (T-bills) to approximate return on cash. We use buying and holding SPY as a benchmark for the active rules. Using monthly closing levels of the S&P 500 Index since April 1992 and dividend-adjusted prices for SPY and T-bill yields since January 1993, all through March 2014, we find that: Keep Reading

Does stock market timing based on simple moving average (SMA) and time-series (intrinsic or absolute) momentum strategies really work? In the November 2013 version of his paper entitled “The Real-Life Performance of Market Timing with Moving Average and Time-Series Momentum Rules”, Valeriy Zakamulin tests realistic long-only implementations of these strategies with estimated trading frictions. The SMA strategy enters (exits) an index when its unadjusted monthly close is above (below) the average over the last 2 to 24 months. The intrinsic momentum strategy enters (exits) an index when its unadjusted return over the last 2 to 24 months is positive (negative). Unadjusted means excluding dividends. He applies the strategies separately to four indexes: the S&P Composite Index, the Dow Jones Industrial Average, long-term U.S. government bonds and intermediate-term U.S. government bonds. When not in an index, both strategies earn the U.S. Treasury bill (T-bill) yield. He considers two test methodologies: (1) straightforward inception-to-date in-sample rule optimization followed by out-of-sample performance measurement, with various break points between in-sample and out-of-sample subperiods; and, (2) average performance across two sets of bootstrap simulations that preserve relevant statistical features of historical data (including serial return correlation for one set). He focuses on Sharpe ratio (including dividends) as the critical performance metric, but also considers terminal value of an initial investment. He assumes the investor is an institutional paying negligible broker fees and trading in small orders that do not move prices, such that one-way trading friction is the average bid-ask half-spread. He ignores tax impacts of trading. With these assumptions, he estimates a constant one-way trading friction of 0.5% (0.1%) for stock (bond) indexes. Using monthly closes and dividends/coupons for the four specified indexes and contemporaneous T-bill yields during January 1926 through December 2012 (87 years), he finds that: Keep Reading

Is there a way to avoid the stock momentum crashes that occur when the positive feedback loop between past and future returns breaks down? In his November 2013 paper entitled “Crowded Trades, Short Covering, and Momentum Crashes“, Philip Yan investigates the power of the interaction between short interest and institutional trading activity to explain stock momentum crashes and thereby offer a way to avoid these crashes. Each month he sorts stocks into ranked tenths (deciles) based on returns from 12 months ago to one month ago (skipping the most recent month to avoid reversals). He reforms each month baseline winner and loser portfolios from the value-weighted deciles of extreme high and low returns, respectively. He then segments the loser portfolio into crowded losers (stocks that are most shorted and have the highest institutional exit rate) and non-crowded losers (stocks that are most shorted but do not have the highest institutional exit rate). The most shorted losers are those within the fifth of stocks with the highest short interest ratios (short interest divided by shares outstanding). The losers with the highest institutional exit rates are those within the fifth of stocks with the most shares completely liquidated by institutional investors divided by shares outstanding. He defines three value-weighted long-short portfolios: (1) the baseline portfolio buys the baseline winners and shorts the baseline losers; (2) the crowded portfolio buys the baseline winners and shorts the crowded losers; and, (3) the “non-crowded portfolio buys the baseline winners and shorts the non-crowded losers”. Using daily and monthly stock return, monthly short interest and quarterly institutional ownership data during January 1980 through September 2012, high-frequency short sales data during 2005 through 2012, and monthly price data for 63 futures contract series as available during January 1980 through June 2013, he finds that: Keep Reading

A subscriber flagged an apparently very attractive exchange-traded fund (ETF) momentum-volatility-correlation strategy that, as presented, generates a optimal compound annual growth rate of 45.7% with modest maximum drawdown. The strategy chooses from among the following seven ETFs:

ProShares Ultra S&P500 (SSO)
SPDR EURO STOXX 50 (FEZ)
iShares MSCI Emerging Markets (EEM)
iShares Latin America 40 (ILF)
iShares MSCI Pacific ex-Japan (EPP)
Vanguard Extended Duration Treasuries Index ETF (EDV)
iShares 1-3 Year Treasury Bond (SHY)

The steps in the strategy are, at the end of each month:

1. For the first six of the above ETFs, compute log returns over the last three months and standard deviation (volatility) of log returns over the past six months.
2. Standardize these the monthly sets of past log returns and volatilities based on their respective means and standard deviations.
3. Rank the six ETFs according to the sum of 0.75 times standardized past log return plus 0.25 times past standardized volatility.
4. Buy the top-ranked ETF for the next month.
5. However, if at the end of any month, the correlation of SSO and EDV monthly log returns over the past four months is greater than 0.75, instead buy SHY for the next month.

The developer describes this strategy as an adaptation of someone else’s strategy and notes that he has tested a number of systems. How material might the implied secondary and primary data snooping bias be in the performance of this system? To investigate, we examine the fragility of performance statistics to variation of each strategy parameter separately. As presented, the author substitutes other ETFs for the two with the shortest histories to extend the test period backward in time. We use only price histories as available for the specified ETFs, limited by EDV with inception January 2008. Using monthly adjusted closing prices for the above seven ETFs and for SPDR S&P 500 (SPY) during January 2008 through February 2014 (74 months), we find that: Keep Reading

Are there parallels at the country stock market level of the size, value and momentum effects observed for individual stocks? In their January 2014 paper entitled “Value, Size and Momentum across Countries”, Adam Zaremba and Przemysław Konieczka investigate country-level value, size and momentum premiums. They measure these factors at the country level as:

• Value (V): book-to-market ratio of country stocks aggregated via the weighting scheme used to construct the country stock index at the time of portfolio formation.
• Size (S): total market capitalization of country stocks at the time of portfolio formation.
• Long-Term Momentum (LTM): country index return during the 12 months before portfolio formation.
• Short-Term Momentum (STM): country index return during the month before portfolio formation.

They calculate these factors using either MSCI equity indexes (47 indexes available at the beginning of the sample period) or local stock indexes (only 24 indexes available at the beginning of the sample period). They measure the country-level premium for each factor as the return on an equally weighted portfolio that is each month long (short) the 30% of countries with the highest (lowest) expected returns for that factor. They fully collateralize short sides with reserves in the risk-free rate. They also calculate a total market return as the capitalization-weighted average return across all country markets. They perform calculations separately in U.S. dollars, euros and yen. Using monthly firm/stock data for listed stocks as available within 66 countries from the end of May 2000 through November 2013, and contemporaneous Fama-French model U.S. factors, they find that: Keep Reading

Does the variation of individual stock returns with liquidity support an investment style? In the January 2014 update of their paper entitled “Liquidity as an Investment Style”, Roger Ibbotson and Daniel Kim examine the viability and distinctiveness of a liquidity investment style and investigate the portfolio-level performance of liquidity in combination with size, value and momentum styles. They define liquidity as annual turnover, number of shares traded divided by number of shares outstanding. They hypothesize that stocks with relatively low (high) turnover tend to be near the bottom (top) of their ranges of expectation. Their liquidity style thus overweights (underweights) stocks with low (high) annual turnover. They define size, value and momentum based on market capitalization, earnings-to-price ratio (E/P) and past 12-month return, respectively. They reform test portfolios via annual sorts into four ranks (quartiles), with initial equal weights and one-year holding intervals. Using monthly data for the 3,500 U.S. stocks with the largest market capitalizations (re-selected each year) over the period 1971 through 2013, they find that: Keep Reading

Does a stronger stock price trend, up or down, indicate a bigger momentum effect? In their February 2014 paper entitled “Trend Salience, Investor Behaviors and Momentum Profitability”, Paul Docherty and Gareth Hurst test variations of a conventional stock momentum strategy that consider both past returns and rate of change of past returns relative to other stocks. Specifically, each year they reform a universe of the 500 stocks listed on the Australian Stock Exchange with the largest market capitalizations. Then each month, they rank stocks in the current universe based on past cumulative returns, designating the top fifth (quintile) as winners and bottom quintile as losers. They then further categorize each winner (loser) stock as salient if the ratio of its geometric mean return over the past 3, 6 or 9 months to its geometric mean return over the past 12 months is greater (less) than the quintile median of this ratio. Finally, they each month form equally weighted momentum and salience portfolios (with a skip-month between ranking and portfolio formation) and hold for overlapping intervals of 3, 6, 9 or 12 months. These portfolios include:

1. Conventional momentum: long (short) the winners (losers).
2. Salient momentum: long (short) salient winners (salient losers).
3. Non-salient momentum: long (short) non-salient winners (non-salient losers).

Using monthly return data for the specified Australian stocks during January 1992 through December 2011, they find that: Keep Reading

Is it possible to predict serial correlation (autocorrelation) of stock returns, and thereby enhance reversal and momentum strategies. In the January 2014 version of his paper entitled “The Information Content of Option Prices Regarding Future Stock Return Serial Correlation”, Scott Murray investigates the relationship between the variance ratio (the ratio of realized to implied stock return variance, a measure of the variance risk premium) to stock return serial correlation. He calculates realized variance at the end of each month from daily log stock returns over the prior three months. He calculates implied variance at the end of each month as the square of the volatility implied by at-the-money 0.5 delta call and put options one month from expiration. He first measures the power of the variance ratio to predict stock return serial correlation. He then tests the effectiveness of this predictive power to enhance reversal and momentum stock trading. Using the specified return and option data for all U.S. stocks with listed options during January 1996 through December 2012, he finds that: Keep Reading

Do trend following strategies widely used by managed futures funds break down during financial crises? In the December 2013 version of their paper entitled “Is This Time Different? Trend Following and Financial Crises”, Mark Hutchinson and John O’Brien examine the effectiveness of trend following strategies as applied to futures contract series during and between financial crises. They define a financial crisis interval as the two to four years after the start of the crisis. They consider six global crises: (1) the Great Depression commencing 1929: (2) the 1973 oil crisis; (3) the third world debt crisis of 1981; (4) the crash of October 1987; (5) the bursting of the dot-com bubble in 2000; and, (6) the sub-prime/euro crisis commencing in 2007. They also consider eight regional crises during 1977 through 2000. They calculate momentum returns for each asset class by each month weighting constituent contract series proportionally to their excess return over the past one to 12 months and inversely to an estimate of their volatility based on lagged data. They include estimates of transaction costs proportional to the value traded that vary by asset class and time period. They also incorporate management and incentive fees (based on high water mark) of 2% and 20%, respectively. Using actual and modeled futures prices encompassing 21 equity indexes, 13 government bonds, nine currency exchange rates and 21 commodities (and contemporaneous risk-free rates) during January 1921 through June 2013, they find that: Keep Reading

Is there a tractable way to combine momentum investing with Modern Portfolio Theory (MPT)? In their December 2013 paper entitled “Tactical MPT and Momentum: the Modern Asset Allocation (MAA)”, Wouter Keller and Hugo van Putten present a tactical, simplified, long-only version of MPT that applies momentum to estimate future asset returns. Specifically, they:

1. Make MPT tactical by using short historical intervals to estimate future asset returns (rate of return, or absolute momentum), return volatilities (based on daily returns) and return correlations (based on daily returns), assuming that behaviors over a short historical interval will materially persist during the next month.
2. Exclude from the portfolio any assets with negative estimated returns (i.e., negative returns over the specified historical interval).
3. Simplify correlation calculations by relating daily historical returns for each asset to those for a single index (the equally weighted average returns for all assets) rather than to those for all other assets separately.
4. Dampen any errors in rapidly changing asset return, volatility and correlation estimates by “shrinking” them toward their respective averages across all assets in the universe, and dampen the predicted market volatility by “shrinking” it toward zero.

They reform the MAA portfolio monthly at the first close. Their baseline historical interval for estimation of all variables is four months (84 trading days). Their baseline shrinkage factor for all variables is 50%. Their benchmark is the equally weighted (EW) “market” of all assets, rebalanced monthly. They assume a one-way trading friction of 0.1%. They consider a range of portfolio performance metrics: annualized return, annual volatility, maximum drawdown, Sharpe ratio, Omega ratio and Calmar ratio. Using daily dividend-adjusted prices for assets allocated to nine universes (of seven to 130 assets, generally consisting of asset class proxy funds) during November 1997 through mid-November 2013, they find that: Keep Reading