Equity Premium

How much should investors who hold a conventionally diversified portfolio (stocks and bonds) be willing to pay for and an additional equity or bond fund that outperforms its benchmark (provides alpha)? In their May 2025 paper entitled “How Much Should You Pay for Alpha? Measuring the Value of Active Management with Utility Calculations”, Andrew Ang and Debarshi Basu estimate the amount an investor is willing to pay for access to an active equity or bond mutual fund, starting from an optimal stocks-bonds portfolio. Specifically, they:

1. Empirically estimate investor risk aversion for a given stocks-bonds base portfolio, focusing on a 60-40 S&P 500 Total Return Index-Bloomberg US Aggregate Bond Index portfolio.
2. Add one of 1,203 active U.S. large-capitalization mutual funds in the Morningstar database or one of 47 fixed income mutual funds in the Morningstar Core Plus US bond category to the base portfolio.
3. For each added fund, compute the utility benefit (certainty equivalent or willingness-to-pay) of adding it.

For robustness, they repeat this analysis for different stocks-bonds base portfolios and different assumptions about equity-bond correlations. Using monthly returns for the selected indexes and mutual funds during January 2016 to December 2024, they find that: Keep Reading

Should investors expect a negative correlation between stock market and bond market returns? In his February 2025 paper entitled “Rethinking the Stock-Bond Correlation”, Thierry Roncalli examines the stocks-bond return correlation from theoretical and empirical perspectives, employing a 4-year rolling window of monthly returns for the latter. Using both long-term and recent returns, he finds that: Keep Reading

Can investors exploit analyst stock price targets by finding the best analysts and overweighting the most extreme target-implied returns? In their March 2025 paper entitled “Alpha in Analysts”, Álvaro Cartea and Qi Jin test the informativeness and exploitability of sell-side analyst stock price targets. To test informativeness of target prices, they each month for each analyst:

• Use price targets to deduce 12-month return forecasts.
• Form a hedge portfolio that is long (short) stocks with positive (negative) return forecasts, with weights proportional to magnitudes of forecasted returns and absolute value of the sum of weights equal to one.
• Compare analyst portfolio performance to that of an equal-weighted, long-only portfolio of the same stocks.

To test exploitability of results, they each month:

• Predict portfolio profitability for each analyst via an inception-to-date regression of six analyst performance metrics up to 12 months ago (capturing historical performance and breadth of stock coverage) versus next-month portfolio return.
• Construct a portfolio of analyst portfolios with higher (lower) allocations to those with higher (lower) predicted returns.

Using daily analyst price targets and associated stock returns/firm characteristics as available for common NYSE/AMEX/NASDAQ stocks during January 1999 through November 2024, they find that: Keep Reading

Are exchange-traded funds (ETF) focused on Initial Public Offerings of stocks (IPO) attractive? To investigate, we consider three of the largest IPO ETFs and one recent Special Purpose Acquisition Company (SPAC) ETF, one of which is no longer available, in order of longest to shortest available histories:

• First Trust US Equity Opportunities ETF (FPX) – seeks to track price and yield of the IPOX-100 U.S. Index.
• Renaissance IPO ETF (IPO) – reflects approximately the top 80% of new public firms weighted by free float capitalization with a 10% cap for any one position. Large IPOs enter quickly and others enter during quarterly reviews. All exit two years after initial trade date.
• First Trust International Equity Opportunities ETF (FPXI) – seeks gross investment results that track price and yield of the IPOX International Index.
• Defiance Next Gen SPAC Derived ETF (SPAK) – 60% weight to IPOs derived from SPACs and 40% weight to common stock of newly listed SPACs, excluding warrants (dead as of the end of August 2022).

We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). For all these ETFs, we use SPDR S&P 500 (SPY) as the benchmark. Using monthly returns for the IPO ETFs and SPY as available through April 2025, we find that:

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Are stock and sector momentum strategies, as implemented by exchange-traded funds (ETF), attractive? To investigate, we consider nine momentum-oriented equity ETFs, all currently available, in order of longest to shortest available histories:

• Invesco Dorsey Wright Momentum ETF (PDP) – invests at least 90% of assets in approximately 100 U.S. common stocks per a proprietary methodology designed to identify powerful relative strength characteristics, reformed quarterly. Benchmark is iShares Russell 3000 ETF (IWV).
• Invesco Dorsey Wright SmallCap Momentum ETF (DWAS) – invests at least 90% of assets in approximately 200 small-capitalization U.S. common stocks per a proprietary methodology designed to identify powerful relative strength characteristics, reformed quarterly. Benchmark is iShares Russell 2000 ETF (IWM).
• iShares Edge MSCI USA Momentum Factor ETF (MTUM) – holds U.S. large-capitalization and mid-capitalization stocks with relatively high momentum. Benchmark is iShares Russell 1000 ETF (IWB).
• First Trust Dorsey Wright Focus 5 ETF (FV) – holds five equally weighted sector and industry ETFs selected via a proprietary relative strength methodology, reformed twice a month. Benchmark is IWV.
• iShares MSCI Intl Momentum Factor ETF (IMTM) – holds international developed market large-capitalization and mid-capitalization stocks with relatively high momentum. Benchmark is iShares MSCI ACWI ex U.S. ETF (ACWX).
• SPDR Russell 1000 Momentum Focus ETF (ONEO) – tracks the Russell 1000 Momentum Focused Factor Index, picking U.S. stocks that have recently outperformed. Benchmark is IWB.
• Alpha Architect U.S. Quantitative Momentum ETF (QMOM) – seeks to buy stocks with the highest quality momentum via a portfolio that generally holds 50 stocks. Benchmark is IWV.
• First Trust Dorsey Wright Dynamic Focus 5 ETF (FVC) – similar to FV but with added risk management via an increasing allocation to cash equivalents when relative strengths of more than one-third of the universe diminish relative to a cash index, reformed twice a month. Benchmark is IWV.
• JPMorgan U.S. Momentum Factor ETF (JMOM) – holds U.S. common stocks with strong risk-adjusted momentum. Benchmark is IWB.

We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). We assign broad market benchmark ETFs according to momentum fund descriptions. Using monthly dividend-adjusted returns for the nine momentum funds and respective benchmarks as available through April 2025, we find that: Keep Reading

What are the implications of stock trading volume spikes for near-term returns? In their February 2025 paper entitled “Volume Shocks and Overnight Returns”, Álvaro Cartea, Mihai Cucuringu, Qi Jin and Mungo Wilson study the effects of stock trading volume shocks during normal trading hours on subsequent overnight and next-day returns. For each stock each day, they identify volume shocks as unusually high or low values of daily volume during normal hours (open-to-close) divided by the exponential moving average of daily volume with 60-day half-life, minus one. They then sort stocks by this metric into fifths, or quintiles, and calculate subsequent overnight (close-to-open) and next-day (open-to-close) gross annualized returns and Sharpe ratios for equal-weighted or value-weighted quintile portfolios. To ensure exploitability, they then employ five linear and machine learning models (trained on data through 2015) to forecast volume shocks and construct long-only portfolios to capture the overnight returns associated with prior-day volume spikes. Using daily trading volume and trading day/overnight price data for all NYSE/AMEX/NASDAQ common stocks during January 2000 through December 2022, they find that:

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Should those aiming to exploit machine learning for portfolio construction focus model training on the broad market or specific industries? In their April 2025 paper entitled “Do Machine Learning Models Need to Be Sector Experts?”, Matthias Hanauer, Amar Soebhag, Marc Stam and Tobias Hoogteijling examine return predictability using several machine learning (ML) models trained on a comprehensive set of firm/stock characteristics in three ways:

1. Generalist – trained on all stocks in the sample.
2. Specialist – trained on stocks only within one of 12 industry classifications.
3. Hybrid – integrates overall sample and industry information via industry-neutral mappings from stock characteristics to expected returns.

They employ four ML models, including elastic nets, gradient boosted regression trees, 3-layer neural networks and an equal-weighted ensemble of the three. They train and tune these models with an expanding window with an initial 18-year training set, 12-year validation set and 1-year test set, shifted forward each year but retaining the initial training start point. Input data consists of monthly stock returns and monthly values of 153 firm-level characteristics for U.S. stocks each month at or above the 20th percentile of NYSE market capitalizations . They assign stocks to the 12 industries (including Other), with average weights ranging from 22.5% for Tech to 1.4% for Durables. They then each month sort stocks into tenths (deciles) by machine learnings ensemble-predicted next-month return and reform a volatility-scaled, value-weighted hedge portfolio that is long the decile with the highest expected returns and short the decile with the lowest. Using the specified inputs during January 1957 (January 1986 for a non-U.S. sample) through December 2023, they find that:

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What are the costs of mitigating tail risk via exchange-traded funds (ETF) designed to manage it? To investigate, we consider seven such ETFs, three dead and four live, as follows:

• • VelocityShares Tail Risk Hedged Large Cap ETF (TRSK) – hedges against tail risk by allocating 85% (15%) of assets to ETFs that track the S&P 500 Index (a volatility component designed to hedge against extreme market declines). This ETF is dead.
  • Cambria Global Tail Risk ETF (FAIL) – invests at least 40% of assets in investment grade, intermediate U.S. treasuries and TIPS, at least 40% in non-U.S. sovereign bonds and about 1% per month in put options. This ETF is dead.
  • Cambria Tail Risk ETF (TAIL) – holds cash and U.S. government bonds and about 1% of assets per month in put options.
  • Global X NASDAQ 100 Tail Risk ETF (QTR) – invests at least 80% of assets in the securities of the Nasdaq-100 Quarterly Protective Put 90 Index, which holds NASDAQ 100 stocks and put options on the NASDAQ 100 Index.
  • Global X S&P 500 Tail Risk ETF (XTR) – invests at least 80% of assets in the S&P 500 and put options on the S&P 500 Index.
  • Simplify Tail Risk Strategy ETF (CYA) – invests 50%-90% of assets in income-generating ETFs and up to 20% in derivatives to hedge tail risk. This ETF is dead.
  • Alpha Architect Tail Risk ETF (CAOS) – normally invests in S&P 500 Index put spreads. 

Note that TRSK, QTR, XTR and CYA are composite portfolios holding equities and embedded tail risk protection, while FAIL, TAIL and CAOS are pure tail risk protection usable as adjuncts to separate equity portfolios. We use SPDR S&P 500 ETF Trust (SPY), iShares MSCI EAFE ETF (EFA) and Invesco QQQ Trust (QQQ) over matched sample periods for reference. We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly total returns for the seven tail risk ETFs, SPY, EFA and QQQ as available through March 2025, we find that:

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Do exchange-traded funds (ETF) designed to make private equity available to individual investors beat the market? To investigate, we consider five ETFs, as follows:

• • Invesco Global Listed Private Equity ETF (PSP) – invests in 40 to 75 private equity companies, including business development companies, master limited partnerships, alternative asset managers and other entities that are listed on a nationally recognized exchange.
  • iShares Listed Private Equity UCITS ETF (IPRV) – tracks the return of the S&P Listed Private Equity Index via exposure to large, liquid and listed private equity companies in developed markets that invest directly into or buy out private companies.
  • VanEck BDC Income ETF (BIZD) – invests at least 80% of its total assets in securities associated with its benchmark (Business Development Company) index.
  • ProShares Global Listed Private Equity ETF (PEX) – invests in the most actively traded private equity companies that directly hold private equity, or in instruments with similar economic characteristics.
  • FlexShares Listed Private Equity UCITS ETF (FLPE) – tracks price and yield performance, before fees and expenses, of the Foxberry Listed Private Equity SDG Screened USD Net Total Return Index.

We use Vanguard Total Stock Market Index Fund ETF (VTI) as the benchmark. We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly total returns for the five private equity ETFs and VTI as available through March 2025, we find that:

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Subscribers asked whether substituting Invesco QQQ Trust (QQQ) for SPDR S&P 500 (SPY) in the Simple Asset Class ETF Value Strategy (SACEVS) and the Simple Asset Class ETF Momentum Strategy (SACEMS) improves outcomes. To investigate, we substitute monthly QQQ dividend-adjusted returns for SPY dividend-adjusted returns in the two model strategies. We then compare the modified performance with the original baseline performance, including: gross compound annual growth rates (CAGR) at various horizons, average gross annual returns, standard deviations of gross annual returns, gross annual Sharpe ratios and maximum drawdowns (MaxDD) based on monthly measurements. In Sharpe ratio calculations, we employ the average monthly yield on 3-month U.S. Treasury bills during a year as the risk-free rate for that year. Using the specified methodology and data to generate SACEVS monthly returns starting August 2002 and SACEMS monthly returns starting July 2006, all through March 2025, we find that:

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