# 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 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

**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

**December 9, 2014** - Economic Indicators, Equity Premium, Fundamental Valuation

How do the major components of U.S. stock market performance behave over time? In his October 2014 paper entitled “Long-Term Sources of Investment Returns and a Simple Way to Enhance Equity Returns”, Baijnath Ramraika decomposes long-term returns from the U.S. stock market (as proxied by Robert Shiller’s S&P Composite Index) into four components:

- Dividend yield
- Inflation
- Real average change in 10-year earnings (E10)
- Change in the Cyclically Adjusted Price-Earnings ratio (CAPE, or P/E10)

He further segments this decomposition by decade. Using his decomposition by decade for 1881 through 2010 (13 decades), *we find that:* Keep Reading

**December 2, 2014** - Big Ideas, Equity Premium

Is equity factor investing a straightforward path to premium capture and diversification? In their October 2014 paper entitled “Facts and Fantasies About Factor Investing”, Zelia Cazalet and Thierry Roncalli summarize the body of research on factor investing and provide examples to address the following questions:

- What is a risk factor?
- Do all risk factors offer attractive premiums?
- How stable and robust are these premiums?
- How can investors translate academic risk factors into portfolios?
- How should investors allocate to different factors?

They define risk factor investing as the attempt to enhance returns in the long run by capturing systematic risk premiums. They focus on the gap between retrospective (academic) analysis and prospective portfolio implementation. They summarize research on the following factors: market beta, size, book-to-market ratio, momentum, volatility, liquidity, carry, quality, yield curve slope, default risk, coskewness and macroeconomic variables. Based on the body of factor investing research and examples, *they conclude that:* Keep Reading

**October 30, 2014** - Big Ideas, Equity Premium

Are the widely used Fama-French three-factor model (market, size, book-to-market ratio) and the Carhart four-factor model (adding momentum) the best factor models of stock returns? In their September 2014 paper entitled “Digesting Anomalies: An Investment Approach”, Kewei Hou, Chen Xue and Lu Zhang construct the q-factor model comprised of market, size, investment and profitability factors and test its ability to predict stock returns. They also test its ability to account for 80 stock return anomalies (16 momentum-related, 12 value-related, 14 investment-related, 14 profitability-related, 11 related to intangibles and 13 related to trading frictions). Specifically, the q-factor model describes the excess return (relative to the risk-free rate) of a stock via its dependence on:

- The market excess return.
- The difference in returns between small and big stocks.
- The difference in returns between stocks with low and high investment-to-assets ratios (change in total assets divided by lagged total assets).
- The difference in returns between high-return on equity (ROE) stocks and low-ROE stocks.

They estimate the q-factors from a triple 2-by-3-by-3 sort on size, investment-to-assets and ROE. They compare the predictive power of this model with the those of the Fama-French and Carhart models. Using returns, market capitalizations and firm accounting data for a broad sample of U.S. stocks during January 1972 through December 2012, *they find that:* Keep Reading