# 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 24, 2021** - Momentum Investing, Strategic Allocation

A subscriber asked for an extended test of a very simple momentum strategy that each month holds Vanguard 500 Index Fund Investor Shares (VFINX) or Vanguard Long-Term Treasury Fund Investor Shares VUSTX according to which of these funds has the highest total return over the last three months. To investigate, based on the way mutual funds report prices, we calculate past 3-month total returns using dividend-adjusted prices for month-ends and strategy returns using dividend adjusted prices for first days of the following month. We assume zero fund switching costs and no restrictions on monthly fund switching. We use buying and holding VFINX as a benchmark. Using the specified fund price series and monthly 3-month U.S. Treasury bill (T-bill) yield from the end of May 1986 (limited by VUSTX) through the beginning of March 2021, *we find that:* Keep Reading

**January 26, 2021** - Momentum Investing, Size Effect, Value Premium

How have value, quality, low-volatility and momentum equity factors, and combinations of these factors, performed in recent years. In their October 2020 paper entitled “Equity Factor Investing: Historical Perspective of Recent Performance”, Benoit Bellone, Thomas Heckel, François Soupé and Raul Leote de Carvalho review and put into context recent performances of these these factors/combinations as applied to medium-capitalization and large-capitalization World, U.S. and European stock universes. They consider both long-short and long-only factor portfolios and further investigate effects of (1) neutralizing beta and sector dependencies, (2) using multiple metrics for each factor and (3) including small stocks. Using firm accounting data and stock returns to support factor portfolio construction during 1995 through early 2020, *they find that:*

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**December 9, 2020** - Calendar Effects, Equity Options, Momentum Investing

Do options of individual stocks exhibit momentum and seasonality patterns? In their November 2020 paper entitled “Momentum, Reversal, and Seasonality in Option Returns”, Christopher Jones, Mehdi Khorram and Haitao Mo investigate momentum and seasonality effects for options on U.S. common stocks. They focus on performance of straddles, combining a put and a call with the same strike price and expiration date. They balance needs for liquidity and sample size by requiring positive open interest during the holding period but not the momentum calculation interval. Specifically, on each monthly option expiration date, they:

- Form two straddles from near-the-money options expiring next month for each for each stock: (1) the pair with call delta closest to 0.5 for calculating momentum; and, (2) the pair with call delta closest to 0.5 and with positive open interest for both the put and the call when selected for calculating momentum portfolio return.
- Construct from these pairs zero-delta straddles using bid-ask midpoints as prices and calculate monthly straddle excess returns relative to the 1-month Treasury bill yield. This process generates about 1,600 straddles per month with average monthly excess return -5.6% and very large standard deviations.
- Calculate momentum as average monthly excess return over a specified lookback interval (rather than cumulative return, to suppress effects of return outliers).
- Rank straddle returns into equal-weighted fifths (quintiles) based on momentum and calculate average return for each quintile and for a portfolio that is long the top quintile and short the bottom quintile.

Using end-of-day open interest and bid-ask quotes for call and put options on U.S. common stocks from OptionMetric and trading data for underlying stocks during January 1996 through June 2019, *they find that:* Keep Reading

**October 22, 2020** - Momentum Investing, Strategic Allocation

Is there a better way to identify attractive and unattractive assets than simply ranking them? In the August 2020 version of their paper entitled “Decoding Systematic Relative Investing: A Pairs Approach”, Christian Goulding, Campbell Harvey and Alex Pickard examine a long-short strategy that periodically reforms a portfolio by evaluating all possible pairs within an asset universe based on:

- High positive signal-future return correlation for each asset on its own in a pair.
- Low (or negative) signal correlation between assets in the pair.
- Low (or negative) signal-future return correlations between one asset and the other in the pair.

They use these three inputs to calculate a (somewhat complex) composite score for each pair. Among pairs with the highest composite scores, the member with the higher (lower) signal goes to the long (short) side of the portfolio. They assess usefulness of the three conditions and the composite score using a momentum signal calculated as average past monthly return over a specified lookback interval minus its inception-to-date mean and divided by its inception-to-date standard deviation. They split their sample roughly in half and use the first half for detection of profitable pair strategies and the second half to measure out-of-sample performance. They further test an explicit tactical allocation strategy using a 12-month momentum lookback interval, a rolling 10-year monthly composite score and a scheme that weights the top four asset pairs according to respective composite scores. As a benchmark, they use a comparable conventional relative momentum strategy that simply ranks assets on momentum signal. Using monthly returns for 13 broad asset-class indexes encompassing equities, bonds, real estate investment trusts (REIT) and commodities (78 possible pairs) as available through May 2020, *they find that:*

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**October 19, 2020** - Momentum Investing

Subscribers have asked whether substituting Market Vectors Gold Miners ETF (GDX) for SPDR Gold Shares (GLD) as a proxy for gold improves the performance of the Simple Asset Class ETF Momentum Strategy (SACEMS)? To check, we backtest the strategy twice using either GLD or GDX to represent gold, and then compare results. Using dividend-adjusted closing prices for SACEMS asset class proxies and the yield for Cash during June 2006 (per tracked SACEMS) through September 2020, *we find that:* Keep Reading

**September 28, 2020** - Momentum Investing, Size Effect, Value Premium

The conventional size (market capitalization) premium is notoriously weak since discovery almost 40 years ago. Does this poor live track record mean it is useless to investors? In their September 2020 paper entitled “Settling the Size Matter”, David Blitz and Matthias Hanauer examine whether the size premium is exploitable as a standalone anomaly or in combination with other anomalies. They consider six versions of a size factor from prior research, as follows:

- Adjusted for value – average of three small-cap stock portfolios minus average of three big-cap stock portfolios after sorting for book-to-market ratio.
- Adjusted for value, investment and profitability – average of nine small-cap stock portfolios minus average of nine big-cap stock portfolios after separately sorting on the other three factors.
- Adjusted for profitability – average of three small-cap stock portfolios minus average of three big-cap stock portfolios after sorting for profitability.
- Adjusted for quality – average of three small-cap stock portfolios minus average of three big-cap stock portfolios after sorting for quality.
- Adjusted for quality beta – average of three small-cap stock portfolios minus average of three big-cap stock portfolios after sorting for quality beta.
- Adjusted for size, investment and return on equity – average of nine small-cap stock portfolios minus average of nine big-cap stock portfolios after separately sorting on the other three factors.

All factor portfolio segments are capitalization-weighted, and all returns are in U.S. dollars. They consider regressions (implying long-short implementations) and long-only sides of these factors. They also consider size factor definitions that do not overweight size inputs, as do those above. Using data required by these definitions for U.S. stocks since July 1963 (or January 1967 for some inputs) and for international stocks since July 1990 (or July 1993 for some inputs), all through December 2019, *they find that:* Keep Reading

**June 29, 2020** - Equity Premium, Momentum Investing, Size Effect, Value Premium

Are widely accepted equity factor exposures available in fact to investors via “smart beta” mutual funds and exchange-traded funds (ETF)? In their May 2020 paper entitled “Smart Beta Made Smart”, Andreas Johansson, Riccardo Sabbatucci and Andrea Tamoni test effectiveness of individual U.S. equity mutual funds and ETFs and combinations of these funds for exploiting several major equity risk factors (value, size, profitability and momentum). After assembling a sample of funds with names that indicate smart beta strategies, they iteratively (annually for size, value and profitability and daily for momentum):

- Apply a double-regression to each fund to identify those that are actually “closet” market index funds.
- Refine factor exposures of each true smart beta fund based on actual fund holdings.
- Construct separately for institutional and retail investors tradable long-side (mutual funds and ETFs) and short-side (ETFs only) risk factors via value-weighted combinations of the 10 funds with the strongest exposures to each factor.

Using daily, monthly, and quarterly data for U.S. equity mutual funds and ETFs with (1) names indicating smart beta strategies, (2) at least one year of returns and (3)assets over $1 billion, data for their individual component U.S. stocks and specified factor returns during January 2003 through May 2019, *they find that:* Keep Reading

**June 26, 2020** - Momentum Investing, Technical Trading

Is there a way to mitigate adverse impact of price trajectory turning points (trend changes) on performance of intrinsic (absolute or time series) momentum strategies? In their May 2020 paper entitled “Breaking Bad Trends”, Ashish Garg, Christian Goulding, Campbell Harvey and Michele Mazzoleni measure impact of turning points on time series momentum strategy performance across asset classes. They define a turning point as a month for which slow (12-month or longer lookback) and fast (3-month or shorter lookback) momentum signals disagree on whether to buy or sell. They test a dynamic strategy to mitigate trend change impact based on turning points defined by disagreement between 12-month (slow) and 2-month (fast) momentum signals. Specifically, their dynamic strategy each month:

- For each asset, measures slow and fast momentum as averages of monthly excess returns over respective lookback intervals.
- Specifies the trend condition for each asset as: (1) Bull (slow and fast signals both non-negative); (2) Correction (slow non-negative and fast negative); Bear (slow and fast both negative); and, Rebound (slow negative and fast non-negative). For Bull and Bear (Correction and Rebound) conditions, next-month return is the same (opposite in sign) for slow and fast signals.
- After trend changes (Corrections and Rebounds separately), empirically determines with at least 48 months of historical data optimal weights for combinations of positions based on slow and fast signals.

They compare performance of this dynamic strategy with several conventional (static) time series momentum strategies, with each competing strategy retrospectively normalized to 10% test-period volatility. They test strategies on 55 futures, forwards and swaps series spanning four asset classes, with returns based on holding the nearest contract and rolling to the next at expiration. Using monthly returns for futures, forwards and swaps for 12 equity indexes, 10 bond indexes, 24 commodities and 9 currency pairs as available during January 1971 through December 2019, *they find that:*

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**June 17, 2020** - Momentum Investing

Does the U.S. stock market exhibit reliable and exploitable trends as measured by intrinsic (absolute or time series) momentum? In their April 2020 paper entitled “Time Series Momentum in the US Stock Market: Empirical Evidence and Theoretical Implications”, Valeriy Zakamulin and Javier Giner examine evidence of time series momentum in the excess returns (relative to the risk-free rate) of the S&P Composite Index. Their approach involves autocorrelations of multi-month (not monthly) excess returns. They then use simulations modeled with actual index return statistics to; (1) assess potential profitability of long-only and long-short time series momentum strategies; and, (2) estimate the optimal lookback interval. Using monthly total returns for the S&P Composite Index and the monthly risk-free rate represented by the U.S. Treasury bill (T-bill) yield during January 1857 through December 2018, *they find that:* Keep Reading

**May 29, 2020** - Momentum Investing, Strategic Allocation

A subscriber asked for an update on whether weekly or biweekly (every two weeks) measurement of asset class momentum works better than monthly measurement as used in “Simple Asset Class ETF Momentum Strategy (SACEMS)” (SACEMS). Do higher measurement frequencies respond more efficiently to market turns? To investigate, we compare performances of strategies based on monthly, weekly and biweekly frequencies with comparable lookback intervals. For this comparison, we align weekly and biweekly results with monthly results, though they differ somewhat due to mismatches between ends of weeks and ends of months. We consider portfolios of past ETF winners based on Top 1 and on equally weighted (EW) Top 2 and Top 3. Using weekly dividend-adjusted closing prices for the asset class proxies per baseline SACEMS and the yield for Cash during February 2006 through April 2020, *we find that:* Keep Reading