# 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.

**May 4, 2016** - Economic Indicators, Equity Premium

Can investors exploit economic data for monthly stock market timing? In their September 2015 paper entitled “Getting the Most Out of Macroeconomic Information for Predicting Excess Stock Returns”, Cem Cakmaklı and Dick van Dijk test whether a model employing 118 economic variables improves prediction of monthly U.S. stock market (S&P 500 Index) excess returns based on conventional valuation ratios (dividend yield and price-earnings ratio) and interest rate indicators (risk-free rate, change in risk-free rate and credit spread). Excess return means above the risk-free rate. They each month apply principal component analysis to distill from the 118 economic variables (or from subsets of these variables with the most individual power to predict S&P 500 Index returns) a small group of independent predictive factors. They then regress next-month S&P 500 Index excess returns linearly on these factors and conventional valuation ratios/interest rate indicators over a rolling 10-year historical window to generate excess return predictions. They measure effectiveness of the economic inputs in two ways:

- Directional accuracy of forecasts (proportion of forecasts that accurately predict the sign of next-month excess returns).
- Explicit economic value of forecasts via mean-variance optimal stocks-cash investment strategies that each month range from 200% long to 100% short the stock index depending on monthly excess return predictions as specified and monthly volatility predictions based on daily index returns over the past month, with transaction costs of 0.0%, 0.1% or 0.3%.

Using monthly values of the 118 economic variables (lagged one month to assure availability), conventional ratios/indicators and monthly and daily S&P 500 Index levels during January 1967 through December 2014, *they find that:* Keep Reading

**May 2, 2016** - Bonds, Equity Premium, Strategic Allocation

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

**April 7, 2016** - Equity Premium

What are the different ways of estimating the equity risk premium, and which one is best? In his March 2016 paper entitled “Equity Risk Premiums (ERP): Determinants, Estimation and Implications – The 2016 Edition”, Aswath Damodaran updates a comprehensive overview of equity risk premium estimation and application. He examines why different approaches to estimating the premium disagree and how to choose among them. Using data from multiple countries (but focusing on the U.S.) over long periods through the end of 2015, *he concludes that:* Keep Reading

**March 4, 2016** - Equity Premium, Fundamental Valuation, Momentum Investing, Value Premium, Volatility Effects

What kinds of smart beta work best? In their January 2016 paper entitled “A Taxonomy of Beta Based on Investment Outcomes”, Sanne De Boer, Michael LaBella and Sarah Reifsteck compare and contrast smart beta (simple, transparent, rules-based) strategies via backtesting of 12 long-only smart beta stock portfolios. They assign these portfolios to a framework that translates diversification, fundamental weighting and factor investing into core equity exposure and style investing (see the figure below). They constrain backtests to long-only positions, relatively investable/liquid stocks and quarterly rebalancing, treating developed and emerging markets separately. Backtest outputs address gross performance, benchmark tracking accuracy and portfolio turnover. Using beta-related data for developed market stocks during 1979 through 2014 and emerging market stocks during 2001 through 2014, *they find that:* Keep Reading

**February 22, 2016** - Equity Premium

Do alternative beta (factor-weighted) stock indexes present an exploitable advantage over traditional market capitalization weighting? In their February 2016 paper entitled “Alternative Beta Strategies”, Frank Benham, Roberto Obregon, Edmund Walsh and Timur Yontar analyze performance and practicality aspects of alternative beta stock indexes that target high value, high momentum, low volatility and high quality/profitability premiums. They also model multi-beta portfolios to assess the net benefits of beta diversification. Using monthly returns for market capitalization-weighted benchmark indexes and various alternative beta indexes as available through March 2015, *they find that:* Keep Reading

**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

**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