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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.

SACEVS Applied to Mutual Funds

“Simple Asset Class ETF Value Strategy” (SACEVS) finds that investors may be able to exploit relative valuation of the term risk premium, the credit (default) risk premium and the equity risk premium via exchange-traded funds (ETF). However, the backtesting period is limited by available histories for ETFs and for series used to estimate risk premiums. To construct a longer test, we make the following substitutions for potential holdings (selected for length of available samples):

To enable estimation of risk premiums over a longer history, we also substitute:

As with ETFs, we consider two alternatives for exploiting premium undervaluation: Best Value, which picks the most undervalued premium; and, Weighted, which weights all undervalued premiums according to degree of undervaluation. Based on the assets considered, the principal benchmark is a monthly rebalanced portfolio of 60% VFINX and 40% VFIIX. Using monthly risk premium calculation data during March 1934 through July 2019 (limited by availability of T-bill data), and monthly dividend-adjusted closing prices for the three asset class mutual funds during June 1980 through July 2019 (39 years, limited by VFIIX), we find that:

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S&P 500 Volatility Indexes as an Asset Class

Should investors consider allocations to products that track equity volatility indexes? In her July 2019 paper entitled “Challenges of Indexation in S&P 500 Index Volatility Investment Strategies”, Margaret Sundberg examines whether behaviors of S&P 500 Index option-based volatility indexes justify treatment of volatility as an asset class. To assess potential strategies, she employs the following indexes:

Using daily time series for these indexes during April 2008 through March 2019, she finds that: Keep Reading

Equity Factor Time Series Momentum

In their July 2019 paper entitled “Momentum-Managed Equity Factors”, Volker Flögel, Christian Schlag and Claudia Zunft test exploitation of positive first-order autocorrelation (time series, absolute or intrinsic momentum) in monthly excess returns of seven equity factor portfolios:

  1. Market (MKT).
  2. Size – small minus big market capitalizations (SMB).
  3. Value – high minus low book-to-market ratios (HML).
  4. Momentum – winners minus losers (WML)
  5. Investment – conservative minus aggressive (CMA).
  6. Operating profitability – robust minus weak (RMW).
  7. Volatility – stable minus volatile (SMV).

For factors 2-7, monthly returns derive from portfolios that are long (short) the value-weighted fifth of stocks with the highest (lowest) expected returns. In general, factor momentum timing means each month scaling investment in a factor from 0 to 1 according its how high its last-month excess return is relative to an inception-to-date window of past levels. They consider also two variations that smooth the simple timing signal to suppress the incremental trading that it drives. In assessing costs of this incremental trading, they assume (based on other papers) that realistic one-way trading frictions are in the range 0.1% to 0.5%. Using monthly data for a broad sample of U.S. common stocks during July 1963 through November 2014, they find that: Keep Reading

OFR FSI as Stock Market Return Predictor

Is the Office of Financial Research Financial Stress Index (OFR FSI), described in “The OFR Financial Stress Index”, useful as a U.S. stock market return predictor? OFR FSI is a daily snapshot of global financial market stress, distilling more than 30 indicators via a dynamic weighting scheme. The index drops and adds indicators over time as some become obsolete and new ones become available. Unlike some other financial stress indicators, past OFR FSI series values do not change due to any periodic renormalization and are therefore suitable for backtesting. To investigate OFR FSI power to predict U.S. stock market returns, we relate level of and change in OFR FSI to SPDR S&P 500 (SPY) returns. Using daily and monthly values of OFR FSI and SPY total returns during January 2000 (OFR FSI inception) through June 2019, we find that:

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T-bills Beat Most Global Stocks?

Do most stocks worldwide beat the risk-free rate of return? In their July 2019 paper entitled “Do Global Stocks Outperform US Treasury Bills?”, Hendrik Bessembinder, Te-Feng Chen, Goeun Choi and John Wei  compare returns of individual global common stocks to that of 1-month U.S. Treasury bills (T-bills). They screen stock price data for obvious errors and filter/correct accordingly. For delisted stocks with no delisting return available, they set the final return to -30%. Using monthly returns with reinvested dividends in U.S. dollars for 17,505 U.S. and 44,476 non-U.S. stocks across 41 other countries (25 developed and 16 emerging) and monthly T-bill yield during 1990 through 2018, they find that:

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Sentiment Indexes and Next-Month Stock Market Return

Do sentiment indexes usefully predict U.S. stock market returns? In his May 2018 doctoral thesis entitled “Forecasting Market Direction with Sentiment Indices”, flagged by a subscriber, David Mascio tests whether the following five sentiment indexes predict next-month S&P 500 Index performance:

  1. Investor Sentiment – the Baker-Wurgler Index, which combines six sentiment proxies.
  2. Improved Investor Sentiment – a modification of the Baker-Wurgler Index that suppresses noise among input sentiment proxies.
  3. Current Business Conditions – the ADS Index of the Philadelphia Federal Reserve Bank, which combines six economic variables measured quarterly, monthly and weekly to develop an outlook for the overall economy.
  4. Credit Spread – an index based on the difference in price between between U.S. corporate bonds and U.S. Treasury instruments with matched cash flows. (See “Credit Spread as an Asset Return Predictor” for a simplified approach.)
  5. Financial Uncertainty – an index that combines forecasting errors for large sets of economic and financial variables to assess overall economic/financial uncertainty.

He also tests two combinations of these indexes, a multivariate regression including all sentiment indexes and a LASSO approach. He each month for each index/combination predicts next-month S&P 500 Index return based on a rolling historical regression of 120 months. He tests predictive power by holding (shorting) the S&P 500 Index when the prediction is for the market to go up (down). In his assessment, he considers: frequency of correctly predicting up and down movements; effectiveness in predicting market crashes; and, significance of predictions. Using monthly data for the five sentiment indexes and S&P 500 Index returns during January 1973 through April 2014, he finds that: Keep Reading

Mean-Variance Optimization vs. Equal Weight for Sectors and Individual Stocks

Are mean-variance (MV) strategies preferable for allocations to asset classes and equal-weight (EW) preferable for allocations to much noisier individual assets? In their May 2019 paper entitled “Horses for Courses: Mean-Variance for Asset Allocation and 1/N for Stock Selection”, Emmanouil Platanakis, Charles Sutcliffe and Xiaoxia Ye address this question. They focus on the Bayes-Stein shrinkage MV strategy, with 10 U.S. equity sector indexes as asset classes and the 10 stocks with the largest initial market capitalizations within each sector (except only three for telecommunications) as individual assets. The Bayes–Stein shrinkage approach dampens the typically large effects of return estimation errors on MV allocations. For estimation of MV return and return covariance inputs, they use an expanding (inception-to-date) 12-month historical window. They focus on one-month-ahead performances of portfolios formed in four ways via a 2-stage process:

  1. MV-EW, which uses MV to determine sector allocations and EW to determine stock allocations within sectors.
  2. EW-EW, which uses EW for both deteriminations.
  3. EW-MV, which uses EW to determine sector allocations and MV to determine stock allocations within sectors.
  4. MV-MV, which uses MV for both deteriminations.

They consider four net performance metrics: annualized certainty equivalent return (CER) gain for moderately risk-averse investors; annualized Sharpe ratio (reward for risk); Omega ratio (average gain to average loss); and, Dowd ratio (reward for value at risk). They assume constant trading frictions of 0.5% of value traded. They perform robustness tests for U.S. data by using alternative MV strategies, different parameter settings and simulations. They perform a global robustness test using value-weighted equity indexes for UK, U.S., Germany, Switzerland, France, Canada and Brazil as asset classes and the 10 stocks with the largest initial market capitalizations within each index as individual assets (all in U.S. dollars). Using monthly total returns for asset classes and individual assets as specified and 1-month U.S. Treasury bill yield as the risk-free rate during January 1994 through August 2017, they find that: Keep Reading

Short-term Equity Risk More Political Than Economic?

How does news flow interact with short-term stock market return? In their April 2019 paper entitled “Forecasting the Equity Premium: Mind the News!”, Philipp Adämmer and Rainer Schüssler test the ability of a machine learning algorithm, the correlated topic model (CTM), to predict the monthly U.S. equity premium based on information in news articles. Their news inputs consist of about 700,000 articles from the New York Times and the Washington Post during June 1980 through December 2018, with early data used for learning and model calibration and data since January 1999 used for out-of-sample testing. They measure the U.S. stock market equity premium as S&P 500 Index return minus the risk-free rate. Specifically, they each month:

  1. Update news time series arbitrarily segmented into 100 topics (with robustness checks for 75, 125 and 150 topics).
  2. Execute a linear regression to predict the equity premium for each of the 100 topical news flows.
  3. Calculate an average prediction across the 100 regressions.
  4. Update a model (CTMSw) that switches between the best individual topic prediction and the average of 100 predictions, combining the flexibility of model selection with the robustness of model averaging.

They use the inception-to-date (expanding window) average historical equity premium as a benchmark. They include mean-variance optimal portfolio tests that each month allocate to the stock market and the risk-free rate based on either the news model or the historical average equity premium prediction, with the equity return variance computed from either 21-day rolling windows of daily returns or an expanding window of monthly returns. They constrain the equity allocation for this portfolio between 50% short and 150% long, with 0.5% trading frictions. Using the specified news inputs and monthly excess return for the S&P 500 Index during June 1980 through December 2018, they find that:

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Expert Estimates of 2019 Country Equity Risk Premiums and Risk-free Rates

What are current estimates of equity risk premiums (ERP) and risk-free rates around the world? In their March 2019 paper entitled “Market Risk Premium and Risk-free Rate Used for 69 Countries in 2019: A Survey”, Pablo Fernandez, Mar Martinez and Isabel Acin summarize results of a February-March 2019 email survey of international finance/economic professors, analysts and company managers “about the Market Risk Premium (MRP or Equity Premium) and Risk-Free Rate that companies, analysts, regulators and professors use to calculate the required return on equity in different countries.” Results are in local currencies. Based on 5,096 specific and credible premium estimates spanning 69 countries with more than eight such responses, they find that: Keep Reading

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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