Equity Premium

What performance should investors expect from the S&P 500 Index based on price-to-earnings (P/E) and Cyclically-Adjusted Price-to-Earnings (CAPE, or P/E10)? In their November 2020 paper entitled “Extreme Valuations and Future Returns of the S&P 500”, Shaun Rowles and Andrew Mitchell take a layered “regression upon a regression” approach to predict S&P 500 Index returns and level. First, to estimate future returns, they run a linear regression on P/E, P/E10, S&P 500 dividend yield, inflation, 10-year U.S. Treasury note yield, historical 1-year, 3-year, 5-year and 10-year S&P 500 Index returns and percentiles of many of these variables within their respective historical distributions. Then, they run separate linear regressions to predict 1-year, 3-year, 5-year and 10-year future annualized returns. Finally, they run a linear regression to model current S&P 500 Index level for comparison to actual current level. Using Robert Shiller’s U.S. stock market and economic data spanning January 1871 through June 2020, they find that: Keep Reading

A subscriber requested evaluation of three retirement investment alternatives, assuming a constant increment invested at the end of each month, as follows:

1. 50-50: allocate each increment via fixed percentages to stocks and bonds (for comparability, we use 50% to each).
2. Seasonal 1: during April through September (October through March), allocate 100% of each increment to stocks (bonds).
3. Seasonal 2: during April through September (October through March), allocate 100% of each increment to bonds (stocks).

The hypothesis is that seasonal variation in asset class allocations could improve overall long-term investment performance. We conduct a short-term test using SPDR S&P 500 ETF Trust (SPY) as a proxy for stocks and iShares iBoxx $ Investment Grade Corporate Bond ETF (LQD) as a proxy for bonds. We then conduct a long-term test using Vanguard 500 Index Fund Investor Shares (VFINX) as a proxy for stocks and Vanguard Long-Term Investment-Grade Fund Investor Shares (VWESX) as a proxy for bonds. Based on the setup, we focus on terminal value as the essential performance metric. Using total (dividend-adjusted) returns for SPY and LQD since July 2002 and for VFINX and VWESX since January 1980, all through December 2020, we find that: Keep Reading

“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):

• Monthly average 3-Month Treasury Bill (T-bill) Secondary Market Rate instead of monthly average 3-Month T-bill Constant Maturity Rate as the risk-free rate and return on Cash.
• Vanguard GNMA Investor Shares (VFIIX) instead of  iShares 20+ Year Treasury Bond (TLT).
• Vanguard Long-Term Investment Grade Investor Shares (VWESX) instead of iShares iBoxx $ Investment Grade Corporate Bond (LQD).
• Vanguard 500 Index Fund Investor Shares (VFINX) instead of SPDR S&P 500 (SPY).

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

• Monthly average Moody’s Seasoned Baa Corporate Bond Yields rather than day before end-of-month Baa yields for calculation of the credit risk premium. This substitution ignores a one-day delay in release of daily data.
• Robert Shiller’s S&P Composite Index monthly average levels instead of S&P 500 Index monthly closes. This substitution ignores any delay in posting of Shiller data (but new data are available elsewhere in real time).
• Robert Shiller’s monthly S&P Composite Index (GAAP, or as-reported) earnings instead of S&P Dow Jones S&P 500 operating earnings. We lag the Shiller earnings by four months to ensure real-time availability. In other words, the earnings yield for a month is the S&P Composite Index level for that month divided by index annual GAAP earnings as of four months ago. GAAP earnings are generally lower than operating earnings (see “Stock Market Valuation Ratio Trends”).
• Robert Shiller’s monthly average Long Interest Rates instead of monthly average yields on 10-year Constant Maturity U.S. Treasury notes. This substitution ignores any delay in posting of Shiller data (but new data are again available elsewhere with little delay).

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 November 2020 (limited by availability of T-bill data), and monthly dividend-adjusted closing prices for the three asset class mutual funds during June 1980 through November 2020 (40+ years, limited by VFIIX), we find that:

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Is there a better way than the Fed model to measure relative attractiveness of equities and bonds. In his October 2020 paper entitled “Towards a Better Fed Model”, Raymond Micaletti examines seven Fed Model alternatives, each comparing a 10-year forward annualized estimate of equity returns to the yield of 10-year constant maturity U.S. Treasury notes (T-note). The seven estimates of future equity returns are based on autocorrelation-corrected quarterly regressions using 10 years of past quarterly data for one of: (1) Aggregate Investor Allocation to Equities (AIAE); (2) Cyclically-Adjusted Price-to-Earnings Ratio (CAPE); (3) Tobin’s Q (QRATIO); (4) Market Capitalization-to-Nominal GDP (MC/GDP); (5) Market Capitalization-to-Adjusted Gross Value Added (MC/AGVANF); (6) Market Capitalization-to-Household and Non-Profit Total Assets (MC/HHNPTA); and, (7) Household and Non-Profit Equity Allocation-to-Nominal GDP (HHNPEQ/GDP). He calculates AIAE as total market value of equities divided by the sum of total market value of equities and total par value of bonds, approximated by adding the liabilities of five categories of borrowers. He then tests for each alternative a tactical asset allocation (TAA) strategy that each month weights equities and bonds based on a modified z-score of the forecasted 10-year equity risk premium (equity return minus T-note yield) computed by subtracting the median and dividing by the standard deviation of actual monthly premiums over the past 10 years. If modified z-score is greater than 1 (less than -1), the strategy is 100% in equities (0% in equities). In between those thresholds, weights are based on linear interpolation. Using quarterly data from the Archival Federal Reserve Economic Database (ALFRED) and Robert Shiller’s data library and daily U.S. equity market returns and U.S. Treasury bond/note roll-adjusted futures returns as available from the end of the fourth quarter of 1951 through the end of the third quarter of 2020, he finds that: Keep Reading

A subscriber asked about a strategy that switches between an equal-weighted portfolio of Invesco QQQ Trust (QQQ) and iShares Russell 2000 ETF (IWM) when the S&P 500 Index is above its 200-day simple moving average (SMA200) and an equal-weighted portfolio of SPDR Gold Shares (GLD) and iShares 20+ Year Treasury Bond ETF (TLT) when below. Also, more generally, is an equal-weighted portfolio of GLD and TLT (GLD:TLT) superior to TLT only for risk-off conditions? To investigate, we (1) backtest the switching strategy and (2) compare performances of GLD:TLT versus TLT when the S&P 500 Index is below its SMA200. We consider both gross and net performance, with the latter accounting for 0.1% portfolio switching frictions 0.001% daily portfolio rebalancing frictions (rebalancing one hundredth of portfolio value). As benchmarks, we consider buying and holding SPDR S&P 500 ETF Trust (SPY) and a strategy that holds SPY (TLT) when the S&P 500 Index is above (below) its SMA200. Using daily S&P 500 Index levels starting February 5, 2004 and daily dividend-adjusted levels of QQQ, IWM, GLD, TLT and SPY starting November 18, 2004 (limited by inception of GLD), all through November 25, 2020, we find that:

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Do extreme equity market valuations represent opportunities in value stocks? In their October 2020 paper entitled “Extrapolators at the Gate: Market-wide Misvaluation and the Value Premium”, Stefano Cassella, Zhaojing Chen, Huseyin Gulen and Ralitsa Petkova test the hypothesis that extrapolating (momentum) investors bid up growth stocks in good times and bid down value stocks in bad times, such that the value premium concentrates during reversion from these conditions. Their principal measure of market valuation is average book value-to-market capitalization ratio (B/M) of all firms, excluding financial stocks, utility stocks and stocks priced ice less than $1. When monthly B/M is in the top (bottom) 10% of monthly values for the past 10 years, they deem the market overvalued (undervalued). For robustness, they consider other percentage cutoffs and an alternative metric that quantifies the distance between the current-month distribution of firm B/Ms and the distributions of over the past 10 years based on the Mann-Whitney U test. They further tie findings to investor expectations based on a long times series constructed from Gallup, American Association of Individual Investors and Investor Intelligence surveys of investors. Using monthly returns and accounting data for U.S. common stocks and the specified survey data during January 1962 through December 2018, they find that:

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Is the currency carry trade, as implemented by exchange-traded funds/notes (ETF/ETN), attractive? To investigate, we consider two currency carry trade ETF/ETNs, one live (with low trading volume) and one dead:

• PowerShares DB G10 Currency Harvest Fund (DBV) – tracks changes in the Deutsche Bank G10 Currency Future Harvest Index. This index consists of futures contracts on certain G10 currencies with up to 2:1 leverage to exploit the tendency that currencies with relatively high interest rates tend to appreciate relative to currencies with relatively low interest rates, reconstituted annually in November.
• iPath Optimized Currency Carry (ICITF) – provides exposure to the Barclays Optimized Currency Carry Index, which reflects the total return of a strategy that holds high-yielding G10 currencies financed by borrowing low-yielding G10 currencies. This fund stopped trading July 2018, but an indicative value is still available.

We focus on monthly return statistics, plus compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). For reference (not benchmarking), we compare results to those for SPDR S&P 500 (SPY) and iShares Barclays 20+ Year Treasury Bond (TLT). Using monthly total returns for the two currency carry trade products, SPY and TLT as available through October 2020, we find that: Keep Reading

How connected are principal measures of U.S. economic activity and U.S. stock market performance? In their October 2020 paper entitled “Has the Stock Market Become Less Representative of the Economy?”, Frederik Schlingemann and René Stulz model and measure relationships between market capitalizations of U.S. publicly listed firms and their contributions to U.S. employment and Gross Domestic Product (GDP). They estimate employment contribution directly based on firm reports, with modeled adjustments. They measure contribution to GDP based on firm value-add, approximated as operating income before depreciation plus labor costs (with labor costs often modeled). They also try other ways of measuring value-add. Using annual non-farm employment and GDP data for the U.S., annual employment and value-add data for U.S. publicly listed firms and annual stock prices for those firms during 1973 (limited by firm employment data) through 2019, they find that:

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“Market Impacts of Growth in Target Date Funds” summarizes research on potential market-wide effects of periodic rebalancing actions of Target Date Funds (TDF), which trade against momentum. One piece of evidence is that monthly autocorrelation of S&P 500 Index returns is significantly negative during 2010-2019 but not during 1986-1995 or 1996-2005. Another is that TDFs accomplish most of quarterly rebalancing within the next quarter. To assess how convincing autocorrelation findings are, we calculate rolling 5-year monthly (60-month) and quarterly (20-calendar quarter) autocorrelations of returns for:

• SPDR S&P 500 ETF Trust (SPY) since January 1993 to represent the U.S. stock market.
• Fidelity Fund (FFIDX) since January 1980 to represent the U.S. stock market
• Fidelity Investment Grade Bond Fund (FBNDX) since January 1980 to represent the U.S. bond market.

Using monthly total (dividend-reinvested) returns for these three assets through October 2020, we find that: Keep Reading

Are aggregate periodic stocks-bonds rebalancing actions of Target Date Funds (TDF), which trade against momentum, increasingly affecting U.S. stock market dynamics? In their October 2020 paper entitled “Retail Financial Innovation and Stock Market Dynamics: The Case of Target Date Funds”, flagged by a subscriber, Jonathan Parker, Antoinette Schoar and Yang Sun examine market impacts of Target Date Funds (TDFs), assets of which have grown from less than $8 billion in 2000 to more than $2.3 trillion (of roughly $21 trillion in U.S. mutual funds) in 2019. Using quarterly data on TDF holdings, monthly U.S. stock market and Vanguard Total Bond Market Index Fund (bond market) returns and monthly data for stocks held by and similar to those held by TDFs during the third quarter of 2008 through the fourth quarter of 2018 (excluding three quarters with suspect data), they find that:

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