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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.

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

Big Three Factors across Countries

Are there parallels at the country stock market level of the size, value and momentum effects observed for individual stocks? In their January 2014 paper entitled “Value, Size and Momentum across Countries”, Adam Zaremba and Przemysław Konieczka investigate country-level value, size and momentum premiums. They measure these factors at the country level as:

  • Value (V): book-to-market ratio of country stocks aggregated via the weighting scheme used to construct the country stock index at the time of portfolio formation.
  • Size (S): total market capitalization of country stocks at the time of portfolio formation.
  • Long-Term Momentum (LTM): country index return during the 12 months before portfolio formation.
  • Short-Term Momentum (STM): country index return during the month before portfolio formation.

They calculate these factors using either MSCI equity indexes (47 indexes available at the beginning of the sample period) or local stock indexes (only 24 indexes available at the beginning of the sample period). They measure the country-level premium for each factor as the return on an equally weighted portfolio that is each month long (short) the 30% of countries with the highest (lowest) expected returns for that factor. They fully collateralize short sides with reserves in the risk-free rate. They also calculate a total market return as the capitalization-weighted average return across all country markets. They perform calculations separately in U.S. dollars, euros and yen. Using monthly firm/stock data for listed stocks as available within 66 countries from the end of May 2000 through November 2013, and contemporaneous Fama-French model U.S. factors, they find that: Keep Reading

Equity Investing Based on Liquidity

Does the variation of individual stock returns with liquidity support an investment style? In the January 2014 update of their paper entitled “Liquidity as an Investment Style”, Roger Ibbotson and Daniel Kim examine the viability and distinctiveness of a liquidity investment style and investigate the portfolio-level performance of liquidity in combination with size, value and momentum styles. They define liquidity as annual turnover, number of shares traded divided by number of shares outstanding. They hypothesize that stocks with relatively low (high) turnover tend to be near the bottom (top) of their ranges of expectation. Their liquidity style thus overweights (underweights) stocks with low (high) annual turnover. They define size, value and momentum based on market capitalization, earnings-to-price ratio (E/P) and past 12-month return, respectively. They reform test portfolios via annual sorts into four ranks (quartiles), with initial equal weights and one-year holding intervals. Using monthly data for the 3,500 U.S. stocks with the largest market capitalizations (re-selected each year) over the period 1971 through 2013, they find that: Keep Reading

Stock Markets Have Value and Size, Too?

Do country stock markets exhibit useful aggregate value and size metrics? In his December 2013 paper entitled “Macro Model for Macro Funds”, Adam Zaremba investigates whether macro size and value factors for country stock markets predict country stock index returns. Specifically, he calculates size and value factors at the country level in each of 66 countries. The size factor is the market capitalization of all listed firms in a country index. The value factor is the book-to-market value ratio (B/M) of all firms in a country index aggregated according to the index weighting methodology. He uses both MSCI country indexes and extant local country indexes to measure country market returns. He tests relationships between country-level size and value factors and future returns by each month separately constructing portfolios of the equally weighted top 30%, middle 40% and bottom 30% of country markets based on aggregate size and value factors. He also measures the performance of fully collateralized portfolios that are each month long (short) the equally weighted top (bottom) 30% of country markets based on aggregate size and value factors separately. To test sensitivity to the currency used, he performs all calculations separately in U.S. dollars, euros and yen. Using monthly accounting and return data as specified during June 2000 through November 2013, he finds that: Keep Reading

Value and Momentum Behaviors in Developed Markets

How do value and momentum interact with each other and with size, economic and liquidity factors worldwide? In the November 2013 version of their paper entitled “Size, Value, and Momentum in Developed Country Equity Returns: Macroeconomic and Liquidity Exposures”, Nusret Cakici and Sinan Tan address this question for developed markets. They use long-short, factor-sorted portfolios to measure size, value and momentum premiums. They consider future Gross Domestic Product (GDP) growth and future consumption growth as economic factors. They consider both funding liquidity (a potential indicator of investor margin cost, focusing on the difference between interbank lending rate and short-term deposit yield) and stock market liquidity (the estimated cost of trading stocks). Using monthly stock returns, firm accounting data and economic data for 23 developed countries during January 1990 through March 2012, they find that: Keep Reading

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