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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.

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

Cyclical Behaviors of Size, Value and Momentum in UK

Do the behaviors of the most widely accepted stock market factors (size, book-to-market or value, and momentum) vary with the economic trend? In the June 2014 version of their paper entitled “Macroeconomic Determinants of Cyclical Variations in Value, Size and Momentum premium in the UK”, Golam Sarwar, Cesario Mateus and Natasa Todorovic examine differences in the sensitivities of UK equity market size, value and momentum factor returns (premiums) to changes in broad and specific economic variables. They define the broad economic state each month as upturn (downturn) when the OECD Composite Leading Indicator for the UK increases (decreases) that month. They also consider contributions of six specific variables to economic trend: GDP growth; unexpected inflation (change in CPI); interest rate (3-month UK Treasury bill yield); term spread (10-year UK Treasury bond yield minus 3-month UK Treasury bill yield); credit spread (Moody’s U.S. BBA yield minus 10-year UK government bond yield); and, money supply growth. They lag economic variables by one or two months to align their releases with stock market premium measurements. Using monthly UK size, value and momentum factors and economic data during July 1982 through December 2012, they find that: Keep Reading

Testing Size, Value and Momentum Return Predictors

Do commonly used indicators reliably predict stock size, value and momentum strategy returns? In the June 2014 version of his paper entitled “A Comprehensive Look at Size, Value and Momentum Return Predictability”, Afonso Januario examines the abilities of 17 fundamental and technical indicators and indicator combinations to anticipate returns for these three factors. He defines factor portfolios based on market capitalization (size), book-to-market ratio (value) and return from 12 months ago to one month ago (momentum), reformed monthly, as follows:

  1. Size = (SmallValue+SmallNeutral+SmallGrowth)/3 – (BigValue+BigNeutral+BigGrowth)/3
  2. Value = (SmallValue+BigValue)/2 – (SmallGrowth+BigGrowth)/2
  3. Momentum = (SmallWinners+BigWinners)/2 – (SmallLosers+BigLosers)/2

He selects the 17 indicators (such as book-to-market ratio, dividend yield, earnings-price ratio, return on equity, lagged return, short interest and implied volatility) from prior published research on predictive variables. He measures indicator values each month as the averages only for stocks in long or short sides (and the spread between them) of each of the above three factor portfolios. He applies linear regressions at monthly and annual frequencies to determine whether an indicator is more effective than the historical average factor portfolio return in predicting future factor portfolio returns. Using relevant sets of data for a broad sample of relatively liquid U.S. stocks from initial set availability (ranging from 1950 to 1995) through 2012, he finds that: Keep Reading

Equity Premiums Overgrazed?

Are investors exhausting the potential of stocks? In his May 2014 presentation packages entitled “Has The Stock Market Been ‘Overgrazed’?” and “Momentum Has Not Been ‘Overgrazed'”, Claude Erb investigates the proposition that sanguine research and ever easier access to investments are exhausting U.S. stock market investment opportunities. In the first package, he focuses on trends in the overall equity risk premium, the size effect and the value premium. In the second, he focuses on momentum investing. Using U.S. stock market and equity factor premium returns and contemporaneous U.S. Treasury bill yields during 1926 through 2013, he concludes that: Keep Reading

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