# 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.

**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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**October 12, 2017** - Equity Premium, Value Premium

How should factor-based (style) investors proceed after picking a factor to exploit? In their September 2017 paper entitled “Craftsmanship Alpha: An Application to Style Investing”, Ronen Israel, Sarah Jiang and Adrienne Ross survey style portfolio implementation options. They start with a brief discussion of style portfolios types and then focus on portfolio design and implementation. They note trade-offs associated with many options. Based on past research and examples, *they conclude that:* Keep Reading

**October 5, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

Do broad (capitalization-weighted) stock market indexes exhibit factor tilts that may indicate concentrations in corresponding risks? In their August 2017 paper entitled “What’s in Your Benchmark? A Factor Analysis of Major Market Indexes”, Ananth Madhavan, Aleksander Sobczyk and Andrew Ang examine past and present long-only factor exposures of several popular market capitalization indexes. Their analysis involves (1) estimating the factor characteristics of each stock in a broad index; (2) aggregating the characteristics across all stocks in the index; and (3) matching aggregated characteristics to a mimicking portfolio of five indexes representing value, size, quality, momentum and low volatility styles, adjusted for estimated expense ratios. For broad U.S. stock indexes, the five long-only style indexes are:

- Value – MSCI USA Enhanced Value Index.
- Size – MSCI USA Risk Weighted Index.
- Quality – MSCI USA Sector Neutral Quality Index.
- Momentum – MSCI USA Momentum Index.
- Low Volatility – MSCI USA Minimum Volatility Index.

For broad international indexes, they use corresponding long-only MSCI World style indexes. Using quarterly stock and index data from the end of March 2002 through the end of March 2017, *they find that:* Keep Reading

**October 3, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium

Does global diversification improve smart beta (equity factor) investing strategies? In their September 2017 paper entitled “Diversification Strikes Again: Evidence from Global Equity Factors”, Jay Binstock, Engin Kose and Michele Mazzoleni examine effects of global diversification on equity factor hedge portfolios. They consider five factors:

- High-Minus-low Value (HML) – book equity divided by market capitalization.
- Small-Minus-Big Size (SMB) – market capitalization.
- Winners-Minus-Losers Momentum (WML) – cumulative return from 12 months ago to one month ago.
- Conservative-Minus-Aggressive Investment (CMA) – change in total assets.
- Robust-Minus-Weak Operating Profitability (RMW) – total sales minus cost of goods sold, selling, general, and administrative expenses and interest, divided by total assets.

They reform each factor portfolio annually at the end of June by: (1) resetting market capitalizations, segregating firms into large (top 90%) and small (bottom 10%); (2) separately for large and small firms, constructing high (top 30% of factor values) minus low (bottom 30%) long-short sub-portfolios; and, (3) averaging returns for the two sub-portfolios to generate factor portfolio returns. They lag firm accounting data by at least six months between fiscal year end and portfolio formation date. They define eight global regions: U.S., Japan, Germany, UK, France, Canada, Other Europe and Asia Pacific excluding Japan. When measuring diversification effects, they consider relatedness of country markets and variation over time. Using the specified firm accounting data and monthly stock returns during October 1990 through February 2016, *they find that:* Keep Reading

**September 7, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

How many, and which, factors should investors include when constructing multi-factor smart beta portfolios? In their August 2017 paper entitled “How Many Factors? Does Adding Momentum and Volatility Improve Performance”, Mohammed Elgammal, Fatma Ahmed, David McMillan and Ali Al-Amari examine whether adding momentum and low-volatility factors enhances the Fama-French 5-factor (market, size, book-to-market, profitability, investment) model of stock returns. They consider statistical significance, economic sense and investment import. Specifically, they:

- Determine whether factor regression coefficient signs and values distinguish between several pairs of high-risk and low-risk style portfolios (assuming stock style portfolio performance differences derive from differences in firm economic risk).
- Relate time-varying factor betas across style portfolios to variation in economic and market risks as proxied by changes in U.S. industrial production and S&P 500 Index implied volatility (VIX), respectively.
- Test an out-of-sample trading rule based on extrapolation of factor betas from 5-year historical rolling windows to predict next-month return for five sets (book-to-market, profitability, investment, momentum, quality) of four style portfolios (by double-sorting with size) and picking the portfolio within a set with the highest predicted returns.

Using monthly factor return data during January 1990 through October 2016, *they find that:* Keep Reading

**September 6, 2017** - Big Ideas, Equity Premium

Are more data, higher levels of signal statistical significance and more sophisticated prediction models better for financial forecasting? In their August 2017 paper entitled “Practical Significance of Statistical Significance”, Ben Jacobsen, Alexander Molchanov and Cherry Zhang perform sensitivity testing of forecasting practices along three dimensions: (1) length of lookback interval (1 to 300 years); (2) required level of statistical significance for signals (1%, 5%, 10%…); and, (3) different signal detection methods that rely on difference from an historical average. They focus on predicting whether returns for specific calendar months will be higher or lower than the market, either excluding or including January. Using monthly UK stock market returns since 1693 and U.S. stock market returns since 1792, both through 2013, *they find that:*

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**August 31, 2017** - Big Ideas, Equity Premium

How serious is the snooping bias (p-hacking) derived from brute force mining of stock trading strategy variations? In their August 2017 paper entitled “p-Hacking: Evidence from Two Million Trading Strategies”, Tarun Chordia, Amit Goyal and Alessio Saretto test a large number of hypothetical trading strategies to estimate an upper bound on the seriousness of p-hacking and to estimate the likelihood that a researcher can discover a truly abnormal trading strategy. Specifically, they:

- Collect historical data for 156 firm accounting and stock price/return variables as available for U.S. common stocks in the top 80% of NYSE market capitalizations with price over $3.
- Exhaustively construct about 2.1 million trading signals from these variables based on their levels, changes and certain combination ratios.
- Calculate three measures of trading signal effectiveness:
- Gross 6-factor alphas (controlling for market, size, book-to-market, profitability, investment and momentum) of value-weighted, annually reformed hedge portfolios that are long the value-weighted tenth, or decile, of stocks with the highest signal values and short the decile with the lowest.
- Linear regressions that test ability of the entire distribution of trading signals to explain future gross returns based on linear relationships.
- Gross Sharpe ratios of the hedge portfolios used for alpha calculations.

- Apply three multiple hypothesis testing methods that account for cross-correlations in signals and returns (family-wise error rate, false discovery rate and false discovery proportion.

They deem a signal effective if it survives both statistical hurdles (alpha t-statistic 3.79 and regression t-statistic 3.12) and has a monthly Sharpe ratio higher than that of the market (0.12). Using monthly values of the 156 specified input variables during 1972 through 2015, *they find that:*

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**August 10, 2017** - Equity Options, Equity Premium

Do aggregate positions in put and call options on individual stocks, as indicators of sentiment of informed traders, predict future market returns? In their July 2017 paper entitled “Stock Return Predictability: Consider Your Open Options”, Farhang Farazmand and Andre de Souza examine the power of average value-weighted put option open interest divided by average value-weighted call option open interest in individual U.S. stocks (PC-OI) to predict U.S. stock market returns. Specifically, they:

- Compute for each stock each day total put option open interest and total call option open interest.
- Average daily values for each stock by month and weight by market capitalization.
- Calculate PC-OI by dividing the sum of monthly capitalization-weighted average put option open interest by the sum of monthly capitalization-weighted call option open interest.
- Each month, relate via regression monthly PC-OI to stock market return the next three months to determine the sign of the future return coefficient.
- Each month, create a net signal from the sum of the signs of these coefficients from the last three monthly regressions. A positive (negative) sum indicates a long (short) position in the stock market and an offsetting short (long) position in the risk-free asset.

They further test whether PC-OI predictive power concentrates in stocks with unique informativeness as represented by high idiosyncratic volatility (individual stock return volatility unexplained via regression versus market returns). For comparison, they also test their model with S&P 500 index options. Using daily open interest for options on AMEX, NYSE and NASDAQ common stocks and on the S&P 500 Index with moneyness 0.8-1.2 and maturities 30-90 days, associated stock characteristics, and contemporaneous U.S. stock market returns during January 1996 through August 2014, *they find that:*

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