# 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.

**March 11, 2019** - Big Ideas, Equity Premium, Momentum Investing, Size Effect, Strategic Allocation, Value Premium, Volatility Effects

How should investors feel about factor/multi-factor investing? In their February 2019 paper entitled “Alice’s Adventures in Factorland: Three Blunders That Plague Factor Investing”, Robert Arnott, Campbell Harvey, Vitali Kalesnik and Juhani Linnainmaa explore three critical failures of U.S. equity factor investing:

- Returns are far short of expectations due to overfitting and/or trade crowding.
- Drawdowns far exceed expectations.
- Diversification of factors occasionally disappears when correlations soar.

They focus on 15 factors most closely followed by investors: the market factor; a set of six factors from widely used academic multi-factor models (size, value, operating profitability, investment, momentum and low beta); and, a set of eight other popular factors (idiosyncratic volatility, short-term reversal, illiquidity, accruals, cash flow-to-price, earnings-to-price, long-term reversal and net share issuance). For some analyses they employ a broader set of 46 factors. They consider both long-term (July 1963-June 2018) and short-term (July 2003-June 2018) factor performances. Using returns for the specified factors during July 1963 through June 2018, *they conclude that:*

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**March 5, 2019** - Equity Premium, Gold, Technical Trading

A reader requested a test of the following hypothesis from the article “Gold’s Bluff – Is a 30 Percent Drop Next?” [no longer available]: “Ironically, gold is more than just a hedge against market turmoil. Gold is actually one of the most accurate indicators of the stock market’s long-term direction. The Dow Jones measured in gold is a forward looking indicator.” To test this assertion, we examine relationships between the spot price of gold and the level of the Dow Jones Industrial Average (DJIA). Using monthly data for the spot price of gold in dollars per ounce and DJIA over the period January 1971 through January 2019 (577 months), *we find that:* Keep Reading

**February 21, 2019** - Calendar Effects, Equity Premium, Momentum Investing, Value Premium, Volatility Effects

Do very old data confirm reliability of widely accepted asset return factor premiums? In their January 2019 paper entitled “Global Factor Premiums”, Guido Baltussen, Laurens Swinkels and Pim van Vliet present replication (1981-2011) and out-of-sample (1800-1908 and 2012-2016) tests of six global factor premiums across four asset classes. The asset classes are equity indexes, government bonds, commodities and currencies. The factors are: time series (intrinsic or absolute) momentum, designated as trend; cross-sectional (relative) momentum, designated as momentum; value; carry (long high yields and short low yields); seasonality (rolling “hot” months); and, betting against beta (BAB). They explicitly account for p-hacking (data snooping bias) and further explore economic explanations of global factor premiums. Using monthly global data as available during 1800 through 2016 to construct the six factors and four asset class return series, *they find that:*

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**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 30, 2018** - 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 look at the following three equal-weighted (50-50) combinations of the two strategies, rebalanced monthly:

- SACEVS Best Value paired with SACEMS Top 1 (aggressive value and aggressive momentum).
- SACEVS Best Value paired with SACEMS Equally Weighted (EW) Top 3 (aggressive value and diversified momentum).
- SACEVS Weighted paired with SACEMS EW Top 3 (diversified value and diversified momentum).

We also test sensitivity of results to deviating from equal SACEVS-SACEMS weights. Using monthly gross returns for SACEVS and SACEMS portfolios since January 2003 for the first strategy and since July 2006 for the latter two, all through October 2018, *we 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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