# 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.

**April 23, 2015** - Bonds, Calendar Effects, Equity Premium, Strategic Allocation

“Effects of Execution Delay on Simple Asset Class ETF Momentum Strategy” investigates how delaying signal execution affects strategy performance. How does execution delay affect the performance of the complementary Best Value version of the “Simple Asset Class ETF Value Strategy”? This latter strategy each quarter allocates all funds to the one of the following asset class exchange-traded funds (ETF) associated with the most undervalued risk premium (term, credit or equity), or to cash if none are 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)

To investigate, we compare 23 variations of the strategy that all use end-of-quarter (EOQ) to determine the best value asset but shift execution from the contemporaneous EOQ to the next open or to closes over the next 21 trading days (about one month). For example, an EOQ+5 Close variation uses an EOQ cycle to determine winners but delays execution until the close five trading days after EOQ. Using daily dividend-adjusted opens and closes for the risk premium proxies and the yield for Cash from the end of September 2002 through the end of March 2015 (51 quarters), *we find that:*

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**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 31, 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 quarterly returns for the SACEVS Best Value and the SACEMS Top 1 exchange-traded fund (ETF) selections and look at the performance of an equally weighted portfolio of these two strategies (50-50). Using quarterly gross returns for SACEVS Best Value and SACEMS Top 1 during January 2003 through December 2014, *we find that:* Keep Reading

**March 30, 2015** - Bonds, Equity Premium, Strategic Allocation

“Simple Asset Class ETF Value Strategy” finds that investors may be able to exploit relative valuation of the term risk premium, the credit (default) risk premium and the equity risk premium via exchange-traded funds (ETF). However, the backtesting period is limited by available histories for ETFs and for the series used to estimate risk premiums. To construct a longer test, we make the following substitutions for potential holdings (selected for length of available samples):

To enable estimation of risk premiums over a longer history, we also substitute:

We retain quarterly average yields for Moody’s Seasoned Baa Corporate Bonds for calculation of the credit risk premium. As with ETFs, we consider two alternative strategies for exploiting premium undervaluation: Best Value, which picks the most undervalued premium; and, Weighted, which weights all undervalued premiums according to degree of undervaluation. Based on the assets considered, the principal benchmark is a quarterly rebalanced portfolio of 60% stocks and 40% U.S. Treasuries (60-40 VWUSX-VFIIX). Using quarterly risk premium calculation data during January 1934 through December 2014 (limited by availability of Moody’s Baa data), and quarterly dividend-adjusted closing prices for the three asset class mutual funds during June 1980 through December 2014 (139 quarters), *we find that:*

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**March 27, 2015** - Bonds, Equity Premium, Strategic Allocation

Does a simple relative value strategy applied to tradable asset class proxies produce attractive results? To investigate, we test a simple strategy on the following three asset class exchange-traded funds (ETF), plus cash:

3-month Treasury bills (Cash)

iShares 7-10 Year Treasury Bond (IEF)

iShares iBoxx $ Investment Grade Corporate Bond (LQD)

SPDR S&P 500 (SPY)

This set of ETFs relates to three factor risk premiums: (1) the difference in yields between Treasury bills and Treasury note/bonds indicates the term risk premium; (2) the difference in yields between corporate bonds and Treasury notes/bonds indicates the credit (default) risk premium; and, (3) the difference in yields between equities and Treasury notes/bonds indicates the equity risk premium. We consider two alternative strategies for exploiting premium undervaluation: Best Value, which picks the most undervalued premium; and, Weighted, which weights all undervalued premiums according to degree of undervaluation. Based on the assets considered, the principal benchmark is a quarterly rebalanced portfolio of 60% stocks and 40% U.S. Treasury notes (60-40 SPY-IEF). Using quarterly S&P 500 Index levels and earnings, quarterly average yields for 3-month Constant Maturity U.S. Treasury bills (T-bills), quarterly average yields for 10-year Constant Maturity U.S. Treasury notes (T-notes), quarterly average yields for Moody’s Seasoned Baa Corporate Bonds during March 1989 through December 2014 (limited by availability of earnings data), and quarterly dividend-adjusted closing prices for the above three asset class ETFs during September 2002 through December 2014 (45 quarters, limited by availability of IEF and LQD), *we find 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

**February 18, 2015** - Bonds, Equity Premium, Strategic Allocation

What is the best mix of stocks and bonds to hold during retirement worldwide? In his January 2015 paper entitled “The Retirement Glidepath: An International Perspective”, Javier Estrada compares outcomes for different stocks-bonds allocation strategies during retirement from a global perspective. He considers declining equity, rising equity and static glidepaths with an annual withdrawal rate of 4% (of the portfolio value at retirement) and annual rebalancing during a 30-year retirement period. He tests the following glidepaths:

- Four declining equity strategies that begin with 100%-0%, 90%‐10%, 80%‐20% and 70%‐30% stocks-bonds allocations and shift toward bonds linearly via annual rebalancing.
- Four mirror-image rising equity strategies that begin with 0%-100%, 10%-90%, 20%-80% and 30%-70% stocks-bonds allocations and shift toward stocks linearly via annual rebalancing.
- Eleven static allocations ranging from 100%-0% to 0%-100% stocks-bonds allocations maintained via annual rebalancing, with focus on conventional or near-conventional 60%-40%, 50%-50% and 40%-60% allocations.

He focuses on the failure rate of these strategies during 81 overlapping 30-year retirement periods during 1900-2009. He also considers average and median terminal wealth/bequest, tail risk, annual volatility (standard deviation of annual returns) and upside potential. He defines tail risk (downside risk) as average terminal wealth for the 1%, 5% or 10% lowest values from the 81 periods. Using annual total real returns for stocks and government bonds for 19 countries (in local currency adjusted by local inflation) and for the world market (in dollars adjusted by U.S. inflation) during 1900 through 2009 (110 years), *he finds that:* Keep Reading

**February 11, 2015** - Equity Premium, Size Effect, Value Premium

Does adding profitability and asset growth (investment) factors improve the performance of the widely used Fama-French three-factor (market, size, book-to-market) model of stock returns? In the September 2014 version of their paper entitled “A Five-Factor Asset Pricing Model” Eugene Fama and Kenneth French assess whether extensions of their three-factor model to include profitability and investment improves model predictive power. They measure profitability as prior-year revenue minus cost of goods sold, interest expense and selling, general and administrative expenses divided by book equity. They define investment as prior-year growth in total assets divided by total assets. Using returns and stock/firm characteristics for a broad sample of U.S. stocks during July 1963 through December 2013 (606 months), *they find that:* Keep Reading

**December 23, 2014** - Equity Premium

How big is the stock liquidity premium and does it subsume other variables widely used to estimate future returns? In their December 2014 paper entitled “A Comparative Analysis of Liquidity Measures”, Yuping Huang and Vasilios Sogiakas investigate the relationships of excess (relative to the risk-free rate) stock returns to three pairs of monthly liquidity metrics:

- Transaction cost: (1) average daily absolute bid-ask spread; or, (2) relative spread (average daily absolute spread divided by stock price).
- Trading activity: (3) turnover ratio (shares traded divided by shares outstanding); or, (4) average daily dollar volume.
- Price impact: (5) average absolute daily return divided by dollar volume; or, (6) average daily ratio of absolute return divided by daily turnover ratio.

They also examine the interaction of these liquidity metrics with widely used risk factors (market capitalization or size, book-to-market ratio and momentum) and other predictive variables (price, earnings yield and dividend yield). They base some analyses on average gross returns of equally weighted portfolios reformed monthly by ranking stocks into fifths (quintiles) by prior-month liquidity metrics. Analyses exploring interaction of liquidity metrics with other factors/variables employ multivariate regressions. In grooming/processing data, they exclude stocks with extremely low and high prices, liquidity metrics, factors and predictive variables. Using daily bid-ask spreads during 1991 through 2011 and monthly values of other trading metrics and factors/variables as described above during 1962 through 2011 for a broad (but filtered) sample of U.S. stocks (an average of 2,050 stocks each month),* they find that:* Keep Reading