Equity Premium

How should the variability of stock market returns shape the outlooks of short-term traders and long-term investors? How strong is the tailwind of the general drift upward in stock prices? How powerful is the turbulence of variability? Does the tailwind ever overcome the turbulence? To investigate we consider all holding periods for the S&P 500 Index ranging from one week to 208 weeks (about four years). Using weekly closes for the index during January 1928 through mid-March 2022 (4,915 weeks or about 94 years), we find that:

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Investors arguably expect that investments generate returns in excess of the inflation rate. Do different measures of the inflation rate indicate materially different yield discounts? To investigate, we relate 12-month trailing S&P 500 annual operating earnings yield (E/P), S&P 500 12-month trailing annual dividend yield, 10-year U.S. Treasury note (T-note) yield and 3-month U.S. Treasury bill (T-bill) yield to four measures of annual U.S. inflation rate:

1. Non-seasonally adjusted inflation rate based on the total Consumer Price Index (CPI) from the Bureau of Labor Statistics (retroactive revisions of seasonal adjustments interfere with historical analysis).
2. Non-seasonally adjusted inflation rate based on core CPI from the Bureau of Labor Statistics.
3. Inflation rate based on the Personal Consumption Expenditures: Chain-type Price Index (PCE) from the Federal Reserve Bank of St. Louis.
4. Trimmed mean PCE from the Federal Reserve Bank of Dallas.

The CPI measurements have a delay of about two weeks, and the PCE measurements have a delay of about a month. Using monthly data for all variables during March 1989 (limited by earnings data) through January 2022, we find that… Keep Reading

What best explains the decades-long pattern of strong overnight and weak intraday returns in most equity markets? In his January 2022 paper entitled “They Still Haven’t Told You”, Bruce Knuteson reviews possible explanations for this pattern and identifies the most likely. His theoretical equity index benchmark is a random walk with slight upward drift (due to general economic expansion and survivorship bias), with intraday return on average larger than overnight return due to higher intraday risk. Using close-to-open and open-to-close levels of 21 major stock market indexes as available during January 1990 through December 2021, he finds that: Keep Reading

A subscriber asked whether the optimal momentum ranking (lookback) interval for the “Simple Asset Class ETF Momentum Strategy” (SACEMS) shrinks during bear markets for U.S. stocks. To investigate, we compare SACEMS monthly performance statistics when the S&P 500 Index at the previous monthly close is above (bull market) or below (bear market) its 10-month simple moving average. We consider Top 1, equal-weighted (EW) Top 2 and EW Top 3 portfolios of monthly winners for the baseline SACEMS lookback interval. We focus on monthly return, monthly volatility and compound annual growth rate (CAGR) as key performance metrics. In a robustness test for the EW Top 2 and EW Top 3 portfolios, we consider lookback intervals ranging from one to 12 months. Using monthly total (dividend-adjusted) returns for SACEMS assets since February 2006 and monthly S&P 500 Index level since September 2005, all through January 2022, we find that:

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Does the number of factors significantly predicting next-month stock returns vary substantially over time? If so, what accounts for the variation? In their December 2021 paper entitled “Time Series Variation in the Factor Zoo”, Hendrik Bessembinder, Aaron Burt and Christopher Hrdlicka investigate time variation in the statistical significance of 205 previously identified equity factors before, during and after the sample periods used for their discoveries. Specifically, they track 1-factor (market) alphas of each factor over rolling 60-month intervals over a long sample period. Their criterion for significance for each factor in each interval is a t-statistic of at least 1.96 (95% confidence that alpha is positive). Using monthly returns for all common stocks listed on NYSE, AMEX and NASDAQ exchanges having at least 60 continuous months of data as available during July 1926 (with alpha series therefore starting June 1931) through December 2020, they find that: Keep Reading

Are some passive exchange-trade-fund (ETF) managers more efficient than others in adjusting to changes in underlying benchmark indexes? In the December 2021 revision of his paper entitled “Should Passive Investors Actively Manage Their Trades?”, Sida Li employs daily holding data of passive ETFs to compare and quantify effects of different approaches to portfolio reformation to track underlying indexes. Using daily and monthly holdings as available for 732 passive and unlevered U.S. equity ETFs (with no survivorship bias), underlying index reformation announcements and associated stock prices during 2012 through 2020, he finds that:

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How do returns of different asset classes recently interact with uncertainty in government economic policy as quantified by the Economic Policy Uncertainty (EPU) Index? This index at the beginning of each month incorporates from the prior month:

1. Coverage of policy-related economic uncertainty by prominent newspapers (50% weight).
2. Number of temporary federal tax code provisions set to expire in future years (one sixth weight).
3. Level of disagreement in one-year forecasts among participants in the Federal Reserve Bank of Philadelphia’s Survey of Professional Forecasters for both (a) the consumer price index (one sixth weight) and (b) purchasing of goods and services by federal, state and local governments (one sixth weight).

Because the historical EPU Index series includes substantial revisions to prior months, we focus on monthly percentage changes in EPU Index and look at lead-lag relationships between change in EPU Index 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 levels of the EPU Index and monthly dividend-adjusted prices for the 10 specified ETFs during December 2007 (limited by EMB) through December 2021, we find 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-commodities producer price index (PPI) from the U.S. Bureau of Labor Statistics? To investigate, we look at lead-lag relationships between change in PPI 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 PPI values and monthly dividend-adjusted prices for the 10 specified ETFs during December 2007 (limited by EMB) through December 2021, we find that: Keep Reading

Does the labor force participation rate, measured monthly by the U.S. Bureau of Labor Statistics along with employment and unemployment rate, predict U.S. stock market returns? An increasing (decreasing) participation rate may may indicate strong (weak) employment demand and therefore a strong (weak) economy. To investigate, we relate participation rate to performance of the S&P 500 Index as a proxy for the stock market. Using monthly participation rate and index level during January 1948 (limited by the former) through December 2021, we find that: Keep Reading

A subscriber asked whether substituting the less volatile Vanguard Dividend Appreciation Index Fund (VIG) for SPDR S&P 500 (SPY) in the Simple Asset Class ETF Value Strategy (SACEVS) and the Simple Asset Class ETF Momentum Strategy (SACEMS) would improve outcomes. To investigate, we substitute monthly VIG dividend-adjusted returns for SPY dividend-adjusted returns in the two model strategies. Because VIG is not available for the entire sample periods used in the tracked models, we splice VIG returns into the SPY position starting with inception of the former in May 2006. We then compare the spliced performance with the original baseline performance, including: gross compound annual growth rates (CAGR), gross annual returns, average gross annual returns, standard deviations of gross annual returns, gross annual Sharpe ratios and maximum drawdowns (MaxDD). 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 December 2021, we find that:

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