# 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 16, 2017** - Momentum Investing, Size Effect, Value Premium, Volatility Effects

Which equity factors have high and low expected returns? In their February 2017 paper entitled “Forecasting Factor and Smart Beta Returns (Hint: History Is Worse than Useless)”, Robert Arnott, Noah Beck and Vitali Kalesnik evaluate attractiveness of eight widely used stock factors. They measure alpha for each factor conventionally via a portfolio that is long (short) stocks with factor values having high (low) expected returns, reformed systematically. They compare factor alpha forecasting abilities of six models:

- Factor return for the last five years.
- Past return over the very long term (multiple decades), a conventionally used assumption.
- Simple relative valuation (average valuation of long-side stocks divided by average valuation of short-side stocks), comparing current level to its past average.
- Relative valuation with shrunk parameters to moderate forecasts by dampening overfitting to past data.
- Relative valuation with shrunk parameters and variance reduction, further moderating Model 4 by halving its outputs.
- Relative valuation with look-ahead full-sample calibration to assess limits of predictability.

They employ simple benchmark forecasts of zero factor alphas. Using 24 years of specified stock data (January 1967 – December 1990) for model calibrations, about 20 years of data (January 1991 – October 2011) to generate forecasts and the balance of data (through December 2016) to complete forecast accuracy measurements, *they find that:* Keep Reading

**October 10, 2017** - Momentum Investing, Size Effect, Value Premium, Volatility Effects

Does transient factor popularity drive factor/smart beta portfolio performance by pushing valuations of associated stocks up and down? In their February 2016 paper entitled “How Can ‘Smart Beta’ Go Horribly Wrong?”, Robert Arnott, Noah Beck, Vitali Kalesnik and John West examine degrees to which factor hedge portfolio and stock factor tilt (smart beta) backtests are attractive due to:

- Steady and clearly sustainable factor premiums; or,
- Changes in factor relative valuations, measured as average price-to-book value ratio of stocks with high expected returns (factor portfolio long side) divided by average price-to-book ratio of stocks with low expected returns (factor portfolio short side). This ratio tends to increase (decrease) as investor assets move into (out of) factor portfolios.

They consider six long-short factor hedge portfolios: value, momentum, market capitalization (size), illiquidity, low beta and gross profitability. They also consider six smart beta portfolios, which they (mostly) require to sever the relationship between stock price and portfolio weight and to have low turnover, substantial market breadth, liquidity, capacity, transparency, ease of testing and low fees: equal weight, fundamental index, risk efficient, maximum diversification, low volatility and quality. Using specified annual and monthly factor measurement data and returns for a broad sample of U.S. stocks during January 1967 through September 2015, *they find that:* Keep Reading

**October 5, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

Do broad (capitalization-weighted) stock market indexes exhibit factor tilts that may indicate concentrations in corresponding risks? In their August 2017 paper entitled “What’s in Your Benchmark? A Factor Analysis of Major Market Indexes”, Ananth Madhavan, Aleksander Sobczyk and Andrew Ang examine past and present long-only factor exposures of several popular market capitalization indexes. Their analysis involves (1) estimating the factor characteristics of each stock in a broad index; (2) aggregating the characteristics across all stocks in the index; and (3) matching aggregated characteristics to a mimicking portfolio of five indexes representing value, size, quality, momentum and low volatility styles, adjusted for estimated expense ratios. For broad U.S. stock indexes, the five long-only style indexes are:

- Value – MSCI USA Enhanced Value Index.
- Size – MSCI USA Risk Weighted Index.
- Quality – MSCI USA Sector Neutral Quality Index.
- Momentum – MSCI USA Momentum Index.
- Low Volatility – MSCI USA Minimum Volatility Index.

For broad international indexes, they use corresponding long-only MSCI World style indexes. Using quarterly stock and index data from the end of March 2002 through the end of March 2017, *they find that:* Keep Reading

**October 3, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium

Does global diversification improve smart beta (equity factor) investing strategies? In their September 2017 paper entitled “Diversification Strikes Again: Evidence from Global Equity Factors”, Jay Binstock, Engin Kose and Michele Mazzoleni examine effects of global diversification on equity factor hedge portfolios. They consider five factors:

- High-Minus-low Value (HML) – book equity divided by market capitalization.
- Small-Minus-Big Size (SMB) – market capitalization.
- Winners-Minus-Losers Momentum (WML) – cumulative return from 12 months ago to one month ago.
- Conservative-Minus-Aggressive Investment (CMA) – change in total assets.
- Robust-Minus-Weak Operating Profitability (RMW) – total sales minus cost of goods sold, selling, general, and administrative expenses and interest, divided by total assets.

They reform each factor portfolio annually at the end of June by: (1) resetting market capitalizations, segregating firms into large (top 90%) and small (bottom 10%); (2) separately for large and small firms, constructing high (top 30% of factor values) minus low (bottom 30%) long-short sub-portfolios; and, (3) averaging returns for the two sub-portfolios to generate factor portfolio returns. They lag firm accounting data by at least six months between fiscal year end and portfolio formation date. They define eight global regions: U.S., Japan, Germany, UK, France, Canada, Other Europe and Asia Pacific excluding Japan. When measuring diversification effects, they consider relatedness of country markets and variation over time. Using the specified firm accounting data and monthly stock returns during October 1990 through February 2016, *they find that:* Keep Reading

**September 7, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

How many, and which, factors should investors include when constructing multi-factor smart beta portfolios? In their August 2017 paper entitled “How Many Factors? Does Adding Momentum and Volatility Improve Performance”, Mohammed Elgammal, Fatma Ahmed, David McMillan and Ali Al-Amari examine whether adding momentum and low-volatility factors enhances the Fama-French 5-factor (market, size, book-to-market, profitability, investment) model of stock returns. They consider statistical significance, economic sense and investment import. Specifically, they:

- Determine whether factor regression coefficient signs and values distinguish between several pairs of high-risk and low-risk style portfolios (assuming stock style portfolio performance differences derive from differences in firm economic risk).
- Relate time-varying factor betas across style portfolios to variation in economic and market risks as proxied by changes in U.S. industrial production and S&P 500 Index implied volatility (VIX), respectively.
- Test an out-of-sample trading rule based on extrapolation of factor betas from 5-year historical rolling windows to predict next-month return for five sets (book-to-market, profitability, investment, momentum, quality) of four style portfolios (by double-sorting with size) and picking the portfolio within a set with the highest predicted returns.

Using monthly factor return data during January 1990 through October 2016, *they find that:* Keep Reading

**April 6, 2017** - Equity Premium, Size Effect, Volatility Effects

Does disentangling measures of stock illiquidity and market capitalization (size) support belief in an illiquidity premium (a reward for holding illiquid assets)? In the December 2016 version of their paper entitled “The Value of True Liquidity”, Robin Borcherding and Michael Stein investigate this question by controlling the most widely used stock illiquidity metric for size. Specifically they define and calculate true stock liquidities by:

- Calculating for each stock the conventional Amihud monthly measure of illiquidity (average absolute price impact of dollar trading volume during a month).
- Capture unexplained residuals from a regression that controls for the linear relationship (negative correlation) between this conventional illiquidity metric and size.
- Sorting stocks by size and capturing more detail regression residuals within size ranges to control for the non-linear relationship between conventional illiquidity and size.

They then form double-sorted portfolios to compare interactions of conventional and true liquidity with stock volatility and size. Using daily returns, trading data and characteristics for 4,739 U.S. common stocks during January 1990 through September 2015, *they find that:* Keep Reading

**March 22, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

How diversifying are different equity factors within and across country stock markets? In his January 2016 paper entitled “The Power of Equity Factor Diversification”, Ulrich Carl analyzes diversification properties of six equity factors (market excess return, size, value, momentum, low-beta and quality) across 20 developed stock markets. He defines each factor conventionally as returns to a portfolio that is each month long (short) stocks with the highest (lowest) expected returns based on that factor. He considers: (1) cross-country correlations for each factor; (2) cross-factor correlations for each country; (3) cross-country, cross-factor correlations; (4) dynamics of cross-country correlations for each factor based on rolling 36-month windows of returns; and, (5) cross-country correlations for each factor for the 30% lowest and 30% highest market excess returns (tail events). He also applies principal component analysis as another way to evaluate how diverse the 120 country-factor return streams are. Finally, he constructs cross-factor and cross-country portfolios to assess economic value of diversification properties. Using monthly returns in U.S. dollars for the six factors in each of the 20 countries during January 1991 through April 2015, *he finds that:* Keep Reading

**March 15, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

Are the returns of factors widely used to predict the cross-section of stock returns themselves predictable? In the January 2016 draft of his paper entitled “Equity Factor Predictability”, Ulrich Carl analyzes predictability of market, size (market capitalization), value (book-to-market ratio), momentum (returns from 12 months ago to one month ago), low beta (betting against beta) and quality factor returns. All factor returns derive from hedge portfolios that are long (short) stocks with high (low) expected returns based on their factor values. He employs a broad range of economic and financial variables in four sets and multiple ways of testing predictability to ensure robustness of findings and limit model/data snooping bias. Predictability tests he applies include: combinations of simple forecasts (mean or median of single-variable regression forecasts); principal component analysis to distill forecasting variables into a few independent predictive factors; and, methods that adjust variable emphasis according to their respective past performances. He considers several predictability evaluation metrics, including: mean squared error compared to that of the historical average return; utility gain of timing based on predictability; and, information ratio (difference in return divided by difference in risk) relative to the historical average return. He mostly examines next-month forecasts with a one-month gap between predictive variable measurement and forecasted return over two test periods: 1975-2013 and 1950-2013. Using monthly returns for the six factors (start dates ranging from 1928 to 1958), a large set of financial variables since 1928 and a large set of economic variables since 1962, all through November 2013, *he finds that:* Keep Reading

**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