# Size Effect

Do the stocks of small firms consistently outperform those of larger companies? If so, why, and can investors/traders exploit this tendency? These blog entries relate to the size effect.

**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

**May 18, 2020** - Momentum Investing, Size Effect, Value Premium, Volatility Effects

Are there equity styles that tend to perform relatively well during and after stock market crashes? In their April 2020 paper entitled “Equity Styles and the Spanish Flu”, Guido Baltussen and Pim van Vliet examine equity style returns around the Spanish Flu pandemic of 1918-1919 and five earlier deep U.S. stock market corrections (-20% to -25%) in 1907, 1903, 1893, 1884 and 1873. They construct three factors by:

- Separating stocks into halves based on market capitalization.
- Sorting the big half only into thirds based on dividend yield as a value proxy, 36-month past volatility or return from 12 months ago to one month ago. They focus on big stocks to avoid illiquidity concerns for the small half.
- Forming long-only, capitalization-weighted factor portfolios that hold the third of big stocks with the highest dividends (HighDiv), lowest past volatilities (Lowvol) or highest past returns (Mom).

They also test a multi-style strategy combining Lowvol, Mom and HighDiv criteria (Lowvol+) and a size factor calculated as capitalization-weighted returns for the small group (Small). Using data for all listed U.S. stocks during the selected crashes, *they find that:* Keep Reading

**August 14, 2019** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

In their July 2019 paper entitled “Momentum-Managed Equity Factors”, Volker Flögel, Christian Schlag and Claudia Zunft test exploitation of positive first-order autocorrelation (time series, absolute or intrinsic momentum) in monthly excess returns of seven equity factor portfolios:

- Market (MKT).
- Size – small minus big market capitalizations (SMB).
- Value – high minus low book-to-market ratios (HML).
- Momentum – winners minus losers (WML)
- Investment – conservative minus aggressive (CMA).
- Operating profitability – robust minus weak (RMW).
- Volatility – stable minus volatile (SMV).

For factors 2-7, monthly returns derive from portfolios that are long (short) the value-weighted fifth of stocks with the highest (lowest) expected returns. In general, factor momentum timing means each month scaling investment in a factor from 0 to 1 according its how high its last-month excess return is relative to an inception-to-date window of past levels. They consider also two variations that smooth the simple timing signal to suppress the incremental trading that it drives. In assessing costs of this incremental trading, they assume (based on other papers) that realistic one-way trading frictions are in the range 0.1% to 0.5%. Using monthly data for a broad sample of U.S. common stocks during July 1963 through November 2014, *they find that:* Keep Reading

**June 26, 2019** - Size Effect

Does stock performance vary with age (since listing), and does any such effect interact with market capitalization (size)? In their April 2019 paper entitled “Age Matters”, Danqiao Guo, Phelim Boyle, Chengguo Weng and Tony Wirjanto examine age and size of U.S. stocks in combination. To disentangle interaction, they generate 20,000 simulations for each of two sets of portfolios separately for holdings of 5, 25, 50 or 100 stocks:

- Rebalanced – a randomly selected equal-weighted portfolio rebalanced each month to equal weight after replacing delisted stocks (roughly 10% of stocks each year) with replacements randomly selected from those in the full sample not already in the portfolio. New stocks are representative of the market in terms of age, while residual stocks age by a month, such that the portfolio tends to grow older.
- Bootstrapped – a randomly selected equal-weighted (also, for reference, value-weighted) portfolio that is each month liquidated and randomly reformed, such that it remains representative of the full sample in terms of age.

If stock return is related to age, these two sets of portfolios perform differently. They further compare performances of 16 portfolios double-sorted into four age groups (quartiles) and four size quartiles. Using monthly returns and listing dates for a broad sample of U.S. stocks during July 1926 through December 2016, *they find that:* Keep Reading

**June 25, 2019** - Currency Trading, Momentum Investing, Size Effect

Do simple factor models help explain future return variations across different cryptocurrencies, as they do for stocks? In their April 2019 paper entitled “Common Risk Factors in Cryptocurrency”, Yukun Liu, Aleh Tsyvinski and Xi Wu examine performances of cryptocurrency (coin) counterparts for 25 price-related and market-related stock market factors, broadly categorized as size, momentum, volume and volatility factors. They first construct a coin market index based on capitalization-weighted returns of all coins in their sample. They then each week sort coins into fifths based on each factor and calculate average excess return for a portfolio that is long (short) coins in the highest (lowest) quintile. Finally, they investigate whether any small group of factors accounts for returns of all significant factors. Using daily prices in U.S. dollars and non-return variables (excluding top and bottom 1% values as potential errors/outliers) for all coins with market capitalizations over $1 million dollars from Coinmarketcap.com during January 2014 through December 2018 (a total of 1,707 coins, growing from 109 in 2014 to 1,583 in 2018), *they find that:*

Keep Reading

**June 18, 2019** - Currency Trading, Size Effect

Are Initial Coin Offerings (ICO), also called token sales or token offerings, typically good investments? ICOs are smart contracts on a blockchain (usually Ethereum) that enable firms to raise money directly from investors. The median time for listing a successful ICO on a token exchange is 42 days. In the May 2019 revision of his paper entitled “The Pricing and Performance of Cryptocurrency”, Paul Momtaz examines the performance of ICOs for horizons of one day to three years after initial listing. He also investigates whether there are robust predictors of initial pricing and longer term performance. His sample consists of all tokens tracked by coinmarketcap.com during January 2013 through April 2018, less confirmed errors and outliers in extreme 1% tails because they are unverifiable. His benchmark for calculating abnormal returns is the market capitalization-weighted return of cryptocurrencies (dominated by Bitcoin and Ethereum). Using daily high, low and closing prices, market capitalizations and trading volumes of 1,403 ICOs and daily closes of major cryptocurrencies during the specified period,* he finds that:* Keep Reading

**March 11, 2019** - Big Ideas, Equity Premium, Momentum Investing, Size Effect, Strategic Allocation, Value Premium, Volatility Effects

How should investors feel about factor/multi-factor investing? In their February 2019 paper entitled “Alice’s Adventures in Factorland: Three Blunders That Plague Factor Investing”, Robert Arnott, Campbell Harvey, Vitali Kalesnik and Juhani Linnainmaa explore three critical failures of U.S. equity factor investing:

- Returns are far short of expectations due to overfitting and/or trade crowding.
- Drawdowns far exceed expectations.
- Diversification of factors occasionally disappears when correlations soar.

They focus on 15 factors most closely followed by investors: the market factor; a set of six factors from widely used academic multi-factor models (size, value, operating profitability, investment, momentum and low beta); and, a set of eight other popular factors (idiosyncratic volatility, short-term reversal, illiquidity, accruals, cash flow-to-price, earnings-to-price, long-term reversal and net share issuance). For some analyses they employ a broader set of 46 factors. They consider both long-term (July 1963-June 2018) and short-term (July 2003-June 2018) factor performances. Using returns for the specified factors during July 1963 through June 2018, *they conclude that:*

Keep Reading

**February 12, 2019** - Momentum Investing, Size Effect, Value Premium

How well do mutual funds exploit theoretical (academic) equity factor premiums, and how well do investors exploit such exploitation? In their January 2019 paper entitled “Factor Investing from Concept to Implementation”, Eduard Van Gelderen, Joop Huij and Georgi Kyosev examine: (1) how performances of mutual funds that target equity factor premiums (low beta, size, value, momentum, profitability, investment) compare to that of funds that do not; and, (2) flow-adjusted performances, indicating how much of any outperformance accrues to fund investors. They classify funds empirically based on factor exposures. Using monthly returns and total assets and quarterly turnover and expense ratios for 3,109 actively managed long-only U.S. equity mutual funds with assets over $5 million (1,334 dead and 1,775 live) since January 1990 and for 4,859 (2,000 dead and 2,859 live) similarly specified global mutual funds since January 1991, all through December 2015, along with contemporaneous monthly equity factor returns, *they find that:* Keep Reading

**January 22, 2019** - Size Effect, Volatility Effects

Do unconventional portfolio construction techniques obscure how, and how well, betting against beta (BAB) works? In their November 2018 paper entitled “Betting Against Betting Against Beta”, Robert Novy-Marx and Mihail Velikov revisit the BAB factor, focusing on interpretation of three unconventional BAB construction techniques:

- Rank weighting of stocks – BAB employs rank weighting rather than equal or value weighting, with each stock in high and low estimated beta portfolios weighted proportionally to the difference between its estimated beta rank and the median rank.
- Hedging by leveraging – BAB seeks market neutrality by deleveraging (leveraging) the high (low) beta portfolio based on estimated betas rather than borrowing to buy the market portfolio to offset BAB’s short market tilt.
- Novel beta estimation – BAB measures stock betas by combining market correlations based on five years of overlapping 3-day returns with volatilities based on one year of daily returns, rather than using slope coefficients of daily stock returns versus daily market returns.

Based on mathematical analysis and empirical results using returns for a broad sample of U.S. stocks during January 1968 through December 2017, *they find that:* Keep Reading