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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.

Alternative Proxy for Small Stocks in Measuring the Size Effect

In response to “Measuring the Size Effect with Capitalization-based ETFs” and in view of the research summarized in “Quality-enhanced Size Effect”, a subscriber suggested using either iShares Core S&P Small-Cap ETF (IJR) or Vanguard S&P Small-Cap 600 Index Fund (VIOO) in place of iShares Russell 2000 ETF (IWM) as a proxy for small stocks. The idea behind this substitution is that IJR and VIOO select profitable companies from the S&P 600, while many Russell 2000 stocks are unprofitable. We choose IJR based on its much longer history, the same length as that for IWM. We again use SPDR S&P 500 ETF Trust (SPY) as a proxy for large stocks. We restate results for IWM for comparison. Using monthly dividend-adjusted closing prices for IWM, IJR and SPY during May 2000 (limited by IWM and IJR) through March 2024, we 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 December 2023, we find that:

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Exhaustively Timing Equity Factor Premiums

Can investors reliably time the market, size, value and profitability long-short equity factor premiums? In their October 2023 paper entitled “Another Look at Timing the Equity Premiums”, Wei Dai and Audrey Dong test strategies that time these four premiums in U.S., developed ex-U.S. and emerging equity markets. They define the premiums as:

  1. Market – the capitalization-weighted market return minus the U.S. Treasury bill yield.
  2. Size – average return on small-capitalization stocks minus average return on large-capitalization stocks.
  3. Value – average return on value stocks minus average return on growth stocks.
  4. Profitability – average return on stocks of high-profitability firms minus average return on stocks of low-profitability firms.

They time each premium separately based on each of:

  1. Valuation ratio – When the difference in aggregate price-to-book ratio between the long and short sides of a premium becomes high (low) relative to its historical distribution, switch to the short (long) side.
  2. Mean reversion – When the premium itself becomes high (low) relative to its historical distribution, switch to the short (long) side  of the premium.
  3. Momentum – When the premium over the last year becomes relatively high (low), switch to the long (short) side of the premium.

To measure historical premium distributions, they consider an expanding window of initial length 10 years or a rolling 10-year window. For switching to the short side of premiums, they consider historical distribution thresholds of top 10%, 20% or 50% (bottom 10%, 20% or 50%) for valuation ratio and mean reversion (momentum). For switching to the long side of premiums, they consider thresholds of bottom 10%, 20% or 50% (top 50%) for valuation ratio and mean reversion (momentum). They consider  monthly or annual portfolio rebalancing. The number of timing strategies tested is thus 720. For the U.S. sample, monthly returns start in July 1963 for profitability and July 1927 for the other three premiums. For the developed ex-U.S. (emerging markets) sample, premium returns start in July 1990 (July 1994). Benchmarks are returns to strategies that continuously hold just the long side of each premium portfolio. Using monthly data as specified through December 2022, they find that: Keep Reading

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:

We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly returns for the seven equity multifactor ETFs and benchmarks as available through August 2023, we find that: Keep Reading

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 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 eight equal-weight ETFs, six alive and two dead:

We focus on average return, standard deviation of returns, reward/risk (average return divided by standard deviation of returns), compound annual growth rate (CAGR) and maximum drawdown (MaxDD), all based on monthly data. Using monthly dividend-adjusted prices for the 16 ETFs as available (limited by equal-weighted funds) through June 2023, we find that: Keep Reading

Comparing Long-term Returns of U.S. Equity Factors

What characteristics of U.S. equity factor return series are most relevant to respective factor performance? In his May 2023 paper entitled “The Cross-Section of Factor Returns” David Blitz explores long-term average returns and market alphas, 60-month market betas and factor performance cyclicality for U.S. equity factors. He also assesses potentials of three factor rotation strategies: low-beta, seasonal and return momentum. Using monthly returns for 153 published U.S. equity market factors, classified statistically into 13 groups, during July 1963 through December 2021, he finds that:

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Boosting Retirement Outcome via Capture of Factor Premiums

Can investors improve long-term retirement portfolio outcomes by targeting equity factor premiums in their stock allocations? In his April 2023 paper entitled “How Targeting the Size, Value, and Profitability Premiums Can Improve Retirement Outcomes”, Mathieu Pellerin investigates whether stock portfolios that target size, value and profitability factor premiums better sustain retirement spending and generate larger bequests than those holding the broad stock market. His hypothetical investor:

  • Starts saving at 25, retires at 65 and dies at 95.
  • Initially allocates 100% to stocks, at age 45 reduces this allocation linearly to 50% at age 65 by shifting to bonds, and thereafter maintains 50%/50% stocks/bonds.
  • Makes $1,042 monthly contributions ($12,500 per year, or $500,000 from age 25 to 65).
  • After retirement, withdraws (consumes) a constant annual 4% in real terms of the balance at retirement.
  • For the stock allocation, chooses either a broad value-weighted market index (CRSP 1-10) or the Dimensional US Adjusted Market 1 index that emphasizes size, value and profitability factors with low turnover.
  • Earns real annual broad stock market returns of either 8.1% (actual historical average) or 5.0% (a conservative 5th percentile of historical return distribution).
  • For the bond allocation, holds 5-year U.S. Treasury notes.

He simulates 100,000 lifecycles by, for each lifecycle: (1) extracting 70-year (840-month) real asset class return subsamples from the full histories; and, (2) applying block bootstrapping with 10-year mean block size to generate lifecycle portfolio returns. Using monthly historical returns for the specified stock/bond proxies and monthly U.S. inflation data during June 1927 through December 2022, he finds that:

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Equity Factor Performance Before and After the End of 2000

Do the widely used U.S. stock return factors exhibit long-term trend changes and shorter-term cyclic behaviors? In his November 2022 paper entitled “Trends and Cycles of Style Factors in the 20th and 21st Centuries”, Andrew Ang applies various methods to compare trends and cycles for equity value, size, quality, momentum and low volatility factors, with focus on a breakpoint at the end of 2000. He measures size using market capitalization, value using book-to-market ratio, quality using operating profitability, momentum using return from 12 months ago to one month ago and low volatility using idiosyncratic volatility relative to the Fama-French 3-factor (market, size, book-to-market) model of stock returns. He each month for each factor sorts stocks into tenths, or deciles, and computes gross monthly factor return from a portfolio that is long (short) the average return of the two deciles with the highest (lowest) expected returns. As a benchmark, he uses the value-weighted market return in excess of the U.S. Treasury bill yield. Using market and factor return data from the Kenneth French data library during July 1963 through August 2022, he finds that:

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Why EW Beats VW

Why do equal-weighted (EW) portfolios outperform their market capitalization-weighted, or value-weighted (VW), counterparts over multiple decades in various investment universes? In their November 2022 paper entitled “Why Do Equally Weighted Portfolios Beat Value-Weighted Ones?”, Alexander Swade, Sandra Nolte, Mark Shackleton and Harald Lohre analyze drivers of differences in performance between EW and VW U.S. stock portfolios over six decades. They also assess consistency of performance drivers. Using monthly returns for a very broad sample of U.S. common stocks and monthly stock factor returns during July 1963 through December 2021, they find that:

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Turn of the Year and Size in U.S. Equities

Is there a reliable and material market capitalization (size) effect among U.S. stocks around the turn-of-the-year (TOTY)? To check, we track cumulative returns from 20 trading days before through 20 trading days after the end of the calendar year for the Russell 2000 Index, the S&P 500 Index and the Dow Jones Industrial Average (DJIA) since the inception of the Russell 2000 Index. We also look at full-month December and January returns for these indexes. Using daily and monthly levels of all three indexes during December 1987 through January 2022 (35 December and 35 January observations), we find that: Keep Reading

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