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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.

Excluding Bad Stock Factor Exposures

The many factor-based indexes and exchange-traded funds (ETFs) that track them now available enable investors to construct multi-factor portfolios piecemeal. Is such piecemeal construction suboptimal? In their July 2018 paper entitled “The Characteristics of Factor Investing”, David Blitz and Milan Vidojevic apply a multi-factor expected return linear regression model to explore behaviors of long-only factor portfolios. They consider six factors: value-weighted market, size, book-to-market ratio, momentum, operating profitability and investment(change in assets). Their model generates expected returns for each stock each month, and further aggregates individual stock expectations into factor-portfolio expectations holding all other factors constant. They use the model to assess performance differences between a group of long-only single-factor portfolios and an integrated multi-factor portfolio of stocks based on combined rankings across factors. The focus on gross monthly excess (relative to the 10-year U.S. Treasury note yield) returns as a performance metric. Using data for a broad sample of U.S. common stocks among the top 80% of NYSE market capitalizations and priced at least $1 during June 1963 through December 2017, they find that: Keep Reading

T-bills Beat Most Stocks?

Does conventional reward-for-risk wisdom about the long-run performance of the U.S. stock market translate to the typical stock? In the May 2018 update of his paper entitled “Do Stocks Outperform Treasury Bills?”, Hendrik Bessembinder compares the performance of the typical U.S. stock to that of the 1-month U.S. Treasury bill (T-bill) over monthly, annual, decade and life-of-stock horizons. He also performs simulations to gauge the effectiveness of holding just one stock and of diversifying across portfolios of five, 25, 50 and 100 stocks. Using monthly total (dividend-reinvested) returns for 25,967 U.S. common stocks while listed during July 1926 through December 2016, he finds that: Keep Reading

Better Five-factor Model of Stock Returns?

Which factor models of stock returns are currently best? In their June 2018 paper entitled “q5,  Kewei Hou, Haitao Mo, Chen Xue and Lu Zhang, introduce the q5 model of stock returns, which adds a fifth factor (expected growth) to the previously developed q-factor model (market, size, asset growth, return on equity). They measure expected growth as 1-year, 2-year and 3-year ahead changes in investment-to-assets (this year total assets minus last year total assets, divided by last year total assets) as forecasted monthly via predictive regressions. They define an expected growth factor as average value-weighted returns for top 30% 1-year expected growth minus bottom 30% 1-year expected growth, calculated separately and further averaged for big and small stocks. They examine expected growth as a standalone factor and then conduct an empirical horse race of recently proposed 4-factor, 5-factor (including q5) and 6-factor models of stock returns based on their abilities to explain average return differences for value-weighted extreme tenth (decile) portfolios for 158 significant anomalies. Using monthly return and accounting data for a broad sample of non-financial U.S. common stocks during July 1963–December 2016, they find that:

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Doubling Down on Size

“Is There Really an Size Effect?” summarizes research challenging the materiality of the equity size effect. Is there a counter? In their June 2018 paper entitled “It Has Been Very Easy to Beat the S&P500 in 2000-2018. Several Examples”, Pablo Fernandez and Pablo Acin double down on the size effect via a combination of market capitalization thresholds and equal weighting. Specifically, they compare values of a $100 initial investment at the beginning of January 2000, held through April 2018, in:

  • The market capitalization-weighted (MW) S&P 500.
  • The equally weighted (EW) 20, 40, 60 and 80 of the smallest stocks in the S&P 1500, reformed either every 12 months or every 24 months.

All portfolios are dividend-reinvested. Their objective is to provide investors with facts to aid portfolio analysis and selection of investment criteria. Using returns for the specified stocks over the selected sample period, they find that:

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Benefits of Volatility Targeting Across Asset Classes

Does volatility targeting improve Sharpe ratios and provide crash protection across asset classes? In their May 2018 paper entitled “Working Your Tail Off: The Impact of Volatility Targeting”, Campbell Harvey, Edward Hoyle, Russell Korgaonkar, Sandy Rattray, Matthew Sargaison, and Otto Van Hemert examine return and risk effects of long-only volatility targeting, which scales asset and/or portfolio exposure higher (lower) when its recent volatility is low (high). They consider over 60 assets spanning stocks, bonds, credit, commodities and currencies and two multi-asset portfolios (60-40 stocks-bonds and 25-25-25-25 stocks-bonds-credit-commodities). They focus on excess returns (relative to U.S. Treasury bill yield). They forecast volatility using realized daily volatility with exponentially decaying weights of varying half-lives to assess sensitivity to the recency of inputs. For most analyses, they employ daily return data to forecast volatility. For S&P 500 Index and 10-year U.S. Treasury note (T-note) futures, they also test high-frequency (5-minute) returns transformed to daily returns. They scale asset exposure inversely to forecasted volatility known 24 hours in advance, applying a retroactively determined constant that generates 10% annualized actual volatility to facilitate comparison across assets and sample periods. Using daily returns for U.S. stocks and industries since 1927, for U.S. bonds (estimated from yields) since 1962, for a credit index and an array of futures/forwards since 1988, and high-frequency returns for S&P 500 Index and 10-year U.S. Treasury note futures since 1988, all through 2017, they find that:

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Skewness Underlies Stock Market Anomalies?

Does retail investor preference for stocks with skewed return distributions explain stock return anomalies? In their April 2018 paper entitled “Skewness Preference and Market Anomalies”, Alok Kumar, Mehrshad Motahari and Richard Taffler investigate whether investor preference for positively-skewed payoffs is a common driver of mispricing as indicated by a wide range of market anomalies. They each month measure the skewness of each stock via four metrics: (1) jackpot probability (probability of a return greater than 100% the next 12 months); (2) lottery index (with high relating to low price, high volatility and high skewness; (3) maximum daily return the past month; and, (4) expected idiosyncratic skewness. They also each month measure aggregate mispricing of each stock as its average decile rank when sorting all stocks into tenths on each of 11 widely used anomaly variables. They assess the role of retail investors based on 1991-1996 portfolio holdings data from a large U.S. discount broker. Using a broad sample of U.S. common stocks (excluding financial stocks, firms with negative book value and stocks priced less than $1) during January 1963 through December 2015, they find that: Keep Reading

Sifting the Factor Zoo

The body of U.S. stock market research offers hundreds of factors (the factor zoo) to explain and predict return differences across stocks. Is there a reduced set of factors that most accurately and consistently captures fundamental equity risks? In their March 2018 paper entitled “Searching the Factor Zoo”, Soosung Hwang and Alexandre Rubesam employ Bayesian inference to test all possible multi-factor linear models of stock returns and identify the best models. This approach enables testing of thousands of individual assets in combination with hundreds of candidate factors. They consider a universe of 83 candidate factors: the market return in excess of the risk-free rate, plus 82 factors measured as the difference in value-weighted average returns between extreme tenths (deciles) of stocks sorted on stock/firm characteristics. Their stock universe consists of all U.S. listed stocks excluding financial stocks, stocks with market capitalizations less than the NYSE 20th percentile (microcaps) and stocks priced less than $1. They test microcaps separately. They further test 20 sets of test portfolios (300 total portfolios). The overall sample period is January 1980 through December 2016. To assess factor model performance consistency, they break this sample period into three or five equal subperiods. Using the specified data as available over the 36-year sample period, they find that: Keep Reading

Revisiting VIX as Stock Return Predictor

Does implied stock market volatility (IV) predict stock market returns? In their March 2018 paper entitled “Implied Volatility Measures As Indicators of Future Market Returns”, Roberto Bandelli and Wenye Wang analyze the relationship between S&P 500 Index IV and future S&P 500 Index returns. They consider volatilities implied either by S&P 500 Index options (VIX) or by 30-day at-the-money S&P 500 Index straddles. Specifically, they each day:

  1. Rank current S&P 500 Index IV according to ranked tenth (decile) of its daily distribution over the past two years. If current IV is higher than any value of IV over the past two years, its rank is 11.
  2. Calculate S&P 500 Index returns over the next one, five and 20 trading days.
  3. Relate these returns to IV rank.

They calculate statistical significance based on the difference between the average IV-ranked log returns and log returns over all intervals of the same length. Using daily data for the selected variables during December 1991 through November 2017, they find that: Keep Reading

Worldwide Long-run Returns on Housing, Equities, Bonds and Bills

How do housing, equities and government bonds/bills perform worldwide over the long run? In their February 2018 paper entitled “The Rate of Return on Everything, 1870-2015”, Òscar Jordà, Katharina Knoll, Dmitry Kuvshinov, Moritz Schularick and Alan Taylor address the following questions:

  1. What is the aggregate real return on investments?
  2. Is it higher than economic growth rate and, if so, by how much?
  3. Do asset class returns tend to decline over time?
  4. Which asset class performs best?

To do so, they compile long-term annual gross returns from market data for housing, equities, government bonds and short-term bills across 16 developed countries (Australia, Belgium, Denmark, Finland, France, Germany, Italy, Japan, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, the UK and the U.S.). They decompose housing and equity performances into capital gains, investment incomes (yield) and total returns (sum of the two). For equities, they employ capitalization-weighted indexes to the extent possible. For housing, they model returns based on country-specific benchmark rent-price ratios. Using the specified annual returns for 1870 through 2015, they find that:

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Expert Estimates of 2018 Country Equity Risk Premiums and Risk-free Rates

What are current estimates of equity risk premiums (ERP) and risk-free rates around the world? In their April 2018 paper entitled “Market Risk Premium and Risk-free Rate Used for 59 Countries in 2018: A Survey”, Pablo Fernandez, Vitaly Pershin and Isabel Acin summarize results of a March 2018 email survey of international finance/economic professors, analysts and company managers “about the Risk Free Rate and the Market Risk Premium (MRP) used to calculate the required return to equity in different countries.” Results are in local currencies. Based on 5,173 specific and credible responses spanning 59 countries with more than five such responses, they find that: Keep Reading

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