# 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.

**October 30, 2017** - Momentum Investing

What makes momentum investing tick? In their September 2017 paper entitled “Understanding the Momentum Risk Premium: An In-Depth Journey Through Trend-Following Strategies”, Paul Jusselin, Edmond Lezmi, Hassan Malongo, Côme Masselin, Thierry Roncalli and Tung-Lam Dao present a theoretical analysis of the momentum risk premium. They assume that asset prices generally exhibit geometric Brownian motion (randomness) with constant volatility, but with a time-varying trend. They examine momentum strategy performance based on this model and test some conclusions empirically on a multi-class set of asset indexes. Based on mathematical derivations and using monthly returns for a universe of four equity, four government bond, three interest rate, five currency and four commodity indexes during January 2000 through July 2017, *they find that:* Keep Reading

**October 24, 2017** - Equity Premium, Momentum Investing, Value Premium, Volatility Effects

Is it better to build equity multifactor portfolios by holding distinct single-factor sub-portfolios, or by picking only stocks that satisfy multiple factor criteria? In their September 2017 paper entitled “Smart Beta Multi-Factor Construction Methodology: Mixing vs. Integrating”, Tzee-man Chow, Feifei Li and Yoseop Shim compare long-only multifactor portfolios constructed in two ways:

- Integrated – each quarter, pick the 20% of stocks with the highest average standardized factor scores and weight by market capitalization.
- Mixed – each quarter, hold an equal-weighted combination of single-factor portfolios, each comprised of the capitalization-weighted 20% of stocks with the highest expected returns for that factor.

They consider five factors: value (book-to-market ratio), momentum (return from 12 months ago to one month ago), operating profitability, investment (asset growth) and low-beta. They reform factor portfolios annually for all except momentum and low-beta, which they reform quarterly. Using firm data required for factor calculations and associated stock returns for a broad sample of U.S. stocks during June 1968 through December 2016, *they find that:* Keep Reading

**October 17, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

How efficiently do mutual funds capture factor premiums? In their April 2017 paper entitled “The Incredible Shrinking Factor Return”, Robert Arnott, Vitali Kalesnik and Lillian Wu investigate whether factor tilts employed by mutual fund managers deliver the alpha found in empirical research. They focus on four factors most widely used by mutual fund managers: market, size, value and momentum. They note that ideal long-short portfolios used to compute factor returns ignore costs associated with real-world implementation: trading costs and commissions, missed trades, illiquidity, management fees, borrowing costs for the short side and inability to short some stocks. Portfolio returns also ignore bias associated with data snooping in factor discovery and market adaptation to published research. They focus on U.S. long-only equity mutual funds, but also consider similar international funds. They apply a two-stage regression first to identify fund factor exposures and then to measure performance shortfalls per unit of factor exposure. Using data for 5,323 U.S. and 2,364 international live and dead long-only equity mutual funds during January 1990 through December 2016, *they find that:*

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**October 16, 2017** - Momentum Investing, Size Effect, Value Premium, Volatility Effects

Which equity factors have high and low expected returns? In their February 2017 paper entitled “Forecasting Factor and Smart Beta Returns (Hint: History Is Worse than Useless)”, Robert Arnott, Noah Beck and Vitali Kalesnik evaluate attractiveness of eight widely used stock factors. They measure alpha for each factor conventionally via a portfolio that is long (short) stocks with factor values having high (low) expected returns, reformed systematically. They compare factor alpha forecasting abilities of six models:

- Factor return for the last five years.
- Past return over the very long term (multiple decades), a conventionally used assumption.
- Simple relative valuation (average valuation of long-side stocks divided by average valuation of short-side stocks), comparing current level to its past average.
- Relative valuation with shrunk parameters to moderate forecasts by dampening overfitting to past data.
- Relative valuation with shrunk parameters and variance reduction, further moderating Model 4 by halving its outputs.
- Relative valuation with look-ahead full-sample calibration to assess limits of predictability.

They employ simple benchmark forecasts of zero factor alphas. Using 24 years of specified stock data (January 1967 – December 1990) for model calibrations, about 20 years of data (January 1991 – October 2011) to generate forecasts and the balance of data (through December 2016) to complete forecast accuracy measurements, *they find that:* Keep Reading

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

Does transient factor popularity drive factor/smart beta portfolio performance by pushing valuations of associated stocks up and down? In their February 2016 paper entitled “How Can ‘Smart Beta’ Go Horribly Wrong?”, Robert Arnott, Noah Beck, Vitali Kalesnik and John West examine degrees to which factor hedge portfolio and stock factor tilt (smart beta) backtests are attractive due to:

- Steady and clearly sustainable factor premiums; or,
- Changes in factor relative valuations, measured as average price-to-book value ratio of stocks with high expected returns (factor portfolio long side) divided by average price-to-book ratio of stocks with low expected returns (factor portfolio short side). This ratio tends to increase (decrease) as investor assets move into (out of) factor portfolios.

They consider six long-short factor hedge portfolios: value, momentum, market capitalization (size), illiquidity, low beta and gross profitability. They also consider six smart beta portfolios, which they (mostly) require to sever the relationship between stock price and portfolio weight and to have low turnover, substantial market breadth, liquidity, capacity, transparency, ease of testing and low fees: equal weight, fundamental index, risk efficient, maximum diversification, low volatility and quality. Using specified annual and monthly factor measurement data and returns for a broad sample of U.S. stocks during January 1967 through September 2015, *they find that:* Keep Reading

**October 5, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

Do broad (capitalization-weighted) stock market indexes exhibit factor tilts that may indicate concentrations in corresponding risks? In their August 2017 paper entitled “What’s in Your Benchmark? A Factor Analysis of Major Market Indexes”, Ananth Madhavan, Aleksander Sobczyk and Andrew Ang examine past and present long-only factor exposures of several popular market capitalization indexes. Their analysis involves (1) estimating the factor characteristics of each stock in a broad index; (2) aggregating the characteristics across all stocks in the index; and (3) matching aggregated characteristics to a mimicking portfolio of five indexes representing value, size, quality, momentum and low volatility styles, adjusted for estimated expense ratios. For broad U.S. stock indexes, the five long-only style indexes are:

- Value – MSCI USA Enhanced Value Index.
- Size – MSCI USA Risk Weighted Index.
- Quality – MSCI USA Sector Neutral Quality Index.
- Momentum – MSCI USA Momentum Index.
- Low Volatility – MSCI USA Minimum Volatility Index.

For broad international indexes, they use corresponding long-only MSCI World style indexes. Using quarterly stock and index data from the end of March 2002 through the end of March 2017, *they find that:* Keep Reading

**October 3, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium

Does global diversification improve smart beta (equity factor) investing strategies? In their September 2017 paper entitled “Diversification Strikes Again: Evidence from Global Equity Factors”, Jay Binstock, Engin Kose and Michele Mazzoleni examine effects of global diversification on equity factor hedge portfolios. They consider five factors:

- High-Minus-low Value (HML) – book equity divided by market capitalization.
- Small-Minus-Big Size (SMB) – market capitalization.
- Winners-Minus-Losers Momentum (WML) – cumulative return from 12 months ago to one month ago.
- Conservative-Minus-Aggressive Investment (CMA) – change in total assets.
- Robust-Minus-Weak Operating Profitability (RMW) – total sales minus cost of goods sold, selling, general, and administrative expenses and interest, divided by total assets.

They reform each factor portfolio annually at the end of June by: (1) resetting market capitalizations, segregating firms into large (top 90%) and small (bottom 10%); (2) separately for large and small firms, constructing high (top 30% of factor values) minus low (bottom 30%) long-short sub-portfolios; and, (3) averaging returns for the two sub-portfolios to generate factor portfolio returns. They lag firm accounting data by at least six months between fiscal year end and portfolio formation date. They define eight global regions: U.S., Japan, Germany, UK, France, Canada, Other Europe and Asia Pacific excluding Japan. When measuring diversification effects, they consider relatedness of country markets and variation over time. Using the specified firm accounting data and monthly stock returns during October 1990 through February 2016, *they find that:* Keep Reading

**September 20, 2017** - Fundamental Valuation, Momentum Investing

Does uncertainty about future firm earnings underlie stock factor returns? In their August 2017 paper entitled “Uncertainty, Momentum, and Profitability”, Claire Liang, Zhenyang Tang and Xiaowei Xu examine relationships between analyst uncertainty about current-year firm earnings and four U.S. stock return anomalies. They each month estimate uncertainty for each stock as square root of the average squared differences between individual analyst forecasts for current-year earnings and reported earnings per share, divided by stock price. They then each month sort firms into fifths (quintiles) by:

- Uncertainty – as specified.
- Price momentum – stock returns from 12 months ago to one month ago.
- Earnings momentum – most recently announced quarterly earnings minus earnings from the same quarter one year ago, divided by the standard deviation of seasonal differences in earnings for the previous eight quarters.
- Operating profitability – annual revenue minus cost of goods sold, interest expense and selling, general, and administrative expenses, divided by book equity for the last fiscal year.
- Return on equity – earnings before extraordinary items from the most recent quarter divided by prior-quarter book equity.

They calculate gross monthly returns for each factor via an equal-weighted or value-weighted hedge portfolio that is each month long (short) the quintile of stocks with the highest (lowest) factor values. They test the power of uncertainty to explain other factor returns via regressions against uncertainty factor returns. Since some stocks may not have analyst coverage, they test whether idiosyncratic volatility and earnings forecast dispersion are effective substitutes for uncertainty. Using the specified monthly data for all NYSE/AMEX/NASDAQ stocks priced at least $1 during 1983 through 2013, *they find that:*

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**September 19, 2017** - Momentum Investing, Strategic Allocation

A subscriber, noting an article on slowing down intrinsic (absolute or time series) momentum for SPDR S&P 500 (SPY) when its return volatility is relatively high, suggested doing the same for the Simple Asset Class ETF Momentum Strategy (SACEMS). The hypothesis is that this dynamic lookback interval approach avoids undesirable whipsaws when asset returns are volatile. SACEMS each month picks winners from the following set of exchange-traded funds (ETF) based on total returns over a fixed lookback 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)

To investigate the suggested dynamic lookback interval, we each month:

- Calculate the average of the standard deviations of daily returns over the last 60 trading days for the individual risky assets (all except Cash).
- Calculate the average of these end-of-month averages over the past 12 months.
- Divide the current month average standard deviation by the 12-month average of averages to get a lookback interval factor.
- Multiply the baseline fixed lookback interval by the current lookback interval factor.
- Round the result to the nearest whole number of months as the current dynamic lookback interval.

We focus on gross compound annual growth rate (CAGR) and gross maximum drawdown (MaxDD) as key performance statistics for the Top 1, equally weighted (EW) Top 2 and EW Top 3 portfolios of monthly winners. Using daily and monthly total (dividend-adjusted) returns for the specified assets during February 2006 (limited by DBC) through August 2017, *we find that:* Keep Reading

**September 7, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

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