Equity Premium

A subscriber asked about an assertion that bitcoin (BTC) price trend/return predicts return of the S&P 500 Index (SP500). To investigate, we relate BTC returns to SP500 returns at daily, weekly and monthly frequencies. We rationalize the different trading schedules for these two series by excluding BTC trading dates that are not also SP500 trading days. Most results are conceptual, but we test three versions of an SP500 timing strategy based on prior BTC returns focused on compound annual growth rate (CAGR) and maximum drawdown (MaxDD). Using daily SP500 levels and (pruned) BTC prices during 9/17/2014 (limited by the BTC series) through 3/18/2025, we find that:

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The “Simple Asset Class ETF Value Strategy” (SACEVS) seeks diversification across a small set of asset class exchanged-traded funds (ETF), plus a monthly tactical edge from potential undervaluation of three risk premiums:

1. Term – monthly difference between the 10-year Constant Maturity U.S. Treasury note (T-note) yield and the 3-month Constant Maturity U.S. Treasury bill (T-bill) yield.
2. Credit – monthly difference between the Moody’s Seasoned Baa Corporate Bonds yield and the T-note yield.
3. Equity – monthly difference between S&P 500 operating earnings yield and the T-note yield.

Premium valuations are relative to historical averages. How might this strategy react to changes in the Effective Federal Funds Rate (EFFR)? Using end-of-month values of the three risk premiums, EFFR, total 12-month U.S. inflation and core 12-month U.S. inflation during March 1989 (limited by availability of operating earnings data) through February 2025, we find that: Keep Reading

A buffer exchange-traded fund (ETF) is designed to limit losses while capping gains over a specific period, usually one year, generally by combining a position in put and call options on a stock index with an ETF that tracks that index. Laddered buffer ETFs smooth this approach by holding a rolling series of buffer ETFs with staggered expiration dates, thereby imposing two layers of fund costs. How do laddered buffer ETFs perform? To investigate, we consider five of the largest such ETFs, all currently available, as follows:

• • FT Vest Laddered Buffer ETF (BUFR)
  • Pacer Swan SOS Fund of Funds ETF (PSFF)
  • FT Vest Laddered Deep Buffer ETF (BUFD)
  • Innovator Laddered Allocation Buffer ETF (BUFB)
  • FT Vest Laddered Nasdaq Buffer ETF (BUFQ)

We use SPDR S&P 500 ETF Trust (SPY) as the benchmark for the first four and Invesco QQQ Trust (QQQ) for the last. We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly total returns for the five laddered buffer ETFs, SPY and QQQ as available through February 2025, we find that:

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Are all stocks except U.S. growth cheap? In his brief February 2025 paper entitled “Decomposing Equity Returns: Earnings Growth vs. Multiple Expansion”, David Blitz decomposes equity returns of different global equity markets and styles (size, low-volatility, value) into dividend yield, earnings growth and multiple expansion. The decomposition consists of:

• Subtracting price return from total return to derive the contribution from dividends.
• Calculating the part of price return due to earnings growth.
• Attributing the part of price return not due to earnings growth to multiple expansion/contraction based on change in price-to-earnings ratio (P/E).

The breakdown exposes different reasons for underperformance of markets and styles relative to the U.S. equity market. Using the specified data for 2015 through 2024, he finds that: Keep Reading

How do returns of different asset classes recently interact with inflation as measured by monthly change in the not seasonally adjusted, all-items consumer price index (CPI) from the U.S. Bureau of Labor Statistics? To investigate, we look at lead-lag relationships between change in CPI and returns for each of the following 10 exchange-traded fund (ETF) asset class proxies:

• Equities:
  • SPDR S&P 500 (SPY)
  • iShares Russell 2000 Index (IWM)
  • iShares MSCI EAFE Index (EFA)
  • iShares MSCI Emerging Markets Index (EEM)
• Bonds:
  • iShares Barclays 20+ Year Treasury Bond (TLT)
  • iShares iBoxx $ Investment Grade Corporate Bond (LQD)
  • iShares JPMorgan Emerging Markets Bond Fund (EMB)
• Real assets:
  • Vanguard REIT ETF (VNQ)
  • SPDR Gold Shares (GLD)
  • Invesco DB Commodity Index Tracking (DBC)

Using monthly total CPI values and monthly dividend-adjusted prices for the 10 specified ETFs during December 2007 (limited by EMB) through January 2025, we find that: Keep Reading

A subscriber requested measurement of a “premium” associated with U.S. stocks relative to those of other developed markets by looking at the difference in returns between the following two exchange-traded funds (ETF):

• SPDR S&P 500 (SPY)
• iShares MSCI EAFE Index Fund (EFA)

Using monthly dividend-adjusted closing prices for these ETFs during August 2001 (limited by EFA) through January 2025, we find that: Keep Reading

Does finance professor David Kass, who presents annual lists of stock picks on Seeking Alpha, make good selections? To investigate, we consider his picks of “10 Stocks for 2020”, “16 Stocks For 2021”, “12 Stocks For 2022”, “10 Stocks For 2023” and “10 Stocks For 2024”. For each year and each stock, we compute total (dividend-adjusted) return. For each year, we then compare the average (equal-weighted) total return for a David Kass portfolio to that of  SPDR S&P 500 ETF Trust (SPY). Using dividend-adjusted returns from Yahoo!Finance for SPY and most stock picks and returns from Barchart.com and Investing.com for three picks during their selection years, we find that: Keep Reading

Do stock-by-stock return forecasts from deep learning produce an exploitable aggregate equity risk premium (ERP) forecast? In the January 2025 revision of their paper entitled “The Aggregated Equity Risk Premium”, Vitor Azevedo, Christoph Riedersberger and Mihail Velikov predict ERP by first applying deep learning to predict returns for individual U.S. stocks and then aggregating these returns at the market level. The firm-level forecasts come from combined outputs of several neural networks of varying complexity applied to 290 firm-level characteristics, 14 U.S. economic variables and 49 industry classification indicators. They iterate these forecasts annually using an expanding training window and a rolling six-year validation window. For comparison, they consider some conventional ERP forecasting approaches. They quantify the economic value of aggregate ERP forecasts via a stock market timing strategy that each month allocates to stocks or U.S. Treasury bills with a 50% leverage limit and conservative 0.5% portfolio rebalancing frictions. Using the specified inputs during March 1957 through December 2021 (with out-of-sample testing commencing January 2000), they find that:

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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 2024, we find 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 2024 (97 years), we find that: Keep Reading