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Equity Premium

Governments are largely insulated from market forces. Companies are not. Investments in stocks therefore carry substantial risk in comparison with holdings of government bonds, notes or bills. The marketplace presumably rewards risk with extra return. How much of a return premium should investors in equities expect? These blog entries examine the equity risk premium as a return benchmark for equity investors.

Best Stock Return Anomaly Double Sorts?

Are portfolios of U.S. stocks that are double-sorted to capture benefits of two complementary return anomalies attractive? In their July 2020 paper entitled “Interacting Anomalies”, Karsten Müller and Simon Schmickler test all possible double-sorted portfolios across 102 stock return anomalies (10,302 double-sorts). They employ 5×5 double-sorts, first ranking stocks into fifths (quintiles) for one anomaly and then re-sorting each of these quintiles into fifths for the second anomaly. They focus on the four “corner” portfolios involving the extreme high and low quintiles for both anomalies. They evaluate average returns, Sharpe ratios and factor model alphas of both equal-weighted (EW) and value-weighted (VW) versions of these portfolios, emphasizing performance gains from anomaly interactions. They correct for multiple hypothesis testing (data snooping bias) using the Bonferroni correction. Using trading and accounting data for a broad sample of U.S. common stocks with annual (quarterly) accounting data lagged by six (four) months during 1970 through 2017, they find that:

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Ending with the Beginning in Mind

How should investors think about the interactions between working years (retirement account contributions) and retirement years (retirement account withdrawals)? In his June 2020 paper entitled “Retirement Planning: From Z to A”, Javier Estrada integrates working and retirement periods to estimate how much an individual should save and how they should invest to achieve a desired retirement income and ultimate bequest to heirs. He illustrates his analytical solution empirically for U.S. stocks and bonds, first using a base case plus sensitivity analysis and then using Monte Carlo simulations. His base case assumes:

  • Work will last 40 years with a 60%/40% stocks/bonds retirement portfolio.
  • Retirement will last 30 years with beginning-of-year real (inflation-adjusted) withdrawals of $60,000 from a 40%/60% stocks/bonds retirement portfolio and ultimate bequest $300,000.

Using annual data for U.S. stocks (the S&P 500 Index total return), bonds (10-year U.S. Treasury notes) and U.S. inflation during 1928 through 2019, he finds that: Keep Reading

Representative Investor Returns on Stocks?

Most stock data sources present Total Return (TR), 100% reinvestment of dividends with no participation in firm rights issuances and share issuances/repurchases, as representative of investment performance. An alternative perspective is Total Return for All Shareholders (TRAS), the return for an investor who maintains a constant fraction of issued shares (see the table below). Can these two measures of returns to investors differ materially? In his May 2020 paper entitled “Total Return (TR) and Total Return for All Shareholders (TRAS). Difference for the Companies in the S&P 100”, Pablo Fernandez compares recent TR and TRAS for stocks in the S&P 100 as of April 2020 that have histories back to the end of 2004 (88 stocks). Using price, dividend, rights issuance and share issuance/repurchase data during December 2004 through April 2020, he finds that: Keep Reading

Pervasive Effects of Preference for Lottery Stocks

Is investor attraction to high-reward/high-risk (lottery) stocks a crucial contributor to stock return anomalies? In their May 2020 paper entitled “Lottery Preference and Anomalies”, Lei Jiang, Quan Wen, Guofu Zhou and Yifeng Zhu aggregate 16 measures of lottery preference into a single long-short factor via time-varying linear combination. Examples of the 16 measures are: maximum daily return last month; average of the five highest daily returns last month; difference between maximum and minimum daily returns last month; and, skewness of daily returns the past three months. They then test the ability of this lottery preference factor to help explain a set of 19 stock return anomalies previously unexplained by a widely used 4-factor (market, size, investment and profitability) model of stock returns. They further study interactions between the lottery preference factor and 11 well-known anomalies by each month during 1980-2018 double-sorting stocks first into fifths (quintiles) based on lottery preference and then within each lottery preference quintile into sub-quintiles based on each anomaly characteristic. Using firm/stock data for a broad sample of U.S. common stocks priced over $1 during January 1962 through December 2018, they find that:

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Open Source Stock Predictor Data and Code

Are published studies that predict higher returns for some U.S. stocks and lower for others based on firm accounting, stock trading and other data reproducible? In their May 2020 paper entitled “Open Source Cross-Sectional Asset Pricing”, Andrew Chen and Tom Zimmermann make available data and code that reproduce many published cross-sectional stock return predictors, allowing other researchers to modify and extend past studies. They commit to annual updates of their study. Defining statistical significance as achieving at least 95% confidence in predictive power, they include:

  • 180 clear predictors that exhibit statistical significance in original studies and are easily reproducible.
  • 30 likely predictors that exhibit statistical significance in original studies but are not precisely reproducible.
  • 315 additional predictors covered in past studies that were not clearly tested or failed, or are variations of these predictors. They further extend this group by separately testing 1-month, 3-month, 6-month and 12-month portfolio reformation frequencies (1,260 total tests).

They compute all predictors on a monthly basis and create for each a long-short portfolio based on the specifications and the sample period of its original study. They check predictive power of each using data available at the end of each month to evaluate long-short portfolio returns the next month. They assume a 6-month lag for availability of annual accounting data and a 1-quarter lag for quarterly accounting data. They make no attempt to account for portfolio reformation frictions or to winnow predictors based on similarity. Using data and sample periods for U.S. firms/stocks as specified in original published studies as described above, they find that: Keep Reading

Investor Access to Factor Premiums via Funds

Are widely accepted equity factor exposures available in fact to investors via “smart beta” mutual funds and exchange-traded funds (ETF)? In their May 2020 paper entitled “Smart Beta Made Smart”, Andreas Johansson, Riccardo Sabbatucci and Andrea Tamoni test effectiveness of individual U.S. equity mutual funds and ETFs and combinations of these funds for exploiting several major equity risk factors (value, size, profitability and momentum). After assembling a sample of funds with names that indicate smart beta strategies, they iteratively (annually for size, value and profitability and daily for momentum):

  1. Apply a double-regression to each fund to identify those that are actually “closet” market index funds.
  2. Refine factor exposures of each true smart beta fund based on actual fund holdings.
  3. Construct separately for institutional and retail investors tradable long-side (mutual funds and ETFs) and short-side (ETFs only) risk factors via value-weighted combinations of the 10 funds with the strongest exposures to each factor.

Using daily, monthly, and quarterly data for U.S. equity mutual funds and ETFs with (1) names indicating smart beta strategies, (2) at least one year of returns and (3)assets over $1 billion, data for their individual component U.S. stocks and specified factor returns during January 2003 through May 2019, they find that: Keep Reading

Returns for Leveraged Securities

Are investors willing to pay for easy access to leverage? In the April 2020 version of their draft paper entitled “Embedded Leverage”, Andrea Frazzini and Lasse Pedersen investigate the relationship between the leverage of a financial asset (absolute percentage price change per one percent change in the underlying) and its return. They consider equity index options and individual stock options for different maturities and levels of moneyness, and leveraged exchange-traded funds (ETF). They consider three ways to test whether securities with more embedded leverage offer lower (monthly) returns: (1) portfolios sorted on leverage; (2) long-short factors that bet against leverage; and, (3) regression analysis. They consider alphas based on four (market, size, book-to-market, momentum) and five (plus market volatility) risk factors. Using groomed daily data for options on around 3,300 individual stocks and 12 stock indexes during 1996 through 2018, and daily data for seven 2X leveraged ETFs for seven major U.S. stock indexes during 2006 through 2018, they find that: Keep Reading

TIPS-based Equity Risk Premium Estimate

How can investors account for inflation expectations in estimating attractiveness of equities? In their March 2020 article entitled “The Equity Risk Premium: A Novel Perspective on the Past Fifty Years”, James White and Victor Haghani offer a perspective on stock market long-term (10-year) attractiveness based on Equity Risk Premium (ERP) calculated as the difference between:

  1. Cyclically adjusted earnings yield as the real expected long-term stock market return. This measure is the inverse of cyclically adjusted price-to-earnings ratio (CAPE, or P/E10); and,
  2. The yield on 10-year U.S. Treasury Inflation Protected Securities (TIPS) as the long-term risk-free return.

Using monthly values of P/E10 since 1970, modeled yield of 10-year TIPS until their initial issue in 1999 and actual yield of 10-year TIPS as issued thereafter, all through March 18, 2020, they find that: Keep Reading

Smart Money Indicator Verification Update

“Verification Tests of the Smart Money Indicator” performs tests of ideas and setup features described in “Smart Money Indicator for Stocks vs. Bonds”. The Smart Money Indicator (SMI) is a complicated variable that exploits differences in futures and options positions in the S&P 500 Index, U.S. Treasury bonds and 10-year U.S. Treasury notes between institutional investors (smart money) and retail investors (dumb money) as published in Commodity Futures Trading Commission Commitments of Traders (COT) reports. Since findings for some variations in that test are attractive, we add two further robustness tests:

Using COT report data, dividend-adjusted SPDR S&P 500 (SPY) as a proxy for a stock market total return index, 3-month Treasury bill (T-bill) yield as return on cash (Cash) and dividend-adjusted iShares 20+ Year Treasury Bond (TLT) as a proxy for government bonds during 6/16/06 through 4/3/20, we find that:

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COVID-19 and U.S. Stock Returns

What does the U.S. stock market at industry/firm levels say about investor expectations during and after the 2019 coronavirus (COVID-19) pandemic? In the April 2020 update of their paper entitled “Feverish Stock Price Reactions to COVID-19”, Stefano Ramelli and Alexander Wagner examine and interpret industry/firm-level reactions to COVID-19 across three pandemic phases:

  1. Incubation: January 2-17,
  2. Outbreak: January 20-February 21,
  3. Fever: February 24-March 20.

They estimate each stock’s abnormal return during these phases as its 1-factor (market) alpha minus its beta times the market excess return. They estimate alpha and beta via regression of daily excess stock returns on daily excess value-weighted market returns during 2019. They use the yield on 1-month U.S. Treasury bills (T-bill) as the risk-free rate for calculating excess return. Using daily dividend-adjusted stock prices for Russell 3000 stocks (excluding financial stocks for leverage-related analyses), market returns and T-bill yields during December 31, 2018 through March 20, 2020, they find that: Keep Reading

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