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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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Do Equal Weight ETFs Beat Cap Weight Counterparts?

“Stock Size and Excess Stock Portfolio Growth” finds that an equal-weighted portfolio of the (each day) 1,000 largest U.S. stocks beats its market capitalization-weighted counterpart by about 2% per year. However, the underlying research does not account for portfolio reformation/rebalancing costs and may not be representative of other stock universes. Do exchange-traded funds (ETF) that implement equal weight for various U.S. stock indexes confirm findings? To investigate, we consider four equal weight ETFs:

We calculate monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly dividend-adjusted prices for the eight ETFs as available (limited by  equal weight funds) through September 2018, we find that: Keep Reading

Stock Size and Excess Stock Portfolio Growth

Why do simple stock portfolios such as equal weighting and random weighting beat market capitalization weighting over the long run? In their June 2018 paper entitled “Diversification, Volatility, and Surprising Alpha”, Adrian Banner, Robert Fernholz, Vassilios Papathanakos, Johannes Ruf and David Schofield tackle this question by decomposing expected stock portfolio log-return into average growth rate and excess growth rate (EGR). They focus on average log-return because, unlike arithmetic and geometric averages, it is an unbiased estimator of long-term performance. They apply two formulas derived in prior work to estimate portfolio log-returns:

  1. Expected portfolio log-return = weighted average stock log-return + EGR
  2. EGR = (weighted average stock return variance – portfolio return variance)/2

They apply these formulas to the following five portfolios, each consisting of monthly overlapping sub-portfolios formed from the 1,000 U.S. stocks with the (each day) largest market capitalizations and rebalanced annually with stock weights normalized to a sum of one:

  1. Capitalization-weighted (CW) – stock weights are proportional to their respective market capitalizations.
  2. Equal-weighted (EW) – weight of each stock is 1/1000.
  3. Large-overweighted (LO) – stock weights are proportional to the square of their respective market capitalizations.
  4. Random-weighted (RW) – stock weights are proportional to random values between zero and one (median of 1,000 trials).
  5. Inverse random-weighted (IRW) – stock weights are proportional to the reciprocals of random values between zero and one (median of 1,000 trials).

EGR quantifies the extent to which portfolio volatility is less than constituent stock volatilities and is always positive for long-only portfolios. Higher constituent stock volatilities generate higher portfolio EGRs. Using daily prices for the 1,000 U.S. stocks with the largest market capitalizations each day during 1964 through 2012 (5,384 distinct stocks over 49 years), they find that:

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Are Equity Multifactor ETFs Working?

Are equity multifactor strategies, as implemented by exchange-traded funds (ETF), attractive? To investigate, we consider seven ETFs, all currently available (in order of decreasing assets):

  • Goldman Sachs ActiveBeta U.S. Large Cap Equity (GSLC) – holds large U.S. stocks based on good value, strong momentum, high quality and low volatility.
  • iShares Edge MSCI Multifactor USA (LRGF) – holds large and mid-cap U.S. stocks with focus on quality, value, size and momentum, while maintaining a level of risk similar to that of the market.
  • iShares Edge MSCI Multifactor International (INTF) – holds global developed market ex U.S. large and mid-cap stocks based on quality, value, size and momentum, while maintaining a level of risk similar to that of the market.
  • JPMorgan Diversified Return U.S. Equity (JPUS) – holds U.S. stocks based on value, quality and momentum via a risk-weighting process that lowers exposure to historically volatile sectors and stocks.
  • John Hancock Multifactor Large Cap (JHML) – holds large U.S. stocks based on smaller capitalization, lower relative price and higher profitability, which academic research links to higher expected returns.
  • John Hancock Multifactor Mid Cap (JHMM) – holds mid-cap U.S. stocks based on smaller capitalization, lower relative price and higher profitability, which academic research links to higher expected returns.
  • Xtrackers Russell 1000 Comprehensive Factor (DEUS) – seeks to track, before fees and expenses, the Russell 1000 Comprehensive Factor Index, which seeks exposure to quality, value, momentum, low volatility and size factors.

Because available sample periods are very short, we focus on daily return statistics, along with cumulative returns. We use four benchmarks according to fund descriptions: SPDR S&P 500 (SPY), iShares MSCI ACWI ex US (ACWX), SPDR S&P MidCap 400 (MDY) and iShares Russell 1000 (IWB). Using daily returns for the seven equity multifactor ETFs and benchmarks as available through September 2018, we find that: Keep Reading

Evolution of Quantitative Stock Investing

Quantitative investing involves disciplined rule-based approaches to help investors structure optimal portfolios that balance return and risk. How has such investing evolved? In their June 2018 paper entitled “The Current State of Quantitative Equity Investing”, Ying Becker and Marc Reinganum summarize key developments in the history of quantitative equity investing. Based on the body of research, they conclude that: Keep Reading

Excluding Bad Stock Factor Exposures

The many factor-based indexes and exchange-traded funds (ETFs) that track them now available enable investors to construct multi-factor portfolios piecemeal. Is such piecemeal construction suboptimal? In their July 2018 paper entitled “The Characteristics of Factor Investing”, David Blitz and Milan Vidojevic apply a multi-factor expected return linear regression model to explore behaviors of long-only factor portfolios. They consider six factors: value-weighted market, size, book-to-market ratio, momentum, operating profitability and investment(change in assets). Their model generates expected returns for each stock each month, and further aggregates individual stock expectations into factor-portfolio expectations holding all other factors constant. They use the model to assess performance differences between a group of long-only single-factor portfolios and an integrated multi-factor portfolio of stocks based on combined rankings across factors. The focus on gross monthly excess (relative to the 10-year U.S. Treasury note yield) returns as a performance metric. Using data for a broad sample of U.S. common stocks among the top 80% of NYSE market capitalizations and priced at least $1 during June 1963 through December 2017, they find that: Keep Reading

Doubling Down on Size

“Is There Really an Size Effect?” summarizes research challenging the materiality of the equity size effect. Is there a counter? In their June 2018 paper entitled “It Has Been Very Easy to Beat the S&P500 in 2000-2018. Several Examples”, Pablo Fernandez and Pablo Acin double down on the size effect via a combination of market capitalization thresholds and equal weighting. Specifically, they compare values of a $100 initial investment at the beginning of January 2000, held through April 2018, in:

  • The market capitalization-weighted (MW) S&P 500.
  • The equally weighted (EW) 20, 40, 60 and 80 of the smallest stocks in the S&P 1500, reformed either every 12 months or every 24 months.

All portfolios are dividend-reinvested. Their objective is to provide investors with facts to aid portfolio analysis and selection of investment criteria. Using returns for the specified stocks over the selected sample period, they find that:

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Style Performance by Calendar Month

Trading Calendar presents full-year and monthly cumulative performance profiles for the overall stock market (S&P 500 Index) based on its average daily behavior since 1950. How much do the corresponding monthly behaviors of the various size and value/growth styles deviate from an overall equity market profile? To investigate, we consider the the following six exchange-traded funds (ETF) that cut across capitalization (large, medium and small) and value versus growth:

iShares Russell 1000 Value Index (IWD) – large capitalization value stocks.
iShares Russell 1000 Growth Index (IWF) – large capitalization growth stocks.
iShares Russell Midcap Value Index (IWS) – mid-capitalization value stocks.
iShares Russell Midcap Growth Index (IWP) – mid-capitalization growth stocks.
iShares Russell 2000 Value Index (IWN) – small capitalization value stocks.
iShares Russell 2000 Growth Index (IWO) – small capitalization growth stocks.

Using monthly dividend-adjusted closing prices for the style ETFs and S&P Depository Receipts (SPY) over the period August 2001 through May 2018 (202 months, limited by data for IWS/IWP), we find that: Keep Reading

Doing Momentum with Style (ETFs)

“Beat the Market with Hot-Anomaly Switching?” concludes that “a trader who periodically switches to the hottest known anomaly based on a rolling window of past performance may be able to beat the market. Anomalies appear to have their own kind of momentum.” Does momentum therefore work for style-based exchange-traded funds (ETF)? To investigate, we apply a simple momentum strategy to the following six ETFs that cut across market capitalization (large, medium and small) and value versus growth:

iShares Russell 1000 Value Index (IWD) – large capitalization value stocks.
iShares Russell 1000 Growth Index (IWF) – large capitalization growth stocks.
iShares Russell Midcap Value Index (IWS) – mid-capitalization value stocks.
iShares Russell Midcap Growth Index (IWP) – mid-capitalization growth stocks.
iShares Russell 2000 Value Index (IWN) – small capitalization value stocks.
iShares Russell 2000 Growth Index (IWO) – small capitalization growth stocks.

We test a simple Top 1 strategy that allocates all funds each month to the one style ETF with the highest total return over a set momentum measurement (ranking or lookback) interval. We focus on the baseline ranking interval from “Simple Asset Class ETF Momentum Strategy”, but test sensitivity of findings to ranking intervals ranging from one to 12 months. As benchmarks, we consider an equally weighted and monthly rebalanced combination of all six style ETFs (EW All), buying and holding S&P Depository Receipts (SPY), and holding SPY when the S&P 500 Index is above its 10-month simple moving average and U.S. Treasury bills (T-bills) when the index is below its 10-month simple moving average (SPY:SMA10). We consider the performance metrics used in “Momentum Strategy (SACEMS)”. Using monthly dividend-adjusted closing prices for the style ETFs and SPY, monthly levels of the S&P 500 index and monthly yields for 3-month T-bills during August 2001 (limited by IWS and IWP) through May 2018 (202 months, ), we find that:

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Is There Really an 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

Ziemba Party Holding Presidency Strategy Update

“Exploiting the Presidential Cycle and Party in Power” summarizes strategies that hold small stocks (large stock or bonds) when Democrats (Republicans) hold the U.S. presidency. How has this strategy performed in recent years? To investigate, we consider three strategy alternatives using exchange-traded funds (ETF):

  1. D-IWM:R-SPY: hold iShares Russell 2000 (IWM) when Democrats hold the presidency and SPDR S&P 500 (SPY) when Republicans hold it.
  2. D-IWM:R-LQD: hold IWM when Democrats hold the presidency and iShares iBoxx Investment Grade Corporate Bond (LQD) when Republicans hold it.
  3. D-IWM:R-IEF: hold IWM when Democrats hold the presidency and iShares 7-10 Year Treasury Bond (IEF) when Republicans hold it.

We use calendar years to determine party holding the presidency. As benchmarks, we consider buying and holding each of SPY, IWM, LQD or IEF and annually rebalanced portfolios of 60% SPY and 40% LQD (60 SPY-40 LQD) or 60% SPY and 40% IEF (60 SPY-40 IEF). We consider as performance metrics: average annual excess return (relative to the yield on 1-year U.S. Treasury notes at the beginning of each year); standard deviation of annual excess returns; annual Sharpe ratio; compound annual growth rate (CAGR); and, maximum annual drawdown (annual MaxDD). We assume portfolio switching/rebalancing frictions are negligible. Except for CAGR, computations are for full calendar years only. Using monthly dividend-adjusted closing prices for the specified ETFs during July 2002 (limited by LQD and IEF) through April 2018, we find that:

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