# 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.

**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 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

**October 19, 2016** - Size Effect, Volatility Effects

Is the finding in “Expected Stock Market Volatility and the Size Effect” that the size effect concentrates in intervals after months of very high stock market volatility robustly evident from liquid exchange-traded funds (ETF)? To investigate, we define the size effect as the difference in returns between iShares Russell 2000 (IWM) and iShares Russell 1000 (IWB) at a monthly frequency and use the CBOE Volatility Index (VIX) as expected market volatility. To check robustness of cited research, we consider:

- Thresholds for high VIX ranging from above average to two standard deviations above average.
- Out-of-sample identification of high monthly VIX values using either inception-to-date (ITD) or rolling 120-month (Rolling120) historical windows of monthly VIX closes.
- Lags between VIX measurements and size effect returns ranging from zero to two months.

We focus on differences in average monthly IWM-IWB returns, standard deviations of IWM-IWB monthly returns and IWM-IWB monthly reward-to-risk ratio (average return divided by standard deviation of returns) for months after high versus not-high values of VIX. Using monthly levels of VIX during January 1990 (inception) through September 2016 and monthly total returns for IWM and IWB during May 2000 (inception) through September 2016, *we find that:* Keep Reading

**October 18, 2016** - Size Effect, Volatility Effects

Is the size effect (small stocks tend to outperform large stocks) related to level of market risk as indicated by expected stock market volatility? In their September 2016 paper entitled “High Risk Episodes and the Equity Size Premium”, Naresh Bansal, Robert Connolly and Chris Stivers investigate the relationship between the size effect and two measures of expected stock market volatility: (1) during 1960 through 1989, realized volatility (RV) calculated from daily stock market returns over the prior 66 trading days; and, (2) during 1990 through 2014, the CBOE Volatility Index (VIX). To measure the size effect, they focus on Fama-French SMB factor portfolio monthly returns (return of the tenth, or decile, of stocks with the smallest market capitalizations minus the return of the decile of stocks with the largest market capitalizations). They also study return differences between each of the next three smallest deciles and the return of the largest decile. They consider both value weighting and equal weighting of stock deciles. They insert a skip-month between the volatility measurement interval and size effect return measurement intervals of 1, 3, 6 or 12 months. Using the specified monthly and daily data, *they find that:* Keep Reading

**September 26, 2016** - Size Effect, Value Premium, Volatility Effects

Do investors exploiting common stock return anomalies risk extraordinarily large drawdowns during market crashes? In their May 2016 paper entitled “Can Exposure to Aggregate Tail Risk Explain Size, Book-to-Market, and Idiosyncratic Volatility Anomalies?”, Sofiane Aboura and Eser Arisoy investigate whether portfolios based on the size, book-to-market ratio and idiosyncratic volatility effects bear elevated stock market tail risk. They measure market tail risk as change in VIX Tail Hedge Index (VXTH), which hedges extreme drops in the S&P 500 Index by holding the index and one-month far out-of-the-money (30-delta) call options on the CBOE Volatility Index (VIX). They test sensitivity of size and book-to-market factors to overall risk and tail risk by adding change in VIX (market volatility risk factor) and change in VXTH (market tail risk factor) to the Fama-French three-factor (market, size, book-to-market) model of stock returns. They consider two equal subperiods, one containing the 2008 financial crisis, to check robustness of findings. Using monthly values of VIX and VXTH, factor model returns and U.S. Treasury bill yields during January 2007 through February 2016 (110 months), *they find that:* Keep Reading

**September 7, 2016** - Equity Premium, Momentum Investing, Size Effect

Are the widely used stock characteristic/factor sorting practices of ranked fifth (quintile) or ranked tenth (decile) portfolios optimal in terms of interpretative power? In their August 2016 paper entitled “Characteristic-Sorted Portfolios: Estimation and Inference”, Matias Cattaneo, Richard Crump, Max Farrell and Ernst Schaumburg formalize the portfolio sorting process. Specifically, they describe how to choose the number of quantile portfolios best suited to source data via a trade-off between variability of outputs and effects of data abnormalities (such as outliers). They illustrate implications of the procedure for the:

- Size effect – each month sorting stocks by market capitalization and measuring the difference in value-weighted average next-month returns between small stocks and large stocks.
- Momentum effect – each month sorting stocks by cumulative return from 12 months ago to one month ago and measuring the difference in value-weighted average next-month returns between past winners and past losers.

Using monthly data for a broad sample of U.S. common stocks during January 1927 through December 2015, *they find that:* Keep Reading

**June 9, 2016** - Calendar Effects, Momentum Investing, Size Effect, Value Premium

How good can factor investing get? In his May 2016 paper entitled “Quantitative Style Investing”, Mike Dickson examines strategies that:

- Aggregate return forecasting power of four or six theoretically-motivated stock factors (or characteristics) via monthly multivariate regressions.
- Use inception-to-date simple averages of regression coefficients, starting after the first 60 months and updating annually, to suppress estimation and sampling error.
- Create equally weighted portfolios that are long (short) the 50%, 20%, 10%, 4%, 2% or 1% of stocks with the highest (lowest) expected returns.

The six stock characteristics are: (1) market capitalization; (2), book-to-market ratio; (3) gross profit-to-asset ratio; (4) investment (annual total asset growth); (5) last-month return; and, (6) momentum (return from 12 months ago to two months ago). He considers strategies employing all six characteristics (Model 1) or just the first four, slow-moving ones (Model 2). He considers samples with or without microcaps (capitalizations less than the 20% percentile for NYSE stocks). He estimates trading frictions as 1% of the value traded each month in rebalancing to equal weight. Using monthly data for a broad sample of U.S. common stocks during July 1963 through December 2013 (with evaluated returns commencing July 1968), *he finds that:* Keep Reading

**May 16, 2016** - Momentum Investing, Size Effect, Value Premium

Do smart beta indexes efficiently exploit factor premiums? In his April 2016 paper entitled “Factor Investing with Smart Beta Indices”, David Blitz investigates how well smart beta indexes, which deviate from the capitalization-weighted market per mechanical rules, capture corresponding factor portfolios. He consider five factors: value, momentum, low-volatility, profitability and investment. He measures their practically exploitable premiums via returns on long-only value-weighted or equal-weighted portfolios of the 30% of large-capitalization U.S. stocks with the most attractive factor values. He tests six smart beta indexes:

- Russell 1000 Value.
- MSCI Value Weighted.
- MSCI Momentum.
- S&P Low Volatility.
- MSCI Quality.
- MSCI High Dividend.

Using monthly data for the five factor portfolios and the six smart beta indexes as available through December 2015, *he finds that:* Keep Reading

**May 13, 2016** - Equity Premium, Momentum Investing, Size Effect, Value Premium

How should investors think about stock factor investing? In his April 2016 paper entitled “The Siren Song of Factor Timing”, Clifford Asness summarizes his current beliefs on exploiting stock factor premiums. He defines factors as ways to select individual stocks based on such firm/stock variables as market capitalization, value (in many flavors), momentum, carry (yield) and quality. He equates factor, smart beta and style investing. He describes factor timing as attempting to predict and exploit variations in factor premiums. Based on past research on U.S. stocks mostly for the past 50 years, *he concludes that:* Keep Reading