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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.

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Small Leveraged Value Stock Ranking System

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

Country Stock Market Factor Strategies

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

Interactions among Stock Size, Stock Price and the January 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

Interaction of Calendar Effects with Other Anomalies

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:

  1. Market capitalization (size) – market capitalization last month.
  2. Book-to-market – book equity (excluding stocks with negative values) divided by market capitalization last December.
  3. Gross profitability – revenue minus cost of goods sold divided by total assets.
  4. Asset growth – Annual change in total assets.
  5. Accruals – change in working capital minus depreciation, divided by average total assets the last two years.
  6. Net stock issuance – growth rate of split-adjusted shares outstanding at fiscal year end.
  7. Change in turnover – difference between turnover last month and average turnover the prior six months.
  8. Illiquidity – average illiquidity the previous year.
  9. Idiosyncratic volatility – standard deviation of residuals from regression of daily excess returns on market, size and book-to-market factors.
  10. Momentum – past six-month return, skipping the last month.
  11. 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

Investor Return versus Mutual Fund Performance

Does the average mutual fund investor accrue the average fund performance, or do investor timing practices alter the equation? In their July 2014 paper entitled “Timing Poorly: A Guide to Generating Poor Returns While Investing in Successful Strategies, Jason Hsu, Brett Myers and Ryan Whitby compare the average dollar-weighted and buy-and-hold returns of different U.S. equity mutual fund styles, with focus on the value style. Dollar weighting adjusts the return stream based on the timing and magnitude of fund flows and is a more accurate measure than buy-and-hold of the returns realized by fund investors who may trade in and out of funds. Using monthly returns, monthly total assets and quarterly fund style information for a broad sample of U.S. equity mutual funds during 1991 through 2013, they find that: Keep Reading

Quality-enhanced Size Effect

Given the conflicting evidence about the import of the size effect, is there a way investors can extract a reliable premium from small stocks? In their January 2015 draft paper entitled “Size Matters, If You Control Your Junk”, Clifford Asness, Andrea Frazzini, Ronen Israel, Tobas Moskowitz and Lasse Pedersen examine whether controlling for firm quality mitigates the following seven unfavorable empirical findings that the size effect:

  1. Is weak overall in the U.S.
  2. Has not worked out-of-sample and varies significantly over time.
  3. Only works for extremely small stocks.
  4. Only works in January.
  5. Only works for market capitalization-based measures of size.
  6. Is subsumed by illiquidity.
  7. Is weak internationally.

They control for quality using a Quality-Minus-Junk (QMJ) factor based on profitability, profit growth, safety and payout. They use a portfolio test approach, ranking stocks into value-weighted tenths (deciles) each month to examine differences among stocks sorted by factor. Focusing on returns and factor metrics for a broad sample of U.S. common stocks during July 1957 (when quality metrics become available) through December 2012 and for 23 other developed country stock markets during January 1983 through December 2012, they find that: Keep Reading

Adding Profitability and Investment to the Three-factor Model

Does adding profitability and asset growth (investment) factors improve the performance of the widely used Fama-French three-factor (market, size, book-to-market) model of stock returns? In the September 2014 version of their paper entitled “A Five-Factor Asset Pricing Model” Eugene Fama and Kenneth French assess whether extensions of their three-factor model to include profitability and investment improves model predictive power. They measure profitability as prior-year revenue minus cost of goods sold, interest expense and selling, general and administrative expenses divided by book equity. They define investment as prior-year growth in total assets divided by total assets. Using returns and stock/firm characteristics for a broad sample of U.S. stocks during July 1963 through December 2013 (606 months), they find that: Keep Reading

Factor Model of Country Stock Market Returns?

Do predictive powers of the size, value and momentum factors observed for individual stocks translate to the country level? In the November 2014 version of his paper entitled “Country Selection Strategies Based on Value, Size and Momentum”, Adam Zaremba investigates country-level value, size and momentum premiums, and tests whether the value and momentum premiums are equally strong across markets of different sizes and evaluates a country-level multi-factor asset pricing model. He measures factors at the country level as:

  • Value: aggregate book-to-market ratio, with aggregate 12-month earnings-to-price-ratio, cash flow-to-price ratio and dividend yield as alternatives where available.
  • Size: total market capitalization of country stocks.
  • Momentum: cumulative return over preceding 12, 9, 6 or 3 months excluding the last month to avoid short-term reversal.

He relies on capitalization-weighted, U.S. dollar-denominated gross total return MSCI equity indexes as available, with Dow Jones and STOXX indexes as fallbacks (an average 56 indexes per month over time). He includes discontinued country indexes. He uses one-month LIBOR as the risk-free rate. Each month, he ranks countries by value, size and momentum into value-weighted or equal-weighted fifths (quintiles). He also performs double-sorts first on size and then on value or momentum. Using monthly firm/stock data for listed stockswithin 78 country indexes as available during February 1999 through September 2014 (147 months), he finds that: Keep Reading

Smart Beta Interactions with Tax-loss Harvesting

Are gains from tax-loss harvesting, the systematic taking of capital losses to offset capital gains, additive to or subtractive from premiums from portfolio tilts toward common factors such as value, size, momentum and volatility (smart beta)? In their October 2014 paper entitled “Factor Tilts after Tax”, Lisa Goldberg and Ran Leshem look at the effects on portfolio performance of combining factor tilts and tax-loss harvesting. They call the incremental return from tax-loss harvesting tax alpha, which (while investor-specific) is typically in the range 1%-2% per year for wealthy investors holding broad capitalization-weighted portfolios. They test six long-only factor tilts based on Barra equity factor models: (1) value (high earnings yield and book-to-market ratio); (2) momentum (high recent past return); (3) value/momentum; (4) small/value; (5) quality (value stocks with low earnings variability, leverage and volatility); and, (6) minimum volatility/value (low volatility with diversification constraint and value tilt). Their overall benchmark is the MSCI All Country World Index (ACWI). Their tax alpha benchmark derives from a strategy that harvests losses in a capitalization-weighted portfolio (no factor tilts) without deviating far from the overall benchmark. The rebalancing interval is monthly for all portfolios. Using monthly returns for stocks in the benchmark index during January 1999 through December 2013, they find that: Keep Reading

Small and Value Stocks Less Risky for Long-term Investors?

Is risk for long-term investors different from that for short-term investors? In his July 2014 paper entitled “Rethinking Risk (II): The Size and Value Effects”, Javier Estrada examines the riskiness of small stocks versus large stocks and value (high book-to-market ratio) stocks versus growth stocks based on conventional and unconventional metrics. Each year during 1927 through 2013, he makes initial investments of $100 in Fama-French small, large, value and growth stock portfolios and holds for 20 or 30 years to generate distributions of 68 or 58 terminal wealths for each style, respectively. He then calculates the following metrics for these two sets of portfolios:

  • Mean (average) of terminal wealths by style.
  • Median (midpoint) of terminal wealths by style.
  • Average of the standard deviations of annual returns (SDD) by style.
  • Standard deviation of the terminal wealths (SDE) by style.
  • Lower‐tail Terminal Wealth (LTWx), the average terminal wealth in the lower x% of the distribution of terminal wealths (with x% being 1%, 5% or 10%) by style.
  • Upper‐tail Terminal Wealth (UTWx), the average terminal wealth in the upper x% of the distribution of terminal wealths (with x% again being 1%, 5% or 10%) by style.

SDD is most like conventional risk (volatility), while the other metrics focus unconventionally on terminal wealth. Using annual gross total returns for Fama‐French U.S. style portfolios during 1927 through 2013, he finds that: Keep Reading

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