# 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.

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

A subscriber proposed adding an equity style momentum underlay to the Best Value version of the “Simple Asset Class ETF Value Strategy” (SACEVS). SACEVS each month allocates all capital to the one of the following asset class exchange-traded funds (ETF) corresponding to the most undervalued of the term, credit and equity risk premiums at prior month end, or to cash if no premium is undervalued:

3-month Treasury bills (Cash)

iShares 7-10 Year Treasury Bond (IEF)

iShares iBoxx $ Investment Grade Corporate Bond (LQD)

SPDR S&P 500 (SPY)

The proposed momentum underlay chooses SPY, iShares S&P 500 Value (IVE) or iShares S&P 500 Growth (IVW) based on highest five-month past return whenever the equity risk premium is most undervalued. Based on availability of inputs for month-end risk premium estimates, return calculations are based on closing prices for the first trading day of the next month. Using SACEVS premium estimate inputs since March 1989, first trading day of the month dividend-adjusted closes for SPY, IVE and IVW since IVE-IVW inception in May 2000 and first trading day of the month dividend-adjusted closes for IEF and LQD since their inception in July 2002, all through July 2016, *we find that:*

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**May 13, 2016** - Equity Premium, Momentum Investing, Size Effect, Value Premium

How should investors think about stock factor investing? In his April 2016 paper entitled “The Siren Song of Factor Timing”, Clifford Asness summarizes his current beliefs on exploiting stock factor premiums. He defines factors as ways to select individual stocks based on such firm/stock variables as market capitalization, value (in many flavors), momentum, carry (yield) and quality. He equates factor, smart beta and style investing. He describes factor timing as attempting to predict and exploit variations in factor premiums. Based on past research on U.S. stocks mostly for the past 50 years, *he concludes that:* Keep Reading

**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

**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 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