# 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.

**January 24, 2019** - Bonds, Equity Premium, Strategic Allocation

Failure rate, the conventional metric for evaluating retirement portfolios, does not distinguish between: (1) failures early versus late in retirement; or, (2) small and large surpluses (bequests). Is there a better way to evaluate retirement portfolios? In their December 2018 paper entitled “Toward Determining the Optimal Investment Strategy for Retirement”, Javier Estrada and Mark Kritzman propose coverage ratio, plus an asymmetric utility function that penalizes shortfalls more than it rewards surpluses, to evaluate retirement portfolios. They test this approach in 21 countries and the world overall. Coverage ratio is number of years of withdrawals supported by a portfolio during and after retirement, divided by retirement period. The utility function increases at decreasing rate (essentially logarithmic) as coverage ratio rises above one and decreases sharply (linearly with slope 10) as it falls below one. They focus on a 30-year retirement with 4% initial withdrawal rate and annual inflation-adjusted future withdrawals. The portfolio rebalances annually to target stocks and bonds allocations. They consider 11 target stocks-bonds allocations ranging from 100%-0% to 0%-100% in increments of 10%. When analyzing historical returns, the first (last) 30-year period is 1900-1929 (1985-2014), for a total of 86 (overlapping) periods. When using simulations, they draw 25,000 annual real returns for stocks and bonds from two uncorrelated normal distributions. For bonds, all simulation runs assume 2% average real annual return with 3% standard deviation. For stocks, simulation runs vary average real annual return and standard deviation for sensitivity analysis. Using historical annual real returns for stocks and bonds for 21 countries and the world overall during 1900 through 2014 from the Dimson-Marsh-Staunton database, *they find that:* Keep Reading

**January 7, 2019** - Equity Premium, Momentum Investing

Is stock price momentum an imperfect proxy for sensitivity of individual stocks to past dispersion of returns across stocks (zeta risk, or return dispersion)? In their November 2018 paper entitled “Market Risk and the Momentum Mystery”, James Kolari and Wei Liu investigate relationships between momentum and return dispersion as predictors of individual U.S. stock returns. They employ both portfolio comparisons and regression tests. For the former, their momentum portfolio is long (short) the equally weighted top (bottom) tenth, or decile, of stocks ranked on past 12-month minus one skip-week returns, reformed monthly. Their main return dispersion portfolio is long (short) the equally weighted decile of stocks with the most positive (negative) sensitivities to the dispersion of all individual daily stock returns over the past 12 months minus one skip-week, reformed monthly. Using daily and monthly returns for a broad sample of U.S. stocks priced over $5 since January 1964, and contemporaneous 1-month U.S. Treasury bill yields and monthly returns of selected stock return model factors since January 1965, all through December 2017, *they find that:*

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**January 4, 2019** - Equity Premium, Fundamental Valuation

Does Cyclically-Adjusted Price-to-Earnings ratio (CAPE, or P/E10) usefully predict stock portfolio returns? In their October 2017 paper entitled “The Many Colours of CAPE”, Farouk Jivraj and Robert Shiller examine validity and usefulness of CAPE in three ways: (1) comparing predictive accuracies of CAPE at different horizons to those of seven competing valuation metrics (ratios of an income proxy or book value to price); (2) exploring alternative constructions of CAPE based on different firm earnings proxies; and, (3) assessing practical uses of CAPE for asset allocation and relative valuation (supporting rotation among asset classes, countries, sectors or individual stocks). They employ a total return CAPE, assuming reinvestment of all dividends. For forward testing, they lag earnings and related data to ensure real time availability for investment decisions. Using quarterly and annual U.S. stock market data from Shiller since the first quarter (Q1) 1871 dovetailed with end-of-quarter data since Q4 1927, and data as available for other valuation metrics, all through the Q2 2017, *they find that:* Keep Reading

**December 27, 2018** - Bonds, Commodity Futures, Currency Trading, Equity Premium

Should investors rely on aggregate positions of speculators (large non-commercial traders) as indicators of expected futures market returns? In their November 2018 paper entitled “Speculative Pressure”, John Hua Fan, Adrian Fernandez-Perez, Ana-Maria Fuertes and Joëlle Miffre investigate speculative pressure (net positions of speculators) as a predictor of futures contract prices across four asset classes (commodity, currency, equity index and interest rates/fixed income) both separately and for a multi-class portfolio. They measure speculative pressure as end-of-month net positions of speculators relative to their average weekly net positions over the past year. Positive (negative) speculative pressure indicates backwardation (contango), with speculators net long (short) and futures prices expected to rise (fall) as maturity approaches. They measure expected returns via portfolios that systematically buy (sell) futures with net positive (negative) speculative pressure. They compare speculative pressure strategy performance to those for momentum (average daily futures return over the past year), value (futures price relative to its price 4.5 to 5.5 years ago) and carry (roll yield, difference in log prices of nearest and second nearest contracts). Using open interests of large non-commercial traders from CFTC weekly legacy Commitments of Traders (COT) reports for 84 futures contracts series (43 commodities, 11 currencies, 19 equity indexes and 11 interest rates/fixed income) from the end of September 1992 through most of May 2018, along with contemporaneous Friday futures settlement prices, *they find that:* Keep Reading

**December 10, 2018** - Equity Premium, Volatility Effects

Is there a distinct systematic asset risk, as measured by its market beta, associated with each return measurement interval (frequency, such as daily, monthly or annually)? In other words, is return measurement frequency a risk factor? In their October 2018 paper entitled “Measuring Horizon-Specific Systematic Risk via Spectral Betas”, Federico Bandi, Shomesh Chaudhuri, Andrew Lo and Andrea Tamoni introduce spectral beta, an asset’s market beta for a given return measurement frequency, as a way to assess this frequency as a source of systematic investment risk. They specify how to combine spectral betas into an overall beta and explore ways to interpret and exploit spectral betas. Using mathematical derivations and samples of monthly and daily returns for broad samples of U.S. stocks and stock portfolios, *they find that:* Keep Reading

**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