# 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.

**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

**September 4, 2015** - Size Effect, Value Premium

What qualifiers can enhance the performance of a small value stock strategy? In their August 2015 paper entitled “Leveraged Small Value Equities”, Brian Chingono and Daniel Rasmussen devise and test a strategy to refine a portfolio of small capitalization value stocks of firms that with relatively high financial leverage. Specifically, their target universe at the end of each year consists of all NYSE/AMEX/NASDAQ stocks with: (1) market capitalizations between the 25th and 75th percentiles; (2) among the 25% of cheapest stocks based on EBITDA divided by enterprise value; and, (3) above median long term debt divided by enterprise value. They then rank the stocks in this universe per a group of quality and technical factors that emphasize reduction in long-term debt and improving asset turnover (revenue growth rate greater than asset growth rate). At the end of the first quarter of each following year, they reform portfolios of the top 25 and top 50 stocks in the specified universe based on this ranking. Using stock return and accounting data for a broad sample of U.S. stocks during January 1963 through December 2014, *they find that:* Keep Reading

**June 2, 2015** - Momentum Investing, Size Effect, Value Premium, Volatility Effects

Do factors that predict returns in U.S. stock data also work on global stock markets at the country level? In the May 2015 version of their paper entitled “Do Quantitative Country Selection Strategies Really Work?”, Adam Zaremba and Przemysław Konieczka test 16 country stock market selection strategies based on relative market value, size, momentum, quality and volatility. For each of 16 factors across these categories, they sort country stock markets into fifths (quintiles) and measure the factor premium as return on the highest minus lowest quintiles. They consider equal, capitalization and liquidity (average turnover) weighting schemes within quintiles. They look at complementary large and small market subsamples, and complementary open (easy to invest) and closed market subsamples. Using monthly total returns adjusted for local dividend tax rates in U.S. dollars for 78 existing and discontinued country stock indexes (primarily MSCI) during 1999 through 2014, *they find that:* Keep Reading

**March 20, 2015** - Animal Spirits, Calendar Effects, Size Effect

Is there an exploitable interaction between a stock’s market capitalization and its price? In their February 2015 paper entitled “Nominal Prices Matter”, Vijay Singal and Jitendra Tayal examine the relationship between stock prices and returns after: (1) controlling for market capitalization (size); (2) isolating the month of January; and, (3) excluding very small stocks. They each year perform double-sorts based on end-of-November data first into ranked tenths (deciles) by size and then within each size decile into price deciles. They calculate returns for January and for the calendar year with and without January. Using monthly prices and end-of-November market capitalizations for the 3,000 largest U.S. common stocks during December 1962 through December 2013, quarterly institutional ownership data for each stock during December 1980 through December 2013, and actual number of shareholders for each stock during 2004 through 2012, *they find that:* Keep Reading

**February 26, 2015** - Calendar Effects, Momentum Investing, Size Effect, Value Premium, Volatility Effects

Do stock return anomalies exhibit January and month-of-quarter (first, second or third, excluding January) effects? In his February 2015 paper entitled “Seasonalities in Anomalies”, Vincent Bogousslavsky investigates whether the following 11 widely cited U.S. stock return anomalies exhibit these effects:

- Market capitalization (size) – market capitalization last month.
- Book-to-market – book equity (excluding stocks with negative values) divided by market capitalization last December.
- Gross profitability – revenue minus cost of goods sold divided by total assets.
- Asset growth – Annual change in total assets.
- Accruals – change in working capital minus depreciation, divided by average total assets the last two years.
- Net stock issuance – growth rate of split-adjusted shares outstanding at fiscal year end.
- Change in turnover – difference between turnover last month and average turnover the prior six months.
- Illiquidity – average illiquidity the previous year.
- Idiosyncratic volatility – standard deviation of residuals from regression of daily excess returns on market, size and book-to-market factors.
- Momentum – past six-month return, skipping the last month.
- 12-month effect – average return in month t−k*12, for k = 6, 7, 8, 9, 10.

Each month, he sorts stocks into tenths (deciles) based on each anomaly variable and forms portfolios that are long (short) the decile with the highest (lowest) values of the variable. He updates all accounting inputs annually at the end of June based on data for the previous fiscal year. Using accounting data and monthly returns for a broad sample of U.S. common stocks during January 1964 to December 2013, *he finds that:* Keep Reading