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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.

FFR Actions, Stock Market Returns and Bond Yields

A subscriber wondered whether U.S. stock market movements predict Federal Funds Rate (FFR) actions taken by the Federal Reserve open market operations committee. To investigate and evaluate usefulness of findings, we relate three series:

  1. FFR actions per the above source, along with recent and historical committee meeting dates.
  2. S&P 500 Index returns.
  3. Changes in yield for the 10-Year U.S. Constant Maturity Treasury note (T-note).

In constructing the first series, for Federal Reserve open market operations committee meeting dates which do not produce FFR changes, we quantify committee actions as 0%. We ignore committee conference calls that result in no changes in FFR. We calculate the second and third series between committee meeting dates because that irregular interval represents new information to the committee and potential exploitation points for investors. Using data for the three series during January 1990 through early August 2019, we find that:

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SACEMS-SACEVS Diversification with Mutual Funds

“SACEMS-SACEVS for Value-Momentum Diversification” finds that the “Simple Asset Class ETF Value Strategy” (SACEVS) and the “Simple Asset Class ETF Momentum Strategy” (SACEMS) are mutually diversifying. Do longer samples available from “SACEVS Applied to Mutual Funds” and “SACEMS Applied to Mutual Funds” confirm this finding? To check, we look at the following three equal-weighted (50-50) combinations of the two strategies, rebalanced monthly:

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

Using monthly gross returns for SACEVS and SACEMS mutual fund portfolios during September 1997 through July 2019, we find that:

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SMA10 vs. OFR FSI for Stock Market Timing

In response to “OFR FSI as Stock Market Return Predictor”, a subscriber suggested overlaying a 10-month simple moving average (SMA10) technical indicator on the Office of Financial Research Financial Stress Index (OFR FSI) fundamental indicator for timing SPDR S&P 500 (SPY). The intent of the suggested overlay is to expand risk-on opportunities safely. To test the overlay, we add four strategies (4 through 7) to the prior three, each evaluated since January 2000 and since January 2009:

  1. SPY – buy and hold SPY.
  2. OFR FSI-Cash – hold SPY (cash as proxied by 3-month U.S. Treasury bills) when OFR FSI at the end of the prior month is negative or zero (positive).
  3. OFR-FSI-VFITX – hold SPY (Vanguard Intermediate-Term Treasury Fund Investor Shares, VFITX, as a more aggressive risk-off asset than cash) when OFR FSI at the end of the prior month is negative or zero (positive).
  4. SMA10-Cash – hold SPY (cash) when the S&P 500 Index is above (at or below) its SMA10 at the end of the prior month.
  5. SMA10-VFITX – hold SPY (VFITX) when the S&P 500 Index is above (at or below) its SMA10 at the end of the prior month.
  6. OFR-FSI-SMA10-Cash – hold SPY (cash) when either signal 2 or signal 4 specifies SPY. Otherwise, hold cash.
  7. OFR-FSI-SMA10-VFITX – hold SPY (cash) when either signal 3 or signal 5 specifies SPY. Otherwise, hold VFITX.

Using end-of-month values of OFR FSI, SPY total return and level of the S&P 500 Index during January 2000 (OFR FSI inception) through June 2019, 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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