Equity Premium

Financial media and expert commentators often cite the U.S. unemployment rate as an indicator of economic and stock market health, generally interpreting a jump (drop) in the unemployment rate as bad (good) for stocks. Conversely, investors may interpret a falling unemployment rate as a trigger for increases in the Federal Reserve target interest rate (and adverse stock market reactions). Is this variable in fact predictive of U.S. stock market behavior in subsequent months, quarters and years? Using monthly seasonally adjusted unemployment rate from the U.S. Bureau of Labor Statistics (BLS) and monthly S&P 500 Index levels during January 1948 (limited by unemployment rate data) through June 2021, we find that: Keep Reading

U.S. job gains or losses receive prominent coverage in the monthly financial news cycle, with media and expert commentators generally interpreting employment changes as an indicator of future economic and stock market health. One line of reasoning is that jobs generate personal income, which spurs personal consumption, which boosts corporate earnings and lifts the stock market. Are employment changes in fact predictive of U.S. stock market behavior in subsequent months, quarters and years? Using monthly seasonally adjusted non-farm employment data from the U.S. Bureau of Labor Statistics (BLS) and monthly S&P 500 Index levels during January 1939 (limited by employment data) through June 2021, we find that: Keep Reading

A reader commented and asked: “A wide credit spread (the difference in yields between Treasury notes or Treasury bonds and investment grade or junk corporate bonds) indicates fear of bankruptcies or other bad events. A narrow credit spread indicates high expectations for the economy and corporate world. Does the credit spread anticipate stock market behavior?” To investigate, we define the U.S. credit spread as the difference in yields between Moody’s seasoned Baa corporate bonds and 10-year Treasury notes (T-note), which are average daily yields for these instruments by calendar month (a smoothed measurement). We use the S&P 500 Index (SP500) as a proxy for the U.S. stock market. We extend the investigation to bond market behavior via:

• Vanguard Long-Term Treasury Investors Fund (VUSTX)
• Vanguard Long-Term Investment-Grade Investors Fund (VWESX)
• Vanguard High-Yield Corporate Investors Fund (VWEHX)

Using monthly Baa bond yields, T-note yields and SP500 closes starting April 1953 and monthly dividend-adjusted closes of VUSTX, VWESX and VWEHX starting May 1986, January 1980 and January 1980, respectively, all through June 2021, we find that: Keep Reading

Is outperformance of green (environmentally friendly) stocks relative to brown (not environmentally friendly) stocks due to firm performance or concern about the climate? In other words, do green stocks carry a climate concern premium? In their June 2021 paper entitled “Dissecting Green Returns”, Lubos Pastor, Robert Stambaugh and Lucian Taylor examine relative performance of green and brown stocks in the context of unexpectedly strong increases in environmental concerns (climate concern jumps). Specifically, they:

• Construct a green factor as the return on a portfolio that is each month long (short) green (brown) stocks weighted by greenness based on environment-focused elements of MSCI ESG Ratings.
• Devise and test a 2-factor (market and green) model of stock returns.
• Compute a monthly measure of public climate concern based on an associated media index, with focus on series jumps.

Using stock return and factor data during November 2012 (based on availability of ESG ratings) through December 2020 and climate concern data during November 2012 through June 2018, they find that: Keep Reading

How sensitive are returns of stocks, bonds and gold to levels real interest rates (nominal rates minus inflation)? To investigate, we consider three nominal interest rates and two measures of inflation, as follows:

• 3-month U.S. Treasury Bill Yield (3-month).
• 1-year U.S. Treasury Constant Maturity Rate (1-year).
• 10-year Treasury Constant Maturity Rate (10-year).
• Personal Consumption Expenditures: Chain-type Price Index (PCEPI).
• Personal Consumption Expenditures Excluding Food and Energy: Chain-Type Price Index (Core PCEPI).

These choices offer six alternative real interest rates. We use end-of-month interest rates and inflation measures lagged by one month to account for release delay. We use the S&P 500 Index (SP500) capital gain only, the 10-year yield (with bond prices moving inversely) and spot gold price, all measured end-of-month, to represent returns for stocks, bonds and gold. We then relate monthly changes in real interest rates to asset class monthly returns in two ways: (1) calculate correlations of monthly real interest rates to asset class returns for each of the next 12 months to get a sense of how real rates lead asset returns; and, (2) calculate average asset class monthly returns by ranked tenths (deciles) of prior-month real interest rates to discover any non-linear relationships. Using monthly PCEPI and Core PCEPI since January 1961, interest rates since January 1962, SP500 level since December 1961 and spot gold price since December 1974 (when controls are removed), all through May 2021, we find that:

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Does the Fama-French  5-factor model (market, size, book-to-market, profitability, investment) of stock returns work for stocks worldwide? In their May 2021 paper entitled “Size, Value, Profitability, and Investment Effects in International Stock Returns: Are They Really There?”, Nusret Cakici and Adam Zaremba test the performance of the 5-factor model in global developed markets. They consider big and small stocks separately. They consider four regions (North America, Europe, Japan and Asia-Pacific), as well as the global market. They lag all accounting data by six months and calculate returns in U.S. dollars. Using data in U.S. dollars for 65,000 stocks from 23 countries during December 1987 through March 2019 (with tests starting July 1990), they find that:

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Should investors consider adding Special Purpose Acquisition Company (SPAC) Initial Public Offerings (IPO), which boomed in 2020, to their portfolios? In the March 2021 revision of their paper entitled “SPACs”, Minmo Gahng, Jay Ritter and Donghang Zhang examine investor returns on SPACs during the two phases of their lifecycle:

1. SPAC phase– from SPAC IPO to five trading days before completion of target business merger or, if no merger within 24 months, liquidation. To measure investor returns for this phase, they assume purchases of one SPAC unit (usually a common share and warrants) at IPO prices for 114 SPACs during January 2010 through May 2018. The investor sells each component at the higher of the market price or the redemption price.
2. deSPAC phase – from the first trading day as a merged company. For this phase, there are 114 completed mergers (105 having warrants), including 97 from the above SPAC phase plus 17 additional SPACs.

Using price data for U.S. SPACs (not those traded in Over-The-Counter markets) during January 2010 through October 2020, they find that:

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How much does accounting for equity factor portfolio maintenance frictions affect usefulness of factor models of stock returns. In their March 2021 paper entitled “Model Selection with Transaction Costs”, Andrew Detzel, Robert Novy-Marx and Mihail Velikov examine effects of transaction costs on six leading models of stock returns:

1. FF5 – Fama-French 5-factor model (market, size, book-to-market , investment and accruals-based profitability, reformed annually).
2. FF6 – FF5 plus a momentum factor.
3. HXZ4 – Hou, Xue, and Zhang 4-factor model (market, size, investment and profitability, all reformed monthly).
4. BS6 – Barillas-Shanken 6-factor model (market, size, book-to-market reformed monthly, investment, return on equity and momentum).
5. FF5_C – FF5 with a cash flow-based profitability factor.
6. FF6_C – FF6 with a cash flow-based profitability factor.

They compare model effectiveness based on maximum squared Sharpe ratio (SR²), which measures how closely a model approaches the in-sample efficient frontier for all test assets. They measure transaction costs using stock-level effective bid-ask spread. Using data to calculate all factors employed by the six models and effective spreads during January 1972 through December 2017, they find that: Keep Reading

Several recent papers find that most studies identifying factors that predict stock returns are not replicable or derive from snooping of many factors. Is there a good counter-argument? In their January 2021 paper entitled “Is There a Replication Crisis in Finance?”, Theis Ingerslev Jensen, Bryan Kelly and Lasse Pedersen apply a Bayesian model of factor replication to a set of 153 factors applied to stocks across 93 countries. For each factor in each country, they each month:

1. Sort stocks into thirds (top/middle/bottom) with breakpoints based on non-micro stocks in that country.
2. For each third, compute a “capped value weight” gross return (winsorizing market equity at the NYSE 80th percentile to ensure that tiny stocks have tiny weights no mega-stock dominates).
3. Calculate the gross return for a hedge portfolio that is long (short) the third with the highest (lowest) expected return.
4. Calculate the corresponding 1-factor gross alpha via simple regression versus the country portfolio.

They further propose a taxonomy that systematically assigns each of the 153 factors to one of 13 themes based on high within-theme return correlations and conceptual similarities. Using firm and stock data required to calculate the specified factors starting 1926 for U.S. stocks and 1986 for most developed countries (in U.S. dollars), and 1-month U.S. Treasury bill yields to compute excess returns, all through 2019, they find that: Keep Reading

Is following the lead of certain types of equity investors as effective as using widely accepted factor models of stock returns? In their March 2021 paper entitled “What Do the Portfolios of Individual Investors Reveal About the Cross-Section of Equity Returns?”, Sebastien Betermier, Laurent Calvet, Samuli Knüpfer and Jens Kvaerner construct a factor model of stocks returns based on demographics of the individual investors who own them. They construct investor factors by each year reforming portfolios that are long (short) the 30% of stocks with the highest (lowest) expected returns based on holdings-weighted investor demographics and then measuring returns of these hedge portfolios the following year. They compare these investor factors to conventional factors constructed from firm/stock characteristics. Using anonymized demographics and direct stock holdings of Norwegian investors (an average 365,000 per year), and associated firm/stock characteristics and returns (over 400 stocks listed on the Oslo Stock Exchange), during 1997 through 2018, they find that:

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