# 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.

**November 26, 2018** - Bonds, Calendar Effects, Equity Premium, Momentum Investing, Size Effect, Strategic Allocation, Value Premium

Is the U.S. equity turn-of-the-month (TOTM) effect exploitable as a diversifier of other assets? In their October 2018 paper entitled “A Seasonality Factor in Asset Allocation”, Frank McGroarty, Emmanouil Platanakis, Athanasios Sakkas and Andrew Urquhart test U.S. asset allocation strategies that include a TOTM portfolio as an asset. The TOTM portfolio buys each stock at the open on the last trading day of each month and sells at the close on the third trading day of the following month, earning zero return the rest of the time. They consider four asset universes with and without the TOTM portfolio:

- A conventional stocks-bonds mix.
- The equity market portfolio.
- The equity market portfolio, a small size portfolio and a value portfolio.
- The equity market portfolio, a small size portfolio, a value portfolio and a momentum winners portfolio.

They consider six sophisticated asset allocation methods:

- Mean-variance optimization.
- Optimization with higher moments and Constant Relative Risk Aversion.
- Bayes-Stein shrinkage of estimated returns.
- Bayesian diffuse-prior.
- Black-Litterman.
- A combination of allocation methods.

They consider three risk aversion settings and either a 60-month or a 120-month lookback interval for input parameter measurement. To assess exploitability, they set trading frictions at 0.50% of traded value for equities and 0.17% for bonds. Using monthly data as specified above during July 1961 through December 2015, *they find that:*

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**November 7, 2018** - Equity Premium

What is the best way to suppress trading frictions for active, long-term stock portfolios? In their September 2018 paper entitled “Comparing Cost-Mitigation Techniques”, Robert Novy-Marx and Mihail Velikov compare three approaches to suppression of trading frictions for long-term stock factor premium capture strategies:

- Limiting selection to stocks that are cheap to trade.
- Rebalancing infrequently.
- Imposing a penalty for opening a new position compared to maintaining an established position (banding).

They also evaluate indirect suppression of trading frictions from exploiting a secondary premium (stock sort) that sometimes delays or even cancels trades targeting the primary premium. They consider three stock universes: large (top 90% of total market capitalization); small (the next 9%); and, micro (the next 0.9%). They estimate trading frictions as effective bid-ask spreads. Their test portfolios are long-short extreme fifths (quintiles) of stocks sorted on seven stock/firm variables as specified in widely cited academic literature: accounting (failure probability and net stock issuance); defensive (beta and idiosyncratic volatility); and, momentum (conventional, unexpected earnings and earnings announcement). Using specified data during January 1975 through December 2016, *they find that:*

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**November 6, 2018** - Big Ideas, Equity Premium

What do basic U.S. stock market return statistics say about consistency of equity risks and predictability of returns? We define basic statistics as first through fourth moments of the return distribution: mean (average), standard deviation, skewness and kurtosis. For tractability, we calculate these four statistics month-by-month based on daily returns. Using daily closes of the Dow Jones Industrial Average (DJIA) since January 1930 and the S&P 500 Index since January 1950, both through September 2018, *we find that: Keep Reading *

**November 1, 2018** - Bonds, Equity Premium, Strategic Allocation

How does use of actuarial estimates of retiree longevity and empirical mean reversion of stock market returns affect estimated retirement portfolio success rates? In the October 2018 revision of his paper entitled “Joint Effect of Random Years of Longevity and Mean Reversion in Equity Returns on the Safe Withdrawal Rate in Retirement”, Donald Rosenthal presents a model of safe inflation-adjusted retirement portfolio withdrawal rates that addresses: (1) uncertainty about the number of years of retirement (rather than the commonly assumed 30 years); and, (2) mean reversion in annual U.S. stock market returns (rather than a random walk). He estimates retirement longevity as a random input based on the Social Security Administration’s 2015 Actuarial Life Table. He estimates stock market real returns and measures their mean reversion using S&P 500 Index inflation-adjusted total annual returns during 1926 through 2017. He models real bond returns using 10-year U.S. Treasury note (T-note) total annual returns during 1928 through 2017. He applies Monte Carlo simulations (3,000 trials for each scenario) to assess retirement portfolio performance by:

- Assuming an initial retirement portfolio either 100% invested in stocks or 60%/40% in stocks/T-notes (rebalanced at each year-end).
- Debiting the portfolio each year-end by a fixed, inflation-adjusted percentage of the initial amount.
- Calculating percentage of simulation trials for which the portfolio is not exhausted before death (success) and average portfolio terminal balance for successful trials.

He considers two benchmarks: (1) no stock market mean reversion (random walk) and fixed 30-year retirement; and, (2) no stock market mean reversion and actuarial estimate of retirement duration. He also runs sensitivity tests to see how changes in assumptions affect success rate. Using the specified data, *he finds that:*

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**October 26, 2018** - Equity Premium

Two major theories of asset pricing include: one based on asset risk (the market compensates inherent riskiness); and, another based on asset illiquidity (the market compensates illiquidity). In his July 2018 paper entitled “Illiquidity and Stock Returns: A Revisit”, Yakov Amihud presents cross-sectional and time series analyses of illiquidity and U.S. stock returns that extend the 1964-1997 sample period of his seminal illiquidity research. Specifically, he:

- Each year, sorts stocks by volatility (standard deviation of daily returns for the 12 months ending November) into three groups.
- Each year, sorts stocks within each volatility group into five illiquidity sub-groups, with illiquidity specified as the 12-month average of absolute daily return divided by same-day dollar volume traded over the same 12 months.
- Each month during the subsequent January through December, calculates the monthly return of each of the resulting 15 portfolios, weighting stocks based on their market capitalization weights at the end of the prior month.
- Each month, calculates an illiquid-minus-liquid factor (IML) as average return of the most illiquid portfolios across volatility groups minus average return of the least illiquid portfolios across volatility groups.

This process controls for interaction between volatility and illiquidity. He segments findings into replicating Period I (1964-1997) and new Period II (1998-2017). He screens source stocks by requiring for each year: price between $5 and $1000; over 200 days of valid returns and volumes; and, not in the top 1% of illiquidities (outliers). Using data for NYSE/AMEX common stocks that meet these criteria during 1964 through 2017, *he finds that:* Keep Reading

**October 24, 2018** - Equity Premium

What are the implications of rapid global adoption of factor (smart beta) investing in single-factor, multi-factor and dynamic multi-factor strategies, most notably via equity exchange-traded funds (ETF). In their September 2018 paper entitled “Smart-Beta Herding and Its Economic Risks: Riding the Dragon?”, Eduard Krkoska and Klaus Schenk-Hoppé summarize the current state of smart beta investing, providing a concise overview of academic research, investment community reports and financial media coverage. They address evidence and implications of investor herding into smart beta vehicles. Based on the body of research and experience, *they conclude that:* Keep Reading

**October 15, 2018** - Equity Premium, Momentum Investing, Sentiment Indicators, Size Effect, Value Premium, Volatility Effects

Quantitative investing involves disciplined rule-based approaches to help investors structure optimal portfolios that balance return and risk. How has such investing evolved? In their June 2018 paper entitled “The Current State of Quantitative Equity Investing”, Ying Becker and Marc Reinganum summarize key developments in the history of quantitative equity investing. Based on the body of research, *they conclude that:* Keep Reading

**October 11, 2018** - Bonds, Economic Indicators, Equity Premium

A reader commented and asked: “A wide credit spread (the difference in yields between Treasury notes or Treasury bonds and investment grade or junk corporate bonds) indicates fear of bankruptcies or other bad events. A narrow credit spread indicates high expectations for the economy and corporate world. Does the credit spread anticipate stock market behavior?” To investigate, we define the U.S. credit spread as the difference in yields between Moody’s seasoned Baa corporate bonds and 10-year Treasury notes (T-note), which are average daily yields for these instruments by calendar month (a smoothed measurement). We use the S&P 500 Index (SP500) as a proxy for the U.S. stock market. We extend the investigation to bond market behavior via:

- Vanguard Long-Term Treasury Investors Fund (VUSTX)
- Vanguard Long-Term Investment-Grade Investors Fund (VWESX)
- Vanguard High-Yield Corporate Investors Fund (VWEHX)

Using monthly Baa bond yields, T-note yields and SP500 closes starting April 1953 and monthly dividend-adjusted closes of VUSTX, VWESX and VWEHX starting May 1986, January 1980 and January 1980, respectively, all through August 2018, *we find that:* Keep Reading

**October 1, 2018** - Equity Premium

A subscriber asked whether the annual equity risk premium estimates of Aswath Damodaran predict stock market returns one year ahead. The cited source offers two 58-year series of annual estimates of the U.S. equity risk premium implied by an S&P 500:

- Dividend Discount Model (DDM).
- Free Cash Flow to Equity (FCFE).

We calculate S&P 500 Index total annual returns from this source as capital gains plus dividends and then relate this total return series to each of these two implied equity risk premium series. Using the specified data during 1960 through 2017, *we find that:* Keep Reading

**September 20, 2018** - Equity Premium, Fundamental Valuation

A subscriber proposed four alternative ways of timing the U.S. stock market based on simple moving averages (SMA) of the market price-earnings ratio (P/E), as follows:

- 5-Year Binary – hold stocks (cash) when P/E is below (above) its 5-year SMA.
- 10-Year Binary – hold stocks (cash) when P/E is below (above) its 10-year SMA.
- 15-Year Binary – hold stocks (cash) when P/E is below (above) its 15-year SMA.
- 5-Year Scaled – hold 100% stocks (cash) when P/E is five or more units below (above) its 5-year SMA. Between these levels, scale allocations linearly.

To obtain a sample long enough for testing these rules, we use the monthly U.S. data of Robert Shiller. While offering a very long history, this source has the disadvantage of blurring monthly data as averages of daily values. How well do these alternative timing strategies work for this dataset? Using monthly data for the S&P Composite Index, annual dividends, annual P/E and 10-year government bond yield since January 1871 and monthly 3-month U.S. Treasury bill (T-bill) yield as return on cash since January 1934, all through August 2018, *we find that:* Keep Reading