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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.

Liquidity an Essential Equity Factor?

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

Stop-losses on Stock Positions in Depth

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

Analyst Disagreement on Risk-free Rate and Equity Risk 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 (RF) 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

Factor Models with Frequent Value and Profitability Updates

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

Tweaking the Five-factor Model of Stock Returns

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

Collective Wisdom of 20 Equity Risk Premium Models

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

Explaining Stock Return Anomalies with a Five-factor Model

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

Combining and Exploiting Stock Market Forecasting Variables

Does the set of variables that have the strongest correlations with subsequent U.S. stock market returns over the prior decade usefully predict market returns out-of-sample? In the July 2015 draft of their paper entitled “A Practitioner’s Defense of Return Predictability”, Blair Hull and Xiao Qiao apply this correlation screening approach to a set of 20 published stock market forecasting variables encompassing technical indicators, macroeconomic variables, return-based predictors, price ratios and commodity prices. Their horizon for historical daily correlation measurements and out-of-sample forecasts is 130 trading days (about six months). Every 20 days just before the market close, they employ regressions using the most recent ten years of data to: (1) determine the form of each forecasting variable (raw value, exponentially-weighted moving average or log value minus exponentially-weight moving average) that maximizes its daily correlation with 130-day returns; and, (2) estimate variable coefficients to predict the return for the next 130 days. For the next 20 days, they then use the estimated coefficients to generate expected returns and take a (market on close) position in SPDR S&P 500 (SPY) eight times the expected return in excess of the risk-free rate (capped at 150% long and 50% short). They consider three expected return models:

  1. Kitchen sink – employing regression coefficients for all 20 forecasting variables (but with four of the variables compressed into a composite).
  2. Correlation Screening – employing regression coefficients only for forecasting variables having absolute correlations with subsequent 130-day market returns at least 0.10 over the past ten years.
  3. Real-time Correlation Screening – same as Correlation Screening, but excluding any forecasting variables not yet discovered (published).

They assume: trading frictions of two cents per share of SPY bought or sold; daily return on cash of the three-month U.S. Treasury bill yield minus 0.3%; and, interest on borrowed shares of the Federal Funds Rate plus 0.3%. To limit trading frictions, they adjust positions only when changes in expected market return reach a threshold of 10%. They ignore tax implications of trading. Using daily total returns for SPY, the 3-month Treasury bill yield and vintage (as-released) values of the 20 forecast variables during 6/8/1990 through 5/4/2015, they find that: Keep Reading

SACEVS Modifications

We have made three changes to the “Simple Asset Class ETF Value Strategy” (SACEVS) based on results of  robustness tests and subscriber comments:

  1. To employ fresher data, we decrease the SACEVS S&P 500 Index level and bond/bill yield measurement interval from quarterly to monthly. S&P 500 Index operating earnings updates are still quarterly.
  2. To employ fresher data, we use end-of-measurement interval (end-of-month) bond/bill yields rather than average yields during the measurement interval.
  3. To account for a lag in availability of bill/bond yield data, we delay signal execution by one trading day.

These changes are logical, but introduce some additional noise. They result in somewhat higher risk-adjusted performance for SACEVS, at the expense of some additional trading. Effects on the Weighted version of the strategy are greater than those on the Best Value version.

We are updating “Value Strategy” and some related tests accordingly.

Update SACEVS with End-of-quarter Instead of Quarterly Average Yields?

“Simple Asset Class ETF Value Strategy” (SACEVS) tests a simple relative value strategy that each quarter allocates funds to one or more of the following three asset class exchange-traded funds (ETF), plus cash, based on degree of undervaluation of measures of the term risk, credit risk and equity risk premiums:

3-month Treasury bills (Cash)
iShares 7-10 Year Treasury Bond (IEF)
iShares iBoxx $ Investment Grade Corporate Bond (LQD)
SPDR S&P 500 (SPY)

One version of SACEVS (Best Value) picks the most undervalued premium. Another (Weighted) weights all undervalued premiums according to degree of undervaluation. Premium calculations and SACEVS portfolio allocations derive from quarterly average yields for 3-month Constant Maturity U.S. Treasury bills (T-bills), 10-year Constant Maturity U.S. Treasury notes (T-notes) and Moody’s Seasoned Baa Corporate Bonds (Baa). A subscriber asked whether fresh end-of-quarter yields might work better than quarterly average yields. Using monthly S&P 500 Index levelsquarterly S&P 500 earnings and daily T-note, T-bill and Baa yields during March 1989 through March 2015 (limited by availability of earnings data), and quarterly dividend-adjusted closing prices for the above three asset class ETFs during September 2002 through March 2015 (154 months, limited by availability of IEF and LQD), we find that: Keep Reading

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