Equity Premium

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

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:

1. High-Minus-low Value (HML) – book equity divided by market capitalization.
2. Small-Minus-Big Size (SMB) – market capitalization.
3. Winners-Minus-Losers Momentum (WML) – cumulative return from 12 months ago to one month ago.
4. Conservative-Minus-Aggressive Investment (CMA) – change in total assets.
5. 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

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

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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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:
  1. 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.
  2. Linear regressions that test ability of the entire distribution of trading signals to explain future gross returns based on linear relationships.
  3. 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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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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How differently does the “Simple Asset Class ETF Value Strategy” (SACEVS) perform when the U.S. stock market rises and falls? This strategy seeks to exploit relative valuation of the term risk premium, the credit (default) risk premium and the equity risk premium via exchange-traded funds (ETF). To investigate, because the sample period available for mutual funds is much longer than that available for ETFs, we use instead data from “SACEVS Applied to Mutual Funds”. Specifically, each month we reform a Best Value portfolio (picking the asset associated with the most undervalued premium, or cash if no premiums are undervalued) and a Weighted portfolio (weighting assets associated with all undervalued premiums according to degree of undervaluation, or cash if no premiums are undervalued) using the following four assets:

• Monthly average 3-Month Treasury Bill (T-bill) Secondary Market Rate as an approximation of the return on Cash.
• Vanguard GNMA Investor Shares (VFIIX).
• Vanguard Long-Term Investment Grade Investor Shares (VWESX).
• Vanguard US Growth Investor Shares (VWUSX).

The benchmark is a monthly rebalanced portfolio of 60% stocks and 40% U.S. Treasuries (60-40 VWUSX-VFIIX). We say that stocks rise (fall) during a month when the return for VWUSX is positive (negative) during the SACEVS holding month. Using monthly risk premium estimates, SR and LR, and Best Value and Weighted returns during June 1980 through June 2017 (444 months), we find that:

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A subscriber asked how the “Simple Asset Class ETF Value Strategy” (SACEVS) performs when interest rates rise. This strategy seeks to exploit relative valuation of the term risk premium, the credit (default) risk premium and the equity risk premium via exchange-traded funds (ETF). To investigate, because the sample period available for mutual funds is much longer than that available for ETFs, we use instead data from “SACEVS Applied to Mutual Funds”. Specifically, each month we reform a Best Value portfolio (picking the asset associated with the most undervalued premium, or cash if no premiums are undervalued) and a Weighted portfolio (weighting assets associated with all undervalued premiums according to degree of undervaluation, or cash if no premiums are undervalued) using the following four assets:

• Monthly average 3-Month Treasury Bill (T-bill) Secondary Market Rate as an approximation of the return on Cash.
• Vanguard GNMA Investor Shares (VFIIX).
• Vanguard Long-Term Investment Grade Investor Shares (VWESX).
• Vanguard US Growth Investor Shares (VWUSX).

The benchmark is a monthly rebalanced portfolio of 60% stocks and 40% U.S. Treasuries (60-40 VWUSX-VFIIX). We use the T-bill yield as the short-term interest rate (SR) and the 10-year Constant Maturity U.S. Treasury note (T-note) yield as the long-term interest rate (LR). We say that each rate rises or falls when the associated average monthly yield increases or decreases during the SACEVS holding month. Using monthly risk premium estimates, SR and LR, and Best Value and Weighted returns during June 1980 through June 2017 (444 months), we find that:

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Is the Capital Asset Pricing Model (CAPM), which relates the return of an asset to its non-diversifiable risk, called beta, worth learning? In his June 2017 paper (provocatively) entitled “Is It Ethical to Teach That Beta and CAPM Explain Something?”, Pablo Fernandez tackles this question. Based on the body of relevant research, he concludes that:

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Can investors predict the return of a stock from its relationship with the dispersion of returns across all stocks? In their May 2017 paper entitled “Building Efficient Portfolios Sensitive to Market Volatility”, Wei Liu, James Kolari and Jianhua Huang examine a 2-factor model which predicts the return on a stock based on its sensitivity to (1) the value-weighted stock market return (beta risk) and (2) the standard deviation of value-weighted returns for all stocks (zeta risk). They first each month estimate zeta for each stock via regressions of daily data over the past year. They then rank stocks by zeta into quantile portfolios and calculate next-month equal-weighted returns across these portfolios and various long-short combinations of these portfolios (hedge portfolios) to measure dependence of future returns on zeta. Finally, they generate performance data for aggregate zeta risk portfolios by adding value-weighted market index returns to returns for each of the long-short zeta-sorted portfolios. Using daily and monthly returns for a broad sample of U.S. stocks in the top 90% of market capitalizations for that year, monthly equity market returns and monthly U.S. Treasury bill yields as the risk-free rate during January 1965 through December 2015, they find that: Keep Reading