# 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 11, 2018** - Size Effect

Do small market capitalization stocks really outperform big ones, as strongly implied by the prominence of the size effect in published research and factor models? In their May 2018 paper entitled “Fact, Fiction, and the Size Effect”, Ron Alquist, Ronen Israel and Tobias Moskowitz survey the body of research on the size effect and employ simple tests to assess claims made about it. Based on published and peer-reviewed academic papers and on tests using data for U.S. stocks and equity factor premiums, international developed and emerging market stocks and stock indexes, U.S. bonds and various currencies as available through December 2017, *they find that:* Keep Reading

**April 12, 2018** - Momentum Investing, Size Effect, Volatility Effects

Is there an easy way for investors to capture jointly the most reliable stock return factor premiums? In their March 2018 paper entitled “The Conservative Formula: Quantitative Investing Made Easy”, Pim van Vliet and David Blitz propose a stock selection strategy based on low return volatility, high net payout yield and strong price momentum. Specifically, at the end of each quarter they:

- Segment the then-current 1,000 largest stocks into 500 with the lowest and 500 with the highest 36-month return volatilities.
- Within each segment, rank stocks based on total net payout yield (NPY), calculated as dividend yield minus change in shares outstanding divided by its 24-month moving average.
- Within each segment, rank stocks based on return from 12 months ago to one month ago (with the skip-month intended to avoid return reversals).
- Within the low-volatility segment, average the momentum and NPY ranks for each stock and equally weight the top 100 to reform the Conservative Formula portfolio.
- Within the high-volatility segment, average the momentum and NPY ranks for each stock and equally weight the bottom 100 to reform the Speculative Formula portfolio.

Limiting the stock universe to the top 1,000 based on market capitalization suppresses liquidity risk. Limiting screening parameters to three intensely studied factors that require no accounting data mitigates data snooping and data availability risks. They focus on the 1,000 largest U.S. stocks to test a long sample, but also consider the next 1,000 U.S. stocks (mid-caps) and the 1,000 largest stocks from each of Europe, Japan and emerging markets. They further examine: (1) sensitivity to economic conditions doe the long U.S. sample; and, (2) impact of trading frictions in the range 0.1%-0.3% for developed markets and 0.2%-0.6% for emerging markets. Using quarterly prices, dividends and shares outstanding for the contemporaneously largest 1,000 U.S. stocks since 1926, European and Japanese stocks since 1986 and emerging markets stocks since 1991, all through 2016, *they find that:*

Keep Reading

**March 12, 2018** - Equity Premium, Momentum Investing, Size Effect, Value Premium

Do technical trend trading/intrinsic momentum strategies work for widely used equity factors such as size (small minus big market capitalizations), value (high minus low book-to-market ratios), profitability (robust minus weak), investment (conservative minus aggressive) and momentum (winners minus losers)? In their January 2018 paper entitled “What Goes up Must Not Come Down – Time Series Momentum in Factor Risk Premiums”, Maximilian Renz investigates time variation and trend-based predictability of these five factors and the market factor. He first constructs price series for the six long-short factor portfolios. He then considers seven rules based on a short simple moving average (SMA) crossing above (bullish) or below (bearish) a long SMA measured in trading days: SMA(1, 20), SMA(1, 40), SMA(1, 120), SMA(1, 180), SMA(1, 240), SMA(20, 180) and SMA(20, 240). He also considers two intrinsic (absolute or time series) momentum rules based on change in price over the past 180 or 240 trading days (positive bullish and negative bearish). Motivated by prior research by others, he focuses on SMA(1, 180), daily price crossing its 180-day SMA. He measures trend-based statistical predictability of factor premiums and investigates economic value via a strategy that levers factor exposures between 0 and 1.5 using trend-based signals. Finally, he examines whether incorporating trend information improves accuracies of 1-factor (market), 3-factor (adding size and value) and 5-factor (further adding profitability and investment) models of stock returns. Using daily returns for the six selected U.S. stock market equity factors and for 30 industries during July 1963 through December 2015, *he finds that:* Keep Reading

**January 9, 2018** - Big Ideas, Momentum Investing, Size Effect, Value Premium, Volatility Effects

What is the best way to think about reliabilities and risks of various anomaly premiums commonly that investors believe to be available for exploitation? In their December 2017 paper entitled “A Framework for Risk Premia Investing”, Kari Vatanen and Antti Suhonen present a framework for categorizing widely accepted anomaly premiums to facilitate construction of balanced investment strategies. They first categorize each premium as fundamental, behavioral or structural based on its robustness as indicated by clarity, economic rationale and capacity. They then designate each premium in each category as either defensive or offensive depending on whether it is feasible as long-only or requires short-selling and leverage, and on its return skewness and tail risk. Based on expected robustness and riskiness of selected premiums as described in the body of research, *they conclude that:* Keep Reading

**October 17, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

How efficiently do mutual funds capture factor premiums? In their April 2017 paper entitled “The Incredible Shrinking Factor Return”, Robert Arnott, Vitali Kalesnik and Lillian Wu investigate whether factor tilts employed by mutual fund managers deliver the alpha found in empirical research. They focus on four factors most widely used by mutual fund managers: market, size, value and momentum. They note that ideal long-short portfolios used to compute factor returns ignore costs associated with real-world implementation: trading costs and commissions, missed trades, illiquidity, management fees, borrowing costs for the short side and inability to short some stocks. Portfolio returns also ignore bias associated with data snooping in factor discovery and market adaptation to published research. They focus on U.S. long-only equity mutual funds, but also consider similar international funds. They apply a two-stage regression first to identify fund factor exposures and then to measure performance shortfalls per unit of factor exposure. Using data for 5,323 U.S. and 2,364 international live and dead long-only equity mutual funds during January 1990 through December 2016, *they find that:*

Keep Reading

**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