# 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.

**December 13, 2017** - Big Ideas, Equity Premium

As described in “Quantifying Snooping Bias in Published Anomalies”, anomalies published in leading journals offer substantial opportunities for exploitation on a gross basis. What profits are left after accounting for portfolio maintenance costs? In their November 2017 paper entitled “Accounting for the Anomaly Zoo: A Trading Cost Perspective”, Andrew Chen and Mihail Velikov examine the combined effects of post-publication return deterioration and portfolio reformation frictions on 135 cross-sectional stock return anomalies published in leading journals. Their proxy for trading frictions is modeled stock-level effective bid-ask spread based on daily returns, representing a lower bound on costs for investors using market orders. Their baseline tests employ hedge portfolios that are long (short) the equally weighted fifth, or quintile, of stocks with the highest (lowest) expected returns for each anomaly. They also consider capitalization weighting, sorts into tenths (deciles) rather than quintiles and portfolio constructions that apply cost-suppression techniques. Using data as specified in published articles for replication of 135 anomaly hedge portfolios, *they find that:*

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**December 12, 2017** - Big Ideas, Equity Premium

Is data snooping bias a material issue for cross-sectional stock return anomalies published in leading journals? In the September 2017 update of their paper entitled “Publication Bias and the Cross-Section of Stock Returns”, Andrew Chen and Tom Zimmermann: (1) develop an estimator for anomaly data snooping bias based on noisiness of associated returns; (2) apply it to replications of 172 anomalies published in 15 highly selective journals; and, (3) compare results to post-publication anomaly returns to distinguish between in-sample bias and out-of-sample market response to publication. If predictability is due to bias, post-publication returns should be (immediately) poor because pre-publication performance is a statistical figment. If predictability is due to true mispricing, post-publication returns should degrade as investors exploit new anomalies. Their baseline tests employ hedge portfolios that are long (short) the equally weighted fifth, or quintile, of stocks with the highest (lowest) expected returns for each anomaly. Results are gross, ignoring the impact of periodic portfolio reformation frictions. Using data as specified in published articles for replication of 172 anomaly hedge portfolios, *they find that:*

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**November 28, 2017** - Bonds, Equity Premium, Fundamental Valuation, Sentiment Indicators

What firm/asset/market conditions signal mispricing? In the November 2017 version of their paper entitled “Bonds, Stocks, and Sources of Mispricing”, Doron Avramov, Tarun Chordia, Gergana Jostova and Alexander Philipov investigate drivers of U.S. corporate stock and bond mispricing based on interactions among asset prices, financial distress of associated firms and investor sentiment. They measure financial distress via Standard & Poor’s long term issuer credit rating downgrades. They measure investor sentiment primarily with the multi-input Baker-Wurgler Sentiment Index, but they also consider the University of Michigan Consumer Sentiment index and the Consumer Confidence Index. They each month measure asset mispricing by:

- Ranking firms into tenths (deciles) based on each of 12 anomalies: price momentum, earnings momentum, idiosyncratic volatility, analyst forecast dispersion, asset growth, investments, net operating assets, accruals, gross profitability, return on assets and two measures of net share issuance.
- Computing for each firm the equally weighted average of its anomaly rankings, such that a high (low) average ranking indicates the firms’s assets are relatively overpriced (underpriced).

Using monthly firm, stock and bond data for a sample of U.S. firms with sufficient data and investor sentiment during January 1986 through December 2016, *they find that:* Keep Reading

**November 14, 2017** - Bonds, Commodity Futures, Currency Trading, Equity Premium, Value Premium

Do value strategy returns vary exploitably over time and across asset classes? In their October 2017 paper entitled “Value Timing: Risk and Return Across Asset Classes”, Fahiz Baba Yara, Martijn Boons and Andrea Tamoni examine the power of value spreads to predict returns for individual U.S. equities, global stock indexes, global government bonds, commodities and currencies. They measure value spreads as follows:

- For individual stocks, they each month sort stocks into tenths (deciles) on book-to-market ratio and form a portfolio that is long (short) the value-weighted decile with the highest (lowest) ratios.
- For global developed market equity indexes, they each month form a portfolio that is long (short) the equally weighted indexes with book-to-price ratio above (below) the median.
- For each other asset class, they each month form a portfolio that is long (short) the equally weighted assets with 5-year past returns below (above) the median.

To quantify benefits of timing value spreads, they test monthly time series (in only when undervalued) and rotation (weighted by valuation) strategies across asset classes. To measure sources of value spread variation, they decompose value spreads into asset class-specific and common components. Using monthly data for liquid U.S. stocks during January 1972 through December 2014, spot prices for 28 commodities during January 1972 through December 2014, spot and forward exchange rates for 10 currencies during February 1976 through December 2014, modeled and 1-month futures prices for ten 10-year government bonds during January 1991 through May 2009, and levels and book-to-price ratios for 13 developed equity market indexes during January 1994 through December 2014, *they find that:*

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**November 9, 2017** - Equity Premium

Is there an effective Betting Against Alpha (BAA) strategy analogous to the widely used Betting Against Beta (BAB) strategy? In his October 2017 paper entitled “Betting Against Alpha”, Alex Horenstein investigates relationships between stock 1-factor (market), 4-factor (market, size, book-to-market, momentum) alpha and 5-factor (profitability and investment instead of momentum) alphas and future stock returns. He specifies BAA as a portfolio that is long (short) the capitalization-weighted stocks with realized alphas lower (higher) than the median alpha, rebalanced annually. He further specifies Betting Against Alpha and Beta (BAAB) that: (1) first divides stocks into a group with market betas below the median beta and a group with betas above the median; and, (2) then forms a capitalization-weighted portfolio that is long low-beta stocks with alphas below the median alpha within the low-beta group, and short high-beta stocks with alphas above the median alpha within the high-beta group. Additionally, he scales the long and short sides of both portfolios by the inverse of weighted betas, such that average portfolio market betas are near one. In other words, he applies leverage to side of the portfolio with high (low) aggregate beta of less (more) than one. For robustness, he also tests 1-month, 6-month, 24-month and 48-month portfolio reformation intervals. Using monthly data for a broad sample of U.S. stocks during January 1968 (with the first five years used for initial alpha and beta values) through December 2015 and contemporaneous factor model alphas, *he finds that:* Keep Reading

**November 7, 2017** - Bonds, Equity Premium

Do widely used charts of equity and bond market performance inculcate harmfully false beliefs among investors? In his September 2017 paper entitled “Stock Market Charts You Never Saw”, Edward McQuarrie dissects some of these charts and outlines cautions to investors in interpreting them. Using very long-term data for U.S. stock and bond markets spanning hundreds of years, *he concludes that:* Keep Reading

**November 6, 2017** - Equity Premium, Sentiment Indicators

How effective is investor sentiment in predicting stock market returns? In his October 2017 paper entitled “Measuring Investor Sentiment”, Guofu Zhou reviews various measures of equity-oriented investor sentiment based on U.S. market, survey and media data. He highlights the Baker-Wurgler Index (the most widely used), which is based on the first principal component of six sentiment inputs: (1) detrended NYSE trading volume; (2) closed-end fund discount relative to net asset value; (3) number of initial public offerings (IPO); (4) average first-day return on IPOs; (5) ratio of equity issues to total market equity/debt; and, (6) dividend premium (difference between average market-to-book ratios of dividend payers and non-dividend payers). Based on the body of research and using monthly inputs for the Baker-Wurgler Index during July 1965 through December 2016, three sets of investor sentiment survey data since inceptions (between Dec 1969 and July 1987) through December 2016 and two sets of textual analysis data spanning Jan 2003 through December 2014 and Jul 2004 through Dec 2011, *he finds that:* Keep Reading

**October 26, 2017** - Equity Premium, Volatility Effects

Does relative demand for call and put options on individual stocks, as measured by average difference in implied volatilities of at-the-money calls and puts (aggregate implied volatility spread), predict stock market returns? In their September 2017 paper entitled “Aggregate Implied Volatility Spread and Stock Market Returns”, Bing Han and Gang Li test aggregate implied volatility spread as a U.S. stock market return predictor. They focus on monthly measurements, but test the daily series in robustness test. They calculate monthly implied volatility spread for each stock with at least 12 daily at-the-money call and put option prices during the month as an average over the last five trading days. They then eliminate outliers by excluding the top and bottom 0.1% of all stock implied volatility spreads before averaging across stocks to calculate aggregate implied volatility spread. They compare the predictive power of aggregate implied volatility spread to those of 22 other predictors from prior research. Using daily at-the-money call and put implied volatilities for U.S. stocks, data for other U.S. stock market predictors and U.S. stock market returns during January 1996 through December 2015, *they find that:*

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**October 24, 2017** - Equity Premium, Momentum Investing, Value Premium, Volatility Effects

Is it better to build equity multifactor portfolios by holding distinct single-factor sub-portfolios, or by picking only stocks that satisfy multiple factor criteria? In their September 2017 paper entitled “Smart Beta Multi-Factor Construction Methodology: Mixing vs. Integrating”, Tzee-man Chow, Feifei Li and Yoseop Shim compare long-only multifactor portfolios constructed in two ways:

- Integrated – each quarter, pick the 20% of stocks with the highest average standardized factor scores and weight by market capitalization.
- Mixed – each quarter, hold an equal-weighted combination of single-factor portfolios, each comprised of the capitalization-weighted 20% of stocks with the highest expected returns for that factor.

They consider five factors: value (book-to-market ratio), momentum (return from 12 months ago to one month ago), operating profitability, investment (asset growth) and low-beta. They reform factor portfolios annually for all except momentum and low-beta, which they reform quarterly. Using firm data required for factor calculations and associated stock returns for a broad sample of U.S. stocks during June 1968 through December 2016, *they find that:* Keep Reading

**October 17, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

How efficiently do mutual funds capture factor premiums? In their April 2017 paper entitled “The Incredible Shrinking Factor Return”, Robert Arnott, Vitali Kalesnik and Lillian Wu investigate whether factor tilts employed by mutual fund managers deliver the alpha found in empirical research. They focus on four factors most widely used by mutual fund managers: market, size, value and momentum. They note that ideal long-short portfolios used to compute factor returns ignore costs associated with real-world implementation: trading costs and commissions, missed trades, illiquidity, management fees, borrowing costs for the short side and inability to short some stocks. Portfolio returns also ignore bias associated with data snooping in factor discovery and market adaptation to published research. They focus on U.S. long-only equity mutual funds, but also consider similar international funds. They apply a two-stage regression first to identify fund factor exposures and then to measure performance shortfalls per unit of factor exposure. Using data for 5,323 U.S. and 2,364 international live and dead long-only equity mutual funds during January 1990 through December 2016, *they find that:*

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