# 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.

**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

**December 15, 2015** - Equity Premium, Momentum Investing, Size Effect, Value Premium

Is it possible to test factor models of stock returns directly on individual stocks rather than on portfolios of stocks sorted per preconceived notions of factor importance. In their November 2015 paper entitled “Tests of Alternative Asset Pricing Models Using Individual Security Returns and a New Multivariate F-Test”, Shafiqur Rahman, Matthew Schneider and Gary Antonacci apply a statistical method that allows testing of equity factor models directly on individual stocks. Results are therefore free from the information loss and data snooping bias associated with sorting stocks based on some factor into portfolios. They test several recently proposed multi-factor models based on five or six of market, size, value (different definitions), momentum, liquidity (based on turnover), profitability and investment factors. They compare alternative models via 100,000 Monte Carlo simulations each in terms of ability to eliminate average alpha and appraisal ratio (absolute alpha divided by residual variance) across individual stocks. Using monthly returns and stock/firm characteristics for the 407 Russell 3000 Index stocks with no missing monthly returns during January 1990 through December 2014 (300 months), *they find that:* Keep Reading

**November 4, 2015** - Size Effect, Technical Trading

Do small capitalization stocks exploitably lag broad market trends? In their October 2015 paper entitled “Slow Trading and Stock Return Predictability”, Matthijs Lof and Matti Suominen investigate whether overall stock market trends predict variation in the size effect and therefore the performance of small capitalization exchange-traded funds (ETF). For size effect testing, they each year at the end of June rank stocks into tenths (deciles) by market capitalization and calculate the size effect as the difference in value-weighted average returns between the smallest and largest deciles. Using daily returns, trading volumes and institutional buying and selling data for a broad sample of U.S. common stocks during 1964 through 2014 and for a selection of small capitalization ETFs as available through 2014, *they find that:* Keep Reading

**September 21, 2015** - Momentum Investing, Size Effect

Are there exploitable size and momentum effects among international stocks? In their August 2015 paper entitled “Size and Momentum Profitability in International Stock Markets”, Peter Schmidt, Urs Von Arx, Andreas Schrimpf, Alexander Wagner and Andreas Ziegler examine the size effect and the interplay between size and momentum strategies via long-short stock portfolios in 23 countries. They measure stock size as market capitalization and consider several ways of measuring the difference in average returns and four-factor (market, size, book-to-market, momentum) alphas between value-weighted portfolios of small stocks and big stocks. They measure stock momentum as return from 12 months ago to one month ago, with a skip-month between ranking and value-weighted portfolio formation. They assess net portfolio performance in three ways: (1) imposing estimated trading frictions (0.3%-0.4% for small stocks and 0.15% for big stocks); (2) calculating the maximum trading frictions an investor could bear; and, (3) calculating U.S. dollar trading volume for each portfolio. Using stock data for the U.S. during 1985 through 2012 and for 22 other countries mostly during 1991 through 2012, *they find that:* Keep Reading