Equity Premium

How do exchange-traded-funds (ETF) focused on space technology/exploration, an arguably hot theme, perform? To investigate, we consider three such ETFs, all currently available, as follows:

• • State Street SPDR S&P Kensho Final Frontiers ETF (ROKT)
  • Procure Space ETF (UFO)
  • ARK Space & Defense Innovation ETF (ARKX)

We use Invesco QQQ Trust (QQQ) as a benchmark, assuming investors look at space stocks as a way to beat other technology stocks. We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly total returns for the three space ETFs and QQQ as available through December 2025, we find that: Keep Reading

Do optimists dominate the pricing of stocks for firms with unusual/difficult to interpret fundamentals, thereby overpricing them? In his December 2025 paper entitled “Hard to Process: Atypical Firms and the Cross-Section of Expected Stock Returns”, Sebastian Weibels relates future stock returns to a measure of the atypicality (ATYP) of firm fundamentals via an autoencoder (unsupervised machine learning model). The autoencoder learns the typical pattern of fundamentals across firms, and ATYP aggregates individual firm deviations from that pattern. High-ATYP firms present unusual combinations of characteristics difficult to understand. Using monthly values for 117 firm fundamentals and associated stock prices for NYSE, AMEX and NASDAQ common stocks, excluding financial and utility sectors and stocks trading below $1, during 1971 through 2023, he finds that: Keep Reading

Past research relating U.S. stock market returns to the party holding the Presidency mostly concludes that Democratic presidents are better for the stock market than Republican presidents. However, Presidents share power conferred by the electorate with Congress. Does historical data confirm that Democratic control of Congress is also better for stock market returns than Republican control of Congress? Is control of the smaller Senate more decisive than control of the House of Representatives? To check, we relate annual U.S. stock market (S&P 500 Index) returns to various combinations of party control of the Presidency, the Senate and the House of Representatives. Using party in power data and annual levels of the S&P 500 Index for December 1927 through December 2025 (98 years), we find that: Keep Reading

How do exchange-traded-funds (ETF) focused on development of robotics-artificial intelligence (AI), an arguably hot area of technology, perform? To investigate, we consider eight of the largest such ETFs, all currently available, as follows:

• • Robo Global Robotics and Automation Index ETF (ROBO)
  • ARK Autonomous Technology & Robotics ETF (ARKQ)
  • Global X Robotics & Artificial Intelligence ETF (BOTZ)
  • First Trust Nasdaq Artificial Intelligence and Robotics ETF (ROBT)
  • Global X Artificial Intelligence & Technology ETF (AIQ)
  • iShares Future AI & Tech ETF (ARTY)
  • Spear Alpha ETF (SPRX)
  • WisdomTree Artificial Intelligence and Innovation Fund (WTAI)

We use Invesco QQQ Trust (QQQ) as a benchmark, assuming investors look at robotics-AI stocks as a way to beat other technology stocks. We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly total returns for the eight robotics-AI ETFs and QQQ as available through December 2025, we find that: Keep Reading

As of November 2025, the MSCI All Country World Index (ACWI) allocates about 65% to U.S. stocks. Is this allocation to a single country crazy high? In the November 2025 revision of their brief paper entitled “How Much Is Too Much? Part 1: Why 60% in US Equities Isn’t as Crazy as It Might Sound”, Arnaud Battistella and Nicholas McLoughlin assess this allocation by deriving the expected returns implied by ACWI allocations across regions (U.S., Europe ex UK, UK, Japan, Pacific ex Japan and Emerging Markets). Using mid-2025 ACWI allocations and monthly returns for specified regions in U.S. dollars during December 1987 through May 2025, they find that:

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In response to our inquiry about Goldman Sachs Panic Index data, Grok responded that the data are proprietary and unavailable. However, Grok offered “several high-quality public proxies and near-replicas…built by traders and quants using only freely available data. These reconstructions correlate extremely closely (often 0.90–0.98) with the snippets Goldman has shown clients over the years.” For one of these proxies, the percentile rank of VIX within its trailing 2-year window (0-100 scale), Grok provided a Python script to generate an historical daily series. Is it predictive of U.S. stock market returns? To investigate, we run the script to generate daily Panic Index Proxy data from the end of 2015 through November 2025 and relate the series to contemporaneous daily S&P 500 Index (SP500) returns. Using these two series, we find that: Keep Reading

Should measures of long-term investment performance incorporate ways in which typical individual investors handle their portfolios over a lifetime rather than an idealized perspective such as buy-and-hold with all distributions reinvested? In his December 2025 paper entitled “Measuring Investor Outcomes”, Hendrik Bessembinder argues that investment performance measures should be realistic and discusses alternative measures of returns. Using monthly performance data for the broad U.S. stock market from the end of 1926 through 2022, he finds that: Keep Reading

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