Equity Premium

Is U.S. equity market valuation outrunning its productive value? For perspective, we compare the trajectories of S&P 500 (SP500) index, earnings and dividends over recent decades and look at some potential explanations for divergences. Using quarterly SP500 data and 10-year U.S. Treasury note (T-note) yield during March 1988 through September 2025 and Shiller data as available through November 2025, we find that: Keep Reading

The equity premium is conventionally the return on stocks minus the risk-free rate (for short-term government bills). What should be the risk-free asset for equities, arguably expected to grow in real terms and never to mature? In the November 2025 draft of their paper entitled “Purifying the Equity Premium”, Christopher Polk and Tuomo Vuolteenaho argue that the risk-free asset as applied to equities should be a long-term inflation-indexed bond and therefore decompose the equity premium into two components:

1. Pure equity premium – stock market return minus the yield on duration-matched inflation-indexed bonds, such as Treasury Inflation-Protected Securities (TIPS). See the chart below.
2. Real term premium – yield on duration-matched inflation-indexed bonds minus the yield on short-term bills.

The conventional equity premium is the sum of these two components. Using value-weighted stock market and U.S. Treasury bonds/bills data for the U.S. since February 1997 and comparable data for the UK since August 1987, along with relevant economic data, all through June 2025, they find that: Keep Reading

“Nixed: The Upside of Getting Dumped”, flagged by a subscriber, finds that “index deletions…could add an abnormal upside to a portfolio when the current growth-dominated bubble starts to deflate.” The authors have quantified findings as the Research Affiliates Deletions Index (NIXT), constructed by:

1. Starting with deletions due to market capitalization changes from the 500 and 1,000 largest U.S. stocks by market capitalization.
2. Removing the bottom 20% of deletions based on firm quality assessments.
3. Holding the equal-weighted remaining deletions up to five years (or until they rejoin a top market capitalization index), rebalancing annually at the end of May.

Do index deletions inherently underperform? To investigate we look at stocks deleted from the S&P 500 Index due to market capitalization changes over the past few years and compare their average performance during the 5, 10, 21, 63, 126 and 252 trading days after deletion to the average performance of date-matched positions in SPDR S&P 500 ETF Trust (SPY). Using dividend-adjusted prices for 61 S&P 500 deletions at closes on deletion dates and corresponding dividend-adjusted prices for SPY during April 2020 through early November 2025, we find that: Keep Reading

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 October 2025, we find that: Keep Reading

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 October 2025, we find that: Keep Reading

A reader requested a test of the following hypothesis from the article “Gold’s Bluff – Is a 30 Percent Drop Next?” [no longer available]: “Ironically, gold is more than just a hedge against market turmoil. Gold is actually one of the most accurate indicators of the stock market’s long-term direction. The Dow Jones measured in gold is a forward looking indicator.” To test this assertion, we examine relationships between the spot price of gold and the level of the Dow Jones Industrial Average (DJIA). Using monthly data for the spot price of gold in dollars per ounce and DJIA over the period January 1971 through September 2025, we find that: Keep Reading

How do exchange-traded-funds (ETF) focused on supplying renewable energy perform? To investigate, we consider nine of the largest renewable energy ETFs, all currently available, as follows:

• • iShares Global Clean Energy (ICLN)
  • Invesco Solar (TAN)
  • First Trust NASDAQ Clean Edge Green Energy Index (QCLN)
  • Invesco WilderHill Clean Energy (PBW)
  • ALPS Clean Energy (ACES)
  • Invesco Global Clean Energy (PBD)
  • SPDR S&P Kensho Clean Power (CNRG)
  • First Trust Global Wind Energy (FAN)
  • Global X Renewable Energy Producers (RNRG)

We use SPDR S&P 500 (SPY) as a benchmark, assuming investors look at renewable energy stocks to beat the market and not to beat the energy sector. We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly returns for the nine renewable energy ETFs and SPY as available through September 2025, we find that: Keep Reading

Do target retirement date funds, offering glidepaths that shift asset allocations away from equities and toward bonds as target dates approach, safely generate attractive returns? To investigate, we consider seven such mutual funds offered by Vanguard, as follows:

• • Vanguard Target Retirement 2020 Fund (VTWNX)
  • Vanguard Target Retirement 2025 Fund (VTTVX)
  • Vanguard Target Retirement 2030 Fund (VTHRX)
  • Vanguard Target Retirement 2035 Fund (VTTHX)
  • Vanguard Target Retirement 2040 Fund (VFORX)
  • Vanguard Target Retirement 2045 Fund (VTIVX)
  • Vanguard Target Retirement 2050 Fund (VFIFX)

We consider as benchmarks SPDR S&P 500 ETF Trust (SPY), iShares iBoxx $ Investment Grade Corporate Bond ETF (LQD) and both 80-20 and 60-40 monthly rebalanced SPY-LQD combinations. We look at monthly and annual return statistics, including compound annual growth rate (CAGR) and maximum drawdown (MaxDD). Using monthly total returns for SPY, LQD, three target retirement date funds since October 2003 and four target retirement date funds since June 2006 (limited by Vanguard inception dates), all through September 2025, we find that:

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Is it reasonable to assume that strong earnings growth and price-to-earnings ratio (P/E) expansion will sustain the unusually strong U.S. stock market returns of the past decade? In his brief September 2025 paper entitled “Expected Stock Returns in Bullish Times”, Javier Estrada decomposes stock returns into: (1) dividend yield, (2) change in earnings and (3) change in P/E. He then employs this decomposition to compare the bullish environments at the end of the 1990s with that of the summer of 2025, including an outlook for the next decade. Using Robert Shiller’s prices, earnings and dividends for the S&P Composite Index during 1872 through June 2025, he finds that: Keep Reading

How can investors and fund managers best exploit premiums associated with value, momentum, profitability, investment and low volatility factors, either to generate absolute return or to beat a market benchmark? In his September 2025 paper entitled “Strategic Style Allocation: Absolute or Relative?”, Pim van Vliet examines strategic allocation across long-only, value-weighted versions of these equity factors, depending on objective: absolute return or benchmark outperformance. To assess absolute return, he evaluates Sharpe ratios of factor allocations. To assess benchmark outperformance, he evaluates information ratios of factor allocations. He also investigates dynamic allocation between low volatility and the other factors, with portfolio adjustment frictions. Using long-only U.S. value-weighted factor returns during July 1963 through May 2025 and global factor index returns during January 1999 through March 2025, he finds that: Keep Reading