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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.

Asset Class Momentum Faster During Bear Markets?

A subscriber asked whether the optimal momentum ranking (lookback) interval for the “Simple Asset Class ETF Momentum Strategy” (SACEMS) shrinks during bear markets for U.S. stocks. This strategy each month picks winners from the following set of exchange-traded funds (ETF) based on total returns over a specified lookback interval:

PowerShares DB Commodity Index Tracking (DBC)
iShares MSCI Emerging Markets Index (EEM)
iShares MSCI EAFE Index (EFA)
SPDR Gold Shares (GLD)
iShares Russell 2000 Index (IWM)
SPDR S&P 500 (SPY)
iShares Barclays 20+ Year Treasury Bond (TLT)
Vanguard REIT ETF (VNQ)
3-month Treasury bills (Cash)

To investigate, we compare SACEMS monthly performance statistics when the S&P 500 Index at the previous monthly close is above (bull market) or below (bear market) its 10-month simple moving average. We consider Top 1, equally weighted (EW) Top 2 and EW Top 3 portfolios of monthly winners for the baseline SACEMS lookback interval. In a robustness test for the EW Top 3 portfolio, we consider lookback intervals ranging from one to 12 months. Using monthly total (dividend-adjusted) returns for the specified assets since February 2006 (limited by DBC) and the monthly level of the S&P 500 Index since September 2005, all through February 2019, we find that:

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Alternative Beta Live

Have long-short alternative beta (style premium) strategies worked well in practice? In their February 2019 paper entitled “A Decade of Alternative Beta”, Antti Suhonen and Matthias Lennkh use actual performance data to assess alternative beta strategies across asset classes from the end of 2007 through the end of 2017, including quantification of fees and potential survivorship bias in public data. Specifically, they form three equal volatility weighted (risk parity) composite portfolios of strategies at the ends of each year during 2007-2016, 2007-2011 and 2012-2016. Each portfolio includes all the strategies launched during the first year and then adds strategies launched each following year at the end of that year. When a strategy dies (is discontinued by the offeror), they reallocate its weight to surviving strategies within the portfolio. They also create two additional portfolios for each period/subperiod that segregate equities and non-equities. They further evaluate alternative beta strategy diversification benefits by comparing them to conventional asset class portfolios. Using weekly post-launch excess returns in U.S. dollars for 349 reasonably unique live and dead alternative beta strategies offered by 17 global investment banks, spanning 14 styles and having at least one year of history during 2008 through 2017, they find that:

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Academia Creating Anomalies?

Does widespread investor acceptance of the capital asset pricing model (CAPM) of stock returns drive undervaluation of stocks with low past alphas? In his February 2019 paper entitled “The Unintended Impact of Academic Research on Asset Returns: The CAPM Alpha”, Alex Horenstein examines whether such acceptance distorts the U.S. stock market. Specifically, he each year at the beginning of January reforms a betting against alpha (BAA) hedge portfolio that is long (short) stocks with alphas lower (higher) than the median based on monthly returns over the past five years. He then weights stocks according to their respective alpha ranks, rescales the long and short sides separately to have market beta 1.0 and holds for one year. He analyzes performance of this portfolio and eight widely accepted equity factors (size, value, momentum, profitability, investment, short-term reversal, long-term reversion and betting against beta) during three subperiods: (1) pre-CAPM era (1932-1964); (2) CAPM era (1965-1992); and, (3) smart beta era (1993-2015). Using total returns for a broad sample of U.S. common stocks and returns for eight accepted equity factors during January 1927 through December 2015, he finds that:

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Stocks Plus Trend Following Managed Futures?

A subscriber asked about an annually rebalanced portfolio of 50% stocks and 50% trend following managed futures as recommended in a 2014 Greyserman and Kaminski book [Trend Following with Managed Futures: The Search for Crisis Alpha], suggesting Equinox Campbell Strategy I (EBSIX) as an accessible managed futures fund. To investigate, we consider not only EBSIX (inception March 2013) but also a longer trend following hedge fund index with monthly returns back to December 1999. This alternative “is an equally weighted index of 37 constituent funds…designed to provide a broad measure of the performance of underlying hedge fund managers who invest with a trend following strategy.” The correlation of monthly returns between this index and EBSIX during April 2013 through February 2019 is 0.84, indicating strong similarity. We use SPDR S&P 500 (SPY) as a proxy for stocks. Using annual returns for EBSIX during 2014-2018 and for the trend following hedge fund index and SPY during 2000-2018, we find that: Keep Reading

Machine Learning Factor?

What are potential monthly returns and alphas from applying machine learning to pick stocks? In their February 2019 paper entitled “Machine Learning for Stock Selection”, Keywan Rasekhschaffe and Robert Jones summarize basic concepts of machine leaning and apply them to select stocks from U.S. and non-U.S. samples, focusing on the cross-section of returns (as in equity factor studies). To alleviate overfitting in an environment with low signal-to-noise ratios, they highlight use of: (1) data feature engineering, and (2) combining outputs from different machine learning algorithms and training sets. Feature engineering applies market/machine learning knowledge to select the forecast variable, algorithms likely to be effective, training sets likely to be informative, factors likely to be informative and factor standardization approach. Their example employs an initial 10-year training period and then walks forecasts forward monthly (as in most equity factor research) for each stock, as follows:

  • Employ 194 firm/stock input variables.
  • Use three rolling training sets (last 12 months, same calendar month last 10 years and bottom half of performance last 10 years), separately for U.S. and non-U.S. samples.
  • Apply four machine learning algorithms, generating 12 signals (three training sets times four algorithms) for each stock each month, plus a composite signal based on percentile rankings of the 12 signals.
  • Rank stocks into tenths (deciles) based on each signal, which forecasts probability of next-month outperformance/underperformance.
  • Form two hedge portfolios that are long the decile of stocks with the highest expected performance and short the decile with the lowest, one equal-weighted and one risk-weighted (inverse volatility over the past 100 trading days), with a 2-day lag between forecast and portfolio reformation to accommodate execution.
  • Calculate gross and net average excess (relative to U.S. Treasury bill yield) returns and 4-factor (market, size, book-to-market, momentum) alphas for the portfolios. To estimate net performance, they assume 0.3% round trip trading frictions. 

They consider two benchmark portfolios that pick long and short side using non-machine learning methods. Using a broad sample of small, medium and large stocks (average 5,907 per month) spanning 22 developed markets, and contemporaneous values for the 194 input variables, during January 1994 through December 2016, they find that: Keep Reading

Inflated Expectations of Factor Investing

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:

  1. Returns are far short of expectations due to overfitting and/or trade crowding.
  2. Drawdowns far exceed expectations.
  3. 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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DJIA-Gold Ratio as a Stock Market Indicator

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

Global Factor Premiums Over the Very Long Run

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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Coverage Ratio and Asymmetric Utility for Retirement Portfolio Evaluation

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

Momentum and Stock Return Dispersion

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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