# 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.

**August 22, 2018** - Equity Premium

Do stock dividends exhibit exploitable risk premiums? In their July 2018 paper entitled “A Model-Free Term Structure of U.S. Dividend Premiums”, Maxim Ulrich, Stephan Florig and Christian Wuchte construct a term structure of the dividend risk premium and test strategies to time this premium at specific horizons. They specify dividend risk premium as the spread between:

- Expected dividend growth rate based on analyst 1-year and 2-year S&P 500 dividend forecasts, extended by analyst 5-year earnings growth estimates assuming constant future payout ratio.
- Expected dividend growth rate derived from equity index put and call option prices across different maturities.

They model an S&P 500 dividend capture portfolio for a given horizon as: long an S&P 500 Index put option of maturity matching the horizon; short an index call option of same maturity and strike price; long the index; and, short the money market in an amount matched to the option strike price. They test two strategies for capturing this premium at a 12-month horizon: (1) each month (last trading day) reform and hold the dividend capture portfolio; or, (2) each month reform and hold the dividend capture portfolio only when the dividend risk premium is positive (analyst-estimated dividends are higher than options-implied dividends). They model the risk-free rate/money market rate across horizons using the U.S. Dollar Overnight Index Swap rate for one day to 10 years. For the S&P 500 Index, they assume annual expense ratio 0.07% and 0.01% average bid-ask spread. For options, they estimate trading frictions with actual bid-ask spreads. Using S&P 500 Index/options and analyst forecast data as specified during January 2004 through October 2017, *they find that:*

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**August 20, 2018** - Equity Premium, Momentum Investing, Value Premium

From a purely statistical perspective, how many factors are optimal for explaining both time series and cross-sectional variations in stock anomaly/stock returns, and how do these statistical factors relate to stock/firm characteristics? In their July 2018 paper entitled “Factors That Fit the Time Series and Cross-Section of Stock Returns”, Martin Lettau and Markus Pelger search for the optimal set of equity factors via a generalized Principal Component Analysis (PCA) that includes a penalty on return prediction errors returns. They apply this approach to three datasets:

- Monthly returns during July 1963 through December 2017 for two sets of 25 portfolios formed by double sorting into fifths (quintiles) first on size and then on either accruals or short-term reversal.
- Monthly returns during July 1963 through December 2017 for 370 portfolios formed by sorting into tenths (deciles) for each of 37 stock/firm characteristics.
- Monthly excess returns for 270 individual stocks that are at some time components of the S&P 500 Index during January 1972 through December 2014.

They compare performance of their generalized PCA to that of conventional PCA. Using the specified datasets, *they find that:* Keep Reading

**August 6, 2018** - Equity Premium

Is there an exploitable way to predict when short-term stock market return will be negative? In his June 2018 paper entitled “Predictable Downturns”, Carter Davis tests a random forest regression-based forecasting model to predict next-day U.S. stock market downturns. He uses the value-weighted return of a portfolio of the 10 U.S. stocks with the largest market capitalizations at the end of the prior year minus the U.S. Treasury bill (T-bill) yield as a proxy for excess market return. He employs a two-step test process:

- Use a rolling 10-year historical window of 143 input variables (economic, equity factor, market volatility, stock trading, calendar) to find when the probability of negative portfolio daily excess return is at least 55%.
- Calculate whether the average portfolio gross excess return of all such days is in fact significantly less than zero.

He corrects for data snooping bias associated with the modeling approach. He further investigates which input variables are most important and tests a market timing strategy that holds the 10-stock portfolio (T-bills) when predicted portfolio return is negative (non-negative) as specified above. Using data for the input variables and returns for test portfolio stocks during July 1926 through July 2017, *he finds that:* Keep Reading

**July 20, 2018** - Equity Premium, Momentum Investing, Size Effect, Value Premium

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

**July 3, 2018** - Equity Premium

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

**June 26, 2018** - Equity Premium, Fundamental Valuation

Which factor models of stock returns are currently best? In their June 2018 paper entitled “q^{5}“, Kewei Hou, Haitao Mo, Chen Xue and Lu Zhang, introduce the q^{5} 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 q^{5}) 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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**June 20, 2018** - Equity Premium, Size Effect

“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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**June 4, 2018** - Bonds, Commodity Futures, Currency Trading, Equity Premium, Volatility Effects

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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**June 1, 2018** - Animal Spirits, Equity Premium

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

**May 29, 2018** - Equity Premium

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