# 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, 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

**August 26, 2015** - Equity Premium

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:

- Kitchen sink – employing regression coefficients for all 20 forecasting variables (but with four of the variables compressed into a composite).
- 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.
- 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

**July 6, 2015** - Bonds, Equity Premium, Strategic Allocation

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

- 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.
- To employ fresher data, we use end-of-measurement interval (end-of-month) bond/bill yields rather than average yields during the measurement interval.
- 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.

**June 29, 2015** - Bonds, Equity Premium, Strategic Allocation

“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 levels, quarterly 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

**June 12, 2015** - Bonds, Equity Premium, Strategic Allocation

“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 are quarterly per the arrival rate of new corporate earnings information. The principal benchmark is a quarterly rebalanced portfolio of 60% SPY and 40% IEF. A subscriber asked whether monthly SACEVS updates outperform quarterly updates. Using monthly S&P 500 Index levels, quarterly S&P 500 earnings and monthly 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 during March 1989 through March 2015 (limited by availability of earnings data), and monthly 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

**May 27, 2015** - Bonds, Commodity Futures, Equity Premium, Gold

Does the interaction of paradigmatic indicators of optimism (lumber demand) and pessimism (gold demand) tell investors when to take risk and when to avoid risk? In their May 2015 paper entitled “Lumber: Worth Its Weight in Gold: Offense and Defense in Active Portfolio Management”, Charles Bilello and Michael Gayed examine the recent relative performance of lumber (a proxy for economic activity via construction) and gold (a safe haven) as an indicator of future stock market and bond market performance. Specifically, if lumber futures outperform (underperform) spot gold over the prior 13 weeks, they go on offense (defense) the next week. They test this strategy on combinations of seven indexes comprising a spectrum of risk (listed lowest to highest): BofA Merrill Lynch 5-7 Year Treasury Index (Treasuries); CBOE S&P 500 Buy-Write Index (BuyWrite); S&P 500 Low Volatility Index (Low Volatility); S&P 500 Index (SP500); Russell 2000 Index (R2000); Morgan Stanley Cyclicals Index (Cyclicals); and, S&P 500 High Beta Index (High Beta). Using weekly nearest futures contract prices for random length lumber, weekly spot gold prices and weekly total returns for the seven test indexes during November 1986 (November 1990 for Low Volatility and High Beta) through January 2015, *they find that:* Keep Reading

**April 8, 2015** - Bonds, Equity Premium, Strategic Allocation

Do variable retirement spending strategies offer greater utility than fixed-amount or fixed-percentage strategies? In his March 2015 paper entitled “Making Sense Out of Variable Spending Strategies for Retirees”, Wade Pfau compares via simulation ten retirement spending strategies based on a common set of assumptions. He classifies these strategies into two categories: (1) those based on decision rules (such as fixed real spending and fixed percentage spending); and, (2) actuarial models based on remaining portfolio balance and estimated remaining longevity. His bases comparisons on 10,000 Monte Carlo runs for each strategy. He assumes a retirement portfolio of 50% U.S. stocks and 50% U.S. government bonds with initial value $100,000, rebalanced annually after end-of-year 0.5% fees and beginning-of-year withdrawals. He calibrates initial spending where feasible by imposing a probability of X% (X=10) that real spending falls below $Y (Y=1,500) by year Z of retirement (Z=30). He treats terminal wealth as unintentional (in fact, undesirable), with the essential trade-off between spending more now and having to cut spending later. He ignores tax implications. Using historical return data from Robert Shiller and current levels of inflation and interest rates (see the chart below), *he finds that:* Keep Reading

**March 19, 2015** - Bonds, Calendar Effects, Commodity Futures, Currency Trading, Economic Indicators, Equity Premium

Does fourth quarter global economic data set the stage for asset class returns the next year? In their February 2015 paper entitled “The End-of-the-year Effect: Global Economic Growth and Expected Returns Around the World”, Stig Møller and Jesper Rangvid examine relationships between level of global economic growth and future asset class returns, focusing on growth at the end of the year. Their principle measure of global economic growth is the equally weighted average of quarterly OECD industrial production growth in 12 developed countries. They perform in-sample tests 30 countries and out-of-sample tests for these same 12 countries (for which more data are available). Out-of-sample tests: (1) generate initial parameters from 1970 through 1989 data for testing during 1990 through 2013 period; and, (2) insert a three-month delay between economic growth data and subsequent return calculations to account for publication lag. Using global industrial production growth as specified, annual total returns for 30 country, two regional and world stock indexes, currency spot and one-year forward exchange rates relative to the U.S. dollar, spot prices on 19 commodities, total annual returns for a global government bond index and a U.S. corporate bond index, and country inflation rates as available during 1970 through 2013, *they find that:* Keep Reading

**February 20, 2015** - Bonds, Equity Premium, Strategic Allocation

Does optimal asset allocation, as measured by Sharpe ratio, depend on investment horizon? In their January 2015 paper entitled “Optimal Asset Allocation Across Investment Horizons”, Ronald Best, Charles Hodges and James Yoder explore the optimal (highest Sharpe ratio) mix of long-term U.S. corporate bonds and large-capitalization U.S. common stocks across investment horizons from one to 25 years. They test portfolios ranging from 100%-0% to 0%-100% stocks-bonds in 5% increments with annual rebalancing. They estimate annual returns for stocks and bonds based on 87 years of historical data. They simulate the portfolio return distribution for a given n-year holding period via 2,500 iterations for each of two methods:

- Randomly select with replacement n years from the 87 years in the historical sample and use the annual returns for U.S. Treasury bills (T-bills, the risk-free rate), stocks and bonds for those n years in the order selected to calculate portfolio gross compound n-year excess returns. This method assumes year-to-year independence (zero autocorrelations) of annual returns for stocks and bonds, meaning no momentum or reversion.
- Randomly select a year from the first 87 – (n-1) years in the historical sample and use the annual returns for T-bills, stocks and bonds for that and the next n-1 consecutive years to calculate portfolio gross compound n-year excess returns. This method preserves historical autocorrelations in return series.

Using annual returns for T-bills, U.S. large-capitalization common stocks and U.S. long-term corporate bonds during 1926 through 2012, *they find that:* Keep Reading