Size Effect

Does bitcoin now behave like a conventional financial asset? In their short November 2025 paper entitled “From Time-Series Momentum to Size-Factor Comovement: Bitcoin’s Continuing Evolution as a Financial Asset”, Samuel Rosen and Hongcheng Wang investigate the evolution of bitcoin. Specifically, they:

1. Perform autoregressions of weekly bitcoin returns to evaluate time-series momentum at horizons of one to eight weeks.
2. Regress bitcoin returns on returns of U.S. market, size and value equity factors and some financial variables to assess bitcoin behavior in equity context.

To assess changes in relationships over time, they employ rolling windows, split samples and dummy regression variables. Using daily bitcoin returns and monthly returns for the selected equity factors and other financial variables during 2011 through 2024, they find that: Keep Reading

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 2025 (38 December and 38 January observations), we find that: Keep Reading

Are equity multifactor strategies, as implemented by exchange-traded funds (ETF), attractive? To investigate, we consider eight multifactor ETFs, all currently available:

• 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. The benchmark is iShares Russell 1000 (IWB).
• 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. The benchmark is iShares MSCI ACWI ex US (ACWX).
• 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. The benchmark is SPDR S&P 500 (SPY).
• 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. The benchmark is SPY.
• 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. The benchmark is SPDR S&P MidCap 400 (MDY).
• 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. The benchmark is SPY.
• 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. The benchmark is IWB.
• Vanguard U.S. Multifactor (VFMF) – uses a rules-based quantitative model to evaluate U.S. common stocks and construct a U.S. equity portfolio that seeks to achieve exposure to multiple factors across market capitalizations (large, mid and small). The benchmark is iShares Russell 3000 (IWV).

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 2025, we find that: Keep Reading

“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, four alive and four dead:

• Invesco S&P 500 Equal Weight ETF (RSP) – seeks to track investment results (before fees and expenses) of the S&P 500 Equal Weight Index. The capitalization-weighted counterpart is SPDR S&P 500 ETF Trust (SPY).
• First Trust NASDAQ-100 Equal Weight ETF (QQEW) – seeks to track investment results (before fees and expenses) of the NASDAQ-100 Equal Weight Index. The capitalization-weighted counterpart is Invesco QQQ Trust (QQQ).
• Invesco S&P 100 Equal Weight ETF (EQWL) – seeks to track investment results (before fees and expenses) of the S&P 100 Equal Weight Index. The capitalization-weighted counterpart is iShares S&P 100 ETF (OEF).
• Invesco Russell MidCap Equal Weight ETF (EQWM) – seeks to track investment results (before fees and expenses) of the Russell Midcap Equal Weight Index. The capitalization-weighted counterpart is iShares Russell Mid-Cap ETF (IWR). The offeror discontinued this fund in July 2019.
• Invesco Russell 2000 Equal Weight ETF (EQWS) – seeks to track investment results (before fees and expenses) of the Russell 2000 Equal Weight Index. The capitalization-weighted counterpart is iShares Russell 2000 ETF (IWM). The offeror discontinued this fund in February 2019.
• Invesco S&P MidCap 400 Equal Weight ETF (EWMC) – seeks to track investment results (before fees and expenses) of the S&P MidCap 400 Equal Weight Index. The capitalization-weighted counterpart is SPDR S&P MidCap 400 ETF Trust (MDY). The offeror effectively discontinued this fund in August 2023 by changing its allocation rules.
• Invesco S&P SmallCap 600 Equal Weight ETF (EWSC) – seeks to track investment results (before fees and expenses) of the S&P SmallCap 600 Equal Weight Index. The capitalization-weighted counterpart is Vanguard S&P Small-Cap 600 Index Fund (VIOO). The offeror discontinued this fund in February 2023.
• Invesco Russell 1000 Equal Weight ETF (EQAL) – seeks to track investment results (before fees and expenses) of the Russell 1000 Equal Weight Index. The capitalization-weighted counterpart is iShares Russell 1000 ETF (IWB).

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 2025, we find that: Keep Reading

Why do factor timing strategies that shine in research papers disappoint in real life? In his May 2025 paper entitled “Caveats of Simple Factor Timing Strategies”, David Blitz discusses the following  simple factor timing strategies with material and statistically significant outperformance per published studies:

• Short-term factor momentum – each month allocates 40%, 30%, 20%, 10% and 0% to the five factors based on prior-month highest to lowest returns.
• Medium-term factor momentum – each month allocates 40%, 30%, 20%, 10% and 0% to the five factors based on past 12-month highest to lowest returns.
• Structurally overweighting momentum – each month gives double weight to the momentum factor and zero weight to size factor.
• Volatility scaling of the momentum factor – each month scales the momentum factor allocation between 40% and 0% based on the ratio of its 20-year volatility to its 12-month volatility, with remaining funds allocated equally to the other four factors.
• Seasonal momentum – each month allocates 40%, 30%, 20%, 10% and 0% to the five factors based on their average historical returns for the same calendar month over the last 20 years.
• Positioning based on investor sentiment – each month takes 200% (0%) exposure to an equal-weighted factor portfolio when last-month Baker-Wurgler investor sentiment is positive (negative).
• Exploiting long-term factor decay – takes an initial 200% exposure to an equal-weighted factor portfolio and linearly reduces exposure to 0% at the end of the sample.

He applies these strategies to five widely accepted U.S. stock market factors: size, value, profitability, investment and momentum. His benchmark is the monthly rebalanced equal-weighted portfolio of these five factors. For each strategy, he addresses general concerns such as portfolio maintenance frictions and recent performance decay, and he identifies strategy-specific concerns. He concludes with minimum standards for future factor timing studies (see the table below). Using monthly returns for the selected factors during July 1963 until December 2024, he finds that:

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Should a long-only equity investor seeking exposure to the size factor (stocks with small market capitalizations tend to outperform) and the value factor (stocks that are cheap with respect to fundamentals tend to outperform) choose two distinct funds or a combined small-value fund? In his March 2025 paper entitled “Small, Value, or Small/Value?”, Javier Estrada tests six annually rebalanced allocations for an investor seeking to enhance a 60% core exposure to the broad U.S. stock market with 40% total exposure to small and value factors:

• 60-40: 40% exposure to one combined small-value fund.
• 60-8-32: 8% exposure to a small fund and 32% exposure to a value fund.
• 60-16-24: 16% to small and 24% to value.
• 60-20-20: 20% to small and 20% to value.
• 60-24-16: 24% to small and 16% to value.
• 60-32-8: 32% to small and 8% to value.

He considers two samples of monthly returns: (1) Fama-French small-cap, value, small-value and market portfolios during July 1926 through December 2024; and, (2) to account for portfolio maintenance frictions and management fees, iShares small-cap (IJR), value (IUSV), small-value (IJS) and market (IVV) exchange-traded funds during August 2000 through December 2024. Using the specified allocations and samples, he finds that: Keep Reading

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. We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly dividend-adjusted closing prices for IWM, IJR and SPY during May 2000 (limited by IWM and IJR) through March 2025, we find that: Keep Reading

Can fund managers, and thereby individual investors, reliably exploit academic research on equity factors? In his January 2025 paper entitled “Do Factor Strategies Beat the Market?”, Edward McQuarrie reviews differences between the results of academic factor studies and fund manager/investor experience, with focus on the size effect (small stocks outperform) and the value premium (value stocks outperform). Based on decades of academic research and actual long-only funds, he concludes that: Keep Reading

“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 2024, we find that:

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“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 specified momentum ranking (lookback) interval. We focus on a 6-month ranking interval as often used in prior research, but test sensitivity of findings to ranking intervals ranging from one to 12 months. As benchmarks, we consider an equal-weighted and monthly rebalanced combination of all six style ETFs (EW All), and buying and holding SPDR S&P 500 (SPY). As an enhancement we consider holding the Top 1 style ETF (3-month U.S. Treasury bills, T-bills) when the S&P 500 Index is above (below) its 10-month simple moving average at the end of the prior month (Top 1:SMA10), with a benchmark substituting SPY for Top 1 (SPY:SMA10). We employ the performance metrics used for SACEMS. Using monthly dividend-adjusted closing prices for the six style ETFs and SPY, monthly levels of the S&P 500 Index and monthly yields for T-bills during August 2001 (limited by IWS and IWP) through June 2024, we find that:

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