# 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.

**February 4, 2016** - Equity Premium

Should equity risk premium (ERP) forecasters assume in their models, because stocks always carry risk, that the premium cannot be negative? In their January 2016 paper entitled “Forecasting the Equity Risk Premium: The Ups and the Downs”, Nick Baltas and Dimitris Karyampas examine recent ERP forecasting research, with focus on simple models constrained to positive values. Their baseline model is a linear regression model that forecasts next-period S&P 500 Index excess return from either the index dividend-price ratio or the 3-month US treasury bill yield. They highlight advantages and disadvantages of models that do and do not constrain ERP to non-negative values for three types of market regimes: (1) up markets (positive actual ERP) versus down markets (negative actual ERP); (2) recessions versus expansions; and, (3) low volatility versus high volatility. Using monthly total returns for the S&P 500 Index and monthly levels of the predictive variables during January 1927 through December 2013 (with initial training period 20 years), *they find that:* Keep Reading

**February 1, 2016** - Bonds, Equity Premium, Strategic Allocation

The home page and “Value Strategy” now show preliminary asset class ETF value strategy positions for February 2016. There may be small shifts in allocations based on final data.

**December 16, 2015** - Bonds, Equity Premium, Momentum Investing, Strategic Allocation

Are the “Simple Asset Class ETF Value Strategy” (SACEVS) and the “Simple Asset Class ETF Momentum Strategy” (SACEMS) mutually diversifying. To check, we relate monthly returns for the SACEVS and the SACEMS exchange-traded fund (ETF) selections and look at the performance of an equally weighted portfolio of the two strategies, rebalanced monthly (50-50). Specifically, we consider: SACEVS Best Value paired with SACEMS Top 1; and, SACEVS Weighted paired with SACEMS Equally Weighted (EW) Top 3. Using monthly gross returns for SACEVS Best Value and SACEMS Top 1 since January 2003 and for SACEVS Weighted and SACEMS EW Top 3 since August 2006, all through November 2015, *we find that:* Keep Reading

**December 15, 2015** - Equity Premium, Momentum Investing, Size Effect, Value Premium

Is it possible to test factor models of stock returns directly on individual stocks rather than on portfolios of stocks sorted per preconceived notions of factor importance. In their November 2015 paper entitled “Tests of Alternative Asset Pricing Models Using Individual Security Returns and a New Multivariate F-Test”, Shafiqur Rahman, Matthew Schneider and Gary Antonacci apply a statistical method that allows testing of equity factor models directly on individual stocks. Results are therefore free from the information loss and data snooping bias associated with sorting stocks based on some factor into portfolios. They test several recently proposed multi-factor models based on five or six of market, size, value (different definitions), momentum, liquidity (based on turnover), profitability and investment factors. They compare alternative models via 100,000 Monte Carlo simulations each in terms of ability to eliminate average alpha and appraisal ratio (absolute alpha divided by residual variance) across individual stocks. Using monthly returns and stock/firm characteristics for the 407 Russell 3000 Index stocks with no missing monthly returns during January 1990 through December 2014 (300 months), *they find that:* Keep Reading

**December 11, 2015** - Equity Premium, Technical Trading

Do stop-losses usefully mitigate downside risk in realistic scenarios? In their November 2015 paper entitled “Stop-Loss Strategies with Serial Correlation, Regime Switching, and Transactions Costs”, Andrew Lo and Alexander Remorov analyze the value of stop-losses when asset returns are autocorrelated (trending), regime switching (bull and bear) and subject to trading costs. They consider daily and 10-day measurement intervals, with respective stop-loss ranges of 0% to -6% and 0% to -14%. If at any daily close the cumulative return on the risky asset over the measurement interval falls below a specified threshold, they immediately switch to the risk-free asset (U.S. Treasury bills). They consider two ways to execute stop-loss signals: (1) assume it is possible to estimate signals just before the close and sell at the same close; or, (2) use a signal from the prior close to trigger a market-on-close sell order the next day (delayed execution). They re-enter the risky asset when its cumulative return over a specified interval exceeds a specified threshold. They employ both simulations and empirical tests. For simulations, they estimate trading cost as 0.2%, the average half bid-ask spread of all sampled stocks during 2013-2014. For empirical tests, they use actual half bid-ask spreads as available and estimates otherwise. Empirical findings are most relevant to short-term traders who employ tight stop-losses. Using daily returns and bid-ask spreads as available for a broad sample of U.S. common stocks during 1964 through 2014, *they find that:* Keep Reading

**November 19, 2015** - Bonds, Equity Premium

What do company valuation experts think about the level of the risk-free rate and the equity risk premium? In their October 2015 paper entitled “Huge Dispersion of the Risk-Free Rate and Market Risk Premium Used by Analysts in 2015”, Pablo Fernandez, Alberto Pizarro and Isabel Acín summarize assumptions about the risk-free rate (R_{F}) and the market/equity risk premium (MRP or ERP) used by expert analysts to value companies in six countries (France, Germany, Italy, Spain, UK and U.S.). Using 156 company valuation reports from 2015, *they find that:* Keep Reading

**November 17, 2015** - Equity Premium

What combination of factors best predicts stock market returns at a monthly frequency? In the October 2015 draft of their paper entitled “Comparing Asset Pricing Models”, Francisco Barillas and Jay Shanken apply a Bayesian procedure to compare all possible pricing models based on subsets of a given set of pricing factors. They consider a total of ten factors: market, two versions of size, two versions of value (book-to-market), momentum, two versions of profitability, and two versions of investment. For each model tested, they include no more than one of any factor with two versions. In addition to comparing models (factor subsets), they also assess the absolute performance of the top-ranked model against an unrestricted set. As usually done, they employ factor returns that are either the excess return relative to the market or the spread between returns of two extreme portfolios formed from factor sorts. Using data for a broad sample of U.S. common stocks during 1972 through 2013, *they find that:* Keep Reading

**October 21, 2015** - Equity Premium

Is the Fama-French five-factor (market, size, book-to-market, profitability, investment) model of stock returns optimal? In the September 2015 draft of their paper entitled “Choosing Factors”, Eugene Fama and Kenneth French investigate potential improvements to the overall predictive power of their five-factor model. Specifically, they examine:

- Using a profitability factor based on cash rather than operating profit, or substituting a quality-minus-junk factor for the profitability factor.
- Calculating the value, investment and profitability factors from small stocks only (where they are stronger) rather than as the average for small stocks and big stocks.

They frame model optimality in terms of: (1) parsimony (simplicity, meaning few explanatory factors); (2) the ability of chosen factors to explain performance of portfolios sorted on other factors; (3) accordance with the dividend discount valuation model. Using factor-related data for a broad sample of U.S. stocks during July 1963 through December 2014 (618 months), *they find that:* Keep Reading

**September 1, 2015** - Equity Premium

Does combining the outputs of many methods of estimating the equity risk premium (ERP) produce a useful result? In their February 2015 paper entitled “The Equity Risk Premium: A Review of Models”, Fernando Duarte and Carlo Rosa estimate ERP via principal component analysis of 20 models, which they assign to five categories: (1) predictors based solely on historical average return; (2) dividend discount analyses; (3) regressions that extract expected market return from the behaviors of individual stocks; (4) regressions that relate stock market performance to economic variables over time; and, (5) surveys of experts. Principal component analysis derives the linear combination of model outputs that explains as much of the variance in outputs as possible. The authors follow common practice in using the S&P 500 Index as a stock market proxy and nominal or real U.S. Treasury yields as risk-free rates. Using monthly model inputs during January 1960 to June 2013, *they find that:* Keep Reading

**August 27, 2015** - Equity Premium

Does the new Fama-French five-factor model of stock returns explain a wider range of anomalies than the workhorse Fama-French three-factor model. In the June 2015 update of their paper entitled “Dissecting Anomalies with a Five-Factor Model”, Eugene Fama and Kenneth French examine the power of their five-factor model of stock returns to explain five anomalies not explicitly related to the five factors model and known to cause problems for the three-factor model (market beta, net share issuance, volatility, accruals, momentum). The five-factor model adds profitability (robust minus weak, or RMW) and investment (conservative minus aggressive, or CMA) factors to the three-factor model (market, size and book-to-market factors). The size, book-to-market, profitability and investment factor portfolios are reformed annually using data that are at least six months old (in contrast, the momentum factor portfolio is reformed monthly). Using data for a broad sample of U.S. firms and associated stocks during July 1963 through December 2014, *they find that:* Keep Reading