Equity Premium

Under what conditions does equity market time series momentum (TSMOM) work and not work? In their June 2026 paper entitled “Boundaries of Time Series Momentum”, Matti Suominen and Erik Hjalmarsson examine performance of equity market TSMOM across ranges of three valuation metrics: cyclically adjusted price-to-earnings ratio (CAPE), dividend yield and term spread (difference between long-maturity and short-maturity Treasury instrument yields). They specify TSMOM as long (short) the market when past market return in excess of the risk-free rate over a specified lookback interval is positive (negative). They specify a Boundaries variable for predicting TSMOM performance as follows:

1. Scale each of the CAPE, dividend yield and term spread to values between -1 and 1 as follows:
   1. Subtract from its 12-month average the past 10-year or 20-year minimum observation and divide the difference by the past 10-year or 20-year range (maximum minus minimum).
   2. Multiply results by two and subtract one.
2. Compute a Boundaries variable as the square of the scaled term spread plus the square of scaled CAPE or scaled dividend yield.

For a given equity market, they construct a TSMOM index as an equal-weighted average of 25 time series momentum strategies, with lookback and investment intervals of 1, 3, 6, 9 or 12 months. They then explore how index returns interact with the Boundaries variable. Using the specified inputs and stock index returns during July 1927 through December 2024 for the U.S. and during January 1989 through December 2024 for a 20-country international sample, they find that: Keep Reading

Has the strong shift in investor flows from active funds to passive funds unexpectedly contributed to a decline in performance of the former? In her June 2026 paper entitled “Passive Flows, Active Woes: Passive Investing and the Decline of Active Mutual Fund Alpha”, Hannah Unterberg studies whether the secular shift from active to passive investing (see the chart below) has depressed active fund performance because outflows force liquidation of active fund holdings. Using holdings and returns for a broad sample of active and passive U.S. equity mutual funds and exchange-traded funds during January 1984 through December 2024, she finds that:

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Do U.S. industry portfolios perform predictably after similar U.S. equity market returns? In his May 2026 paper entitled “Industry Rotation Using Market-State Similarity”,  Valeriy Zakamulin studies whether current market returns exploitably predict subsequent industry returns. Specifically, he:

1. Examines general market-to-industry monthly return predictability.
2. Assesses monthly market-to-industry predictability across ranges of market returns by:
   • Standardizing market excess return using a 120-month rolling window of past returns.
   • Identifying the 20% of market states most similar to the current state over a 480-month rolling window of past returns, excluding the latest 36 months.
   • Computing subsequent average industry returns for these similar market states.
3. Backtests a strategy that each month buys (sells) those of 30 industry portfolios with positive (negative) expected returns based on current market state. For robustness, he considers alternative industry classifications with 10, 12, 17, 38 and 48 portfolios and different market similarity parameters.

Using monthly returns for the U.S. stock market/industry portfolios and the monthly risk-free rate from the Kenneth French data library during July 1926 through December 2025, he finds that: Keep Reading

Are low volatility stock strategies, as implemented by exchange-traded funds (ETF), attractive? To investigate, we consider eight of the largest low volatility ETFs, all currently available, in order of longest to shortest available histories:

• Invesco S&P 500 Low Volatility Portfolio (SPLV) – the 100 stocks from the S&P 500 Index with the lowest realized volatility over the past 12 months, reformed quarterly. The benchmark ETF for SPLV is SPDR S&P 500 (SPY).
• iShares Edge MSCI Min Vol USA (USMV) – seeks to track an index composed of U.S. equities that, in the aggregate, have lower volatility characteristics relative to the broader U.S. equity market. The benchmark ETF for USMV is iShares Russell 3000 (IWV).
• iShares Edge MSCI Min Vol EAFE (EFAV) – seeks to track an index composed of developed market equities that, in the aggregate, have lower volatility characteristics relative to the broader developed equity markets, excluding the U.S. and Canada. The benchmark ETF for EFAV is iShares MSCI EAFE Index (EFA).
• iShares Edge MSCI Min Vol Emerging Markets (EEMV) – seeks to track an index composed of emerging market equities that, in the aggregate, have lower volatility characteristics relative to the broader emerging equity markets. The benchmark ETF for EEMV is iShares MSCI Emerging Markets Index (EEM).
• iShares Edge MSCI Min Vol Global (ACWV) – seeks to track an index composed of developed and emerging market equities that, in the aggregate, have lower volatility characteristics relative to the broader developed and emerging equity markets. The benchmark ETF for ACWV is iShares MSCI ACWI (ACWI).
• Invesco S&P International Developed Low Volatility Portfolio (IDLV) – the 200 least volatile stocks of the S&P Developed excluding U.S. and South Korea LargeMid Cap BMI Index over the past 12 months, reformed quarterly. The Index is computed using net return, which withholds taxes applicable to non-resident investors. The benchmark ETF for IDLV is Vanguard FTSE All-Wld ex-US ETF (VEU).
• Invesco S&P MidCap Low Volatility Portfolio (XMLV) –  the 80 out of 400 medium-capitalization stocks from the S&P MidCap 400 Index with the lowest realized volatility over the past 12 months, reformed quarterly. The benchmark ETF for XMLV is SPDR S&P MidCap 400 (MDY).
• Invesco S&P SmallCap Low Volatility Portfolio (XSLV) – the 120 out of 600 small-capitalization stocks from the S&P SmallCap 600 Index with the lowest realized volatility over the past 12 months, reformed quarterly. The benchmark ETF for XSLV is iShares Core S&P Small-Cap (IJR).

We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly returns for the low volatility stock ETFs and their benchmark ETFs as available through May 2026, we 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 2026, we find that:

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How do exchange-traded-funds (ETF) that employ artificial intelligence (AI) to pick assets perform? To investigate, we consider ten such ETFs, eight of which are currently available:

• • Amplify AI Powered Equity ETF (AIEQ) – picks U.S. stocks based on a quantitative model that runs on the IBM Watson platform.
  • QRAFT AI-Enhanced U.S. Large Cap ETF (QRFT) – picks large capitalization U.S. stocks via an investment strategy enhanced by the use of AI.
  • QRAFT AI-Enhanced U.S. Large Cap Momentum ETF (AMOM) – picks momentum stocks via an investment strategy enhanced by the use of AI.
  • VanEck Social Sentiment ETF (BUZZ) – picks U.S. stocks with the most positive sentiment as determined from online sources via a rules-based quantitative methodology.
  • WisdomTree International Al Enhanced Value Fund (AIVI) – picks developed market value stocks outside the U.S. and Canada via a quantitative AI model. [We use data only since retention of an AI-oriented advisor at the beginning of 2022.]
  • WisdomTree U.S. Al Enhanced Value Fund (AIVL) – picks U.S. value stocks via a quantitative AI model. [We use data only since retention of an AI-oriented advisor at the beginning of 2022.]
  • Teucrium Aila Long-Short Agriculture Strategy ETF (OAIA) – takes long and short positions in agricultural securities via a strategy employing machine learning. [Dead as of August 2024.]
  • Teucrium Aila Long-Short Base Metals Strategy ETF (OAIB) – takes long and short positions in base metals securities via a strategy employing machine learning. [Dead as of May 2024.]
  • LG QRAFT AI-Powered U.S. Large Cap Core ETF (LQAI) – – picks large capitalization U.S. stocks via an investment strategy enhanced by the use of AI.
  • Stocksnips AI-Powered Sentiment US ALL Cap ETF (NEWZ) – picks U.S. stocks by leveraging AI to generate News Media Sentiment Signals.

We use SPDR S&P 500 ETF Trust (SPY) for comparison, though it is not conceptually matched to some of the ETFs. We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly total returns for the ten AI-powered ETFs and SPY as available through April 2026, we find that: Keep Reading

What are current estimates of equity risk premiums (ERP) and risk-free rates around the world? In their April 2026 paper entitled “Survey: Market Risk Premium and Risk-Free Rate used for 97 countries in 2026”, Pablo Fernandez, Amir Habibian and Lucia Acin summarize results of a March-April 2026 email survey of international finance and economic professors, analysts and company managers about the risk-free rate and the Market Risk Premium (MRP) used to calculate the required return to equity in different countries. Results are in local currencies. Based on 3,637 specific and credible premium estimates spanning 97 countries for which there are at least eight estimates, they find that: Keep Reading

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 2026, we find that:

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A subscriber forwarded the following chart with summary performances of State Street Energy Select Sector SPDR ETF (XLE), State Street Technology Select Sector SPDR ETF (XLK) and an equal-weighted, annually rebalanced combination of the two and encouraged further investigation. The chart indicates that XLE and XLK are materially diversifying since 2020, but the sample is extremely short and includes unusual COVID-19 and Iran war disruptors.

We extend the backtest to inceptions of XLE and XLK at both monthly and annual measurement frequencies, with respective monthly and annual rebalancing of the equal-weighted portfolio of the two ETFs (50-50). We consider statistical, cumulative and dynamic perspectives. Using month-end XLE and XLK dividend-adjusted prices during December 1998 through March 2026, we find that: Keep Reading

Much prior research indicates that most stock anomalies fail to deliver due to data snooping in their discovery, post-publication market adaptation and, especially, implementation costs. In their March 2026 paper entitled “Reviving Anomalies”, Heiner Beckmeyer, Florian Berg, Timo Wiedemann and Jonas Wortmann describe and test a framework to address the poor performance of simple long-short portfolios by double-sorting based first on anomaly rules and then on expected next-month net returns of anomaly stocks. They employ machine learning return forecasts based on  153 firm/stock characteristics to compute expected returns. They quantify expected trading frictions with impact of trading scaled by fund size (micro, small, medium and large). Using data for the 153 firm/stock characteristics and return data for a broad sample of U.S. stocks during January 2004 to December 2023, they find that: Keep Reading