# 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.

**March 22, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

How diversifying are different equity factors within and across country stock markets? In his January 2016 paper entitled “The Power of Equity Factor Diversification”, Ulrich Carl analyzes diversification properties of six equity factors (market excess return, size, value, momentum, low-beta and quality) across 20 developed stock markets. He defines each factor conventionally as returns to a portfolio that is each month long (short) stocks with the highest (lowest) expected returns based on that factor. He considers: (1) cross-country correlations for each factor; (2) cross-factor correlations for each country; (3) cross-country, cross-factor correlations; (4) dynamics of cross-country correlations for each factor based on rolling 36-month windows of returns; and, (5) cross-country correlations for each factor for the 30% lowest and 30% highest market excess returns (tail events). He also applies principal component analysis as another way to evaluate how diverse the 120 country-factor return streams are. Finally, he constructs cross-factor and cross-country portfolios to assess economic value of diversification properties. Using monthly returns in U.S. dollars for the six factors in each of the 20 countries during January 1991 through April 2015, *he finds that:* Keep Reading

**March 21, 2017** - Equity Options, Momentum Investing

Are strategies that exploit return autocorrelation good places to look for complementary (diversifying) return streams? In the March 2017 version of their paper entitled “Momentum and Covered Calls almost Everywhere”, Stephen Choi, Gil-Lyeol Jeong and Hogun Park examine trend following and covered call strategies at the asset class level both separately and in combination. Their asset class universe consists of three equity indexes, three bond indexes, three commodity indexes and one real estate investment trust (REIT) index. Their trend following (or time series momentum) strategy, which exploits positive autocorrelation of monthly index returns, is long (short) an index when its end-of-month level is above (below) its 12-month simple moving average. Their covered call strategy, which exploits negative autocorrelation (reversion) of index returns, is continuous, such as specified for the CBOE S&P 500 BuyWrite Index. They compare trend following and covered call strategies, separately and in combination, with buy-and-hold for single-class indexes and for multi-class portfolios of indexes. They consider three ways to construct multi-class portfolios (see “Tests of Strategic Allocations Based on Risk Metrics”): (1) maximum diversification (MDR), which maximizes the ratio of the sum of volatilities for individual assets divided by overall portfolio volatility; (2) equal risk contribution (ERC), a form of risk parity with adjustments for correlation; and, (3) equal weight (EW). They rebalance these portfolios quarterly, with volatility/correlation inputs for MDR and ERC based on a 3-year rolling window of historical data. They focus portfolio testing for only 10 years (2007-2016) based on availability of data for covered call indexes. Using the specified data as available from the end of 1971 through 2016, *they find that:* Keep Reading

**March 15, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

Are the returns of factors widely used to predict the cross-section of stock returns themselves predictable? In the January 2016 draft of his paper entitled “Equity Factor Predictability”, Ulrich Carl analyzes predictability of market, size (market capitalization), value (book-to-market ratio), momentum (returns from 12 months ago to one month ago), low beta (betting against beta) and quality factor returns. All factor returns derive from hedge portfolios that are long (short) stocks with high (low) expected returns based on their factor values. He employs a broad range of economic and financial variables in four sets and multiple ways of testing predictability to ensure robustness of findings and limit model/data snooping bias. Predictability tests he applies include: combinations of simple forecasts (mean or median of single-variable regression forecasts); principal component analysis to distill forecasting variables into a few independent predictive factors; and, methods that adjust variable emphasis according to their respective past performances. He considers several predictability evaluation metrics, including: mean squared error compared to that of the historical average return; utility gain of timing based on predictability; and, information ratio (difference in return divided by difference in risk) relative to the historical average return. He mostly examines next-month forecasts with a one-month gap between predictive variable measurement and forecasted return over two test periods: 1975-2013 and 1950-2013. Using monthly returns for the six factors (start dates ranging from 1928 to 1958), a large set of financial variables since 1928 and a large set of economic variables since 1962, all through November 2013, *he finds that:* Keep Reading

**March 10, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

How attractive are purified factor portfolios, constructed to focus on one factor by avoiding exposures to other factors? In their January 2017 paper entitled “Pure Factor Portfolios and Multivariate Regression Analysis”, Roger Clarke, Harindra de Silva and Steven Thorley explore a multivariate regression approach to generating pure factor portfolios. They consider five widely studied factors: value (earnings yield); momentum (cumulative return from 12 months ago to one month ago); size (market capitalization); equity market beta; and, profitability (gross profit margin). They also consider bond beta (regression of stock returns on 10-year U.S. Treasury note returns) to examine interest rate risk. They each month reform two types of factor portfolios:

- Primary – a factor portfolio with weights that deviate simply from market weights based on analysis of just one factor, with differences from market portfolio weights scaled by market capitalization.
- Pure – a factor portfolio derived from a multiple regression that isolates each factor, ensuring that it has zero exposures to all other factors.

They measure factor portfolio performance based on: average difference in monthly returns between each factor portfolio and the market portfolio; annualized standard deviation of the underlying monthly return differences; 1-factor (market) alpha; and, information ratio (alpha divided by incremental risk to the market portfolio). Using return and factor data for the 1,000 largest U.S. stocks during 1967 through 2016, *they find that:* Keep Reading

**February 27, 2017** - Momentum Investing, Size Effect, Value Premium, Volatility Effects

Are there plenty of exchange-traded funds (ETF) offering positive or negative exposures to widely accepted factor premiums? In his February 2017 paper entitled “Are Exchange-Traded Funds Harvesting Factor Premiums?”, David Blitz analyzes the exposures of U.S. equity ETFs to market, size, value, momentum and volatility factors. Specifically, he calculates factor betas (exposures) from a multi-factor regression of monthly excess (relative to the risk-free rate) total returns for each ETF versus market, small-minus-big size (SMB), high-minus-low value (HML), winners-minus-losers momentum (WML) and low-minus-high volatility (LV-HV) factor returns during 2011 through 2015. His overall sample consists of 415 U.S. equity ETFs with least 36 months of return history as of the end of 2015. He also considers subsamples consisting of: (1) 103 smart beta ETFs that explicitly target factor premiums, including fundamentally weighted and high-dividend funds; and, (2) the remaining 312 conventional ETFs, including sector funds and funds with conflicting factor exposures. He includes lists of the 10 ETFs with the most positive and the 10 ETFs with the most negative exposures to each factor from among the 100 largest ETFs. Using monthly Assets under Management (AuM) and total returns for the specified 415 ETFs, along with the monthly risk-free rate and the selected factor premiums during January 2011 through December 2015, *he finds that:* Keep Reading

**February 14, 2017** - Momentum Investing

Are there profitable intraday stock price momentum and/or reversal strategies? In his January 2017 paper entitled “Intra-Day Momentum”, Oleg Komarov examines the profitability of intraday times series (intrinsic or absolute) and cross-sectional stock price momentum and reversal strategies. Time series strategies involve predicting the behavior of a stock based on its own past return. Cross-sectional strategies involve predicting the behaviors of equally weighted groups of stocks sorted into tenths (deciles) based on their respective past returns. Specifically, he segments the trading day into half-hours and overnight and then examines whether returns for past half-hours predict returns for future half-hours, focusing empirically on whether: (1) returns during 9:30-12:00 predict returns during 15:30-1600; and, (2) returns during 9:30-13:00 predict returns during 13:30-15:30. He conducts purely statistical tests and tests based on trading strategies. He concludes with consideration of overnight returns. Using cleaned data for a broad sample of U.S. common stocks (excluding microcaps) during January 1993 through May 2010, *he finds that:* Keep Reading

**February 3, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

Does suppressing unrelated risks from stock factor portfolios improve performance? In their January 2017 paper entitled “Diversify and Purify Factor Premiums in Equity Markets”, Raul Leote de Carvalho, Lu Xiao, François Soupé and Patrick Dugnolle investigate how to improve the capture of four types of stock factor premiums: value (12 measures); quality (16 measures); low-risk (two measures); and, momentum (10 measures). They standardize the different factor measurement scales based on respective medians and standard deviations, and they discard outliers. Their baseline factors portfolios employ constant leverage (CL) by each month taking 100% long (100% short) positions in stocks with factor values associated with the highest (lowest) expected returns. They strip unrelated risks from baseline portfolios by:

- SN – imposing sector neutrality by segregating stocks into 10 sectors before ranking them for assignment to long and short sides of the factor portfolio.
- CV – replacing constant leverage by each month weighting each stock in the portfolio to target a specified volatility based on its actual volatility over the past three years.
- HB – hedging the market beta of the portfolio each month based on market betas of individual stocks calculated over the past three years by taking positions in the capitalization-weighted market portfolio and cash.
- HS – hedging the size beta of the portfolio each month based on size betas of individual stocks calculated over the past three years by taking positions in the equal-weighted market portfolio and the capitalization-weighted market portfolio.

They examine effects of combining measures within factor types, combining types of factors and excluding short sides of factor portfolios. They also look at U.S., Europe and Japan separately. Their portfolio performance metric is the information ratio, annualized average return divided by annualized standard deviation of returns. Using data for stocks in the MSCI World Index since January 1997, in the S&P 500 Index since January 1990, in the STOXX Europe 600 Index since January 1992 and in the Japan Topix 500 Index since August 1993, all through November 2016, *they find that:* Keep Reading

**February 1, 2017** - Fundamental Valuation, Momentum Investing

Are trend in stock fundamentals and stock price momentum mutually reinforcing return predictors? In their January 2017 paper entitled “Dual Momentum”, Dashan Huang, Huacheng Zhang and Guofu Zhou combine a measure of fundamentals trend and past return to form a U.S. stock portfolio designed to exploit the powers of both to select outperforming stocks. To construct their measure of fundamentals trend, they each month:

- For each stock, collect the last eight quarters of seven variables: return on equity; return on assets; earnings per share; accrual-based operating profit to equity; cash-based operating profit to assets; gross profit to assets; and, net payout ratio.
- For each stock, calculate four moving averages for each fundamental variable over the last 1, 2, 4 and 8 quarters (for a total of 28 moving averages per stock).
- Across all stocks, relate next-month excess stock return to the most recent 28 fundamentals moving averages via multiple regression to obtain 28 fundamentals trend betas.
- For each fundamentals beta for each stock, calculate an expected beta as the average of the last 12 monthly betas.
- For each stock, calculate a fundamentals-implied return (FIR) by applying the 28 expected betas to the most recently available 28 fundamentals moving averages.

They then each month rank stocks into value-weighted fifths (quintiles) based on FIR. Separately, they each month rank the same stocks into value-weighted quintiles based on conventional price momentum (cumulative return from 12 months ago to one month ago). Using quarterly fundamentals and monthly returns for a broad sample of U.S. stocks during January 1973 through September 2015, *they find that:* Keep Reading

**January 25, 2017** - Bonds, Equity Premium, Momentum Investing, Strategic Allocation

“Cross-asset Class Intrinsic Momentum” summarizes research finding that past country stock index (government bond index) returns relate positively (positively) to future country stock market index returns and negatively (positively) to future country government bond index returns. Is this finding useful for specifying a simple strategy using exchange-traded fund (ETF) proxies for the U.S. stock market and U.S. government bonds? To investigate we test the following five strategies:

- Buy and hold.
- TSMOM Long Only – Each month, hold the asset (cash) if its own 12-month past return is positive (negative).
- TSMOM Long or Short – Each month, hold (short) the asset if its own 12-month past return is positive (negative).
- XTSMOM Long Only – Each month hold stocks if 12-month past returns for stocks and government bonds are both positive, and otherwise hold cash. Each month hold bonds if 12-month past returns are negative for stocks and positive for government bonds, and otherwise hold cash.
- XTSMOM L-S-N (Long, Short or Neutral) – Each month hold (short) stocks if 12-month past returns for both are positive (negative), and otherwise hold cash. Each month hold (short) bonds if 12-month past returns are negative (positive) for stocks and positive (negative) for bonds, and otherwise hold cash.

We use SPDR S&P 500 (SPY) and iShares 7-10 Year Treasury Bond (IEF) as proxies for the U.S. stock market and U.S. government bonds. We use the 3-month U.S. Treasury bill (T-bill) yield as the return on cash. We apply the five strategies separately to SPY and IEF, and to an equally weighted, monthly rebalanced combination of the two for a total of 15 scenarios. Using monthly total returns for SPY and IEF and monthly T-bill yield during July 2002 (inception of IEF) through December 2016, *we find that:* Keep Reading

**January 24, 2017** - Bonds, Equity Premium, Momentum Investing, Strategic Allocation

Are stock and bond markets mutually reinforcing with respect to time series (intrinsic or absolute return) momentum? In their December 2016 paper entitled “Cross-Asset Signals and Time Series Momentum”, Aleksi Pitkajarvi, Matti Suominen and Lauri Vaittinen examine a strategy that times each of country stock and government bond (constant 5-year maturity) indexes based on past returns for both. Specifically:

- For stocks, they each month take a long (short) position in a country stock index if past returns for both the country stock and government bond indexes are positive (negative). If past stock and bond index returns have different signs, they take no position.
- For bonds, they each month take a long (short) position in a country government bond index if past return for bonds is positive (negative) and past return for stocks is negative (positive). If past stock and bond index returns have the same sign, they take no position.

They call this strategy cross-asset time series momentum (XTSMOM). For initial strategy tests, they consider past return measurement (lookback) and holding intervals of 1, 3, 6, 9, 12, 24, 36 or 48 months. For holding intervals longer than one month, they average monthly returns for overlapping positions. For most analyses, they focus on lookback interval 12 months and holding interval 1 month. For a given lookback and holding interval combination, they form a diversified XTSMOM portfolio by averaging all positions for all countries. They measure excess returns relative to one-month U.S. Treasury bills. They employ the MSCI World Index and the Barclays Capital Aggregate Bond Index as benchmarks. Using monthly stock and government bond total return indexes for 20 developed countries as available during January 1980 through December 2015, *they find that:* Keep Reading