Equity Premium

Should investors consider portfolio volatility when choosing allocations to stocks and bonds in their retirement accounts? In his October 2023 paper entitled “Retirement Planning: The Volatility-Adjusted Coverage Ratio”, Javier Estrada introduces volatility-adjusted coverage ratio (VAC) as an alternative retirement portfolio metric. He defines this metric as coverage ratio (C, number of years of withdrawals supported relative to retirement period length) divided by annual portfolio volatility during retirement. He compares optimal stocks-bonds allocations for different fixed real annual withdrawal rates across 22 country markets and the world market using either C of VAC. For all markets and withdrawal rates, he uses historical returns for stocks and bonds with annual portfolio rebalancing and 30-year retirement periods. Using annual returns for stocks and bonds and annual inflation rates in the U.S. during 1872 through 2022 (Shiller data) and in 21 other countries during 1900 through 2019 (Dimson-Marsh-Staunton data), he finds that: Keep Reading

Is there a clearly superior multi-factor model of next-month stock returns? In the November 2023 revision of their paper entitled “A Quantum Leap in Asset Pricing: Explaining Anomalous Returns”, James Kolari, Jianhua Huang, Wei Liu and Huiling Liao compare abilities of the following eight multi-factor models of stock returns to explain 133 stubbornly persistent stock return anomalies via out-of-sample (one-month-ahead) cross-sectional regression tests:

1. Capital Asset Pricing Model (CAPM, 1-factor)
2. Fama-French 3-factor model (FF3, adding size and book-to-market)
3. Carhart 4-factor model (adding momentum to FF3)
4. Fama-French 5-factor model (FF5, adding profitability and investment to FF3)
5. Fama-French 6-factor model (FF6, adding momentum to FF5)
6. Hou-Xue-Zhang 4-factor model (market, size, profitability, investment)
7. Stambaugh-Yuan 4-factor model (market, size, management, performance)
8. Kolari-Liu-Huang ZCAPM (market, return dispersion)

They specify return dispersion as the standard deviation of daily returns across all stocks aggregated over the past year. They call dependence of each stock’s return on this metric the stock’s zeta (analogous to beta for the interaction of a stock’s return with the market return). The goal of the study is to identify the model that best account for those pricing anomalies that are historically most difficult to explain. Using publicly available daily return data for 133 stock return anomalies and for the factors used in the above multi-factor models as available during July 1972 through December 2021, they find that: Keep Reading

Can investors reliably time the market, size, value and profitability long-short equity factor premiums? In their October 2023 paper entitled “Another Look at Timing the Equity Premiums”, Wei Dai and Audrey Dong test strategies that time these four premiums in U.S., developed ex-U.S. and emerging equity markets. They define the premiums as:

1. Market – the capitalization-weighted market return minus the U.S. Treasury bill yield.
2. Size – average return on small-capitalization stocks minus average return on large-capitalization stocks.
3. Value – average return on value stocks minus average return on growth stocks.
4. Profitability – average return on stocks of high-profitability firms minus average return on stocks of low-profitability firms.

They time each premium separately based on each of:

1. Valuation ratio – When the difference in aggregate price-to-book ratio between the long and short sides of a premium becomes high (low) relative to its historical distribution, switch to the short (long) side.
2. Mean reversion – When the premium itself becomes high (low) relative to its historical distribution, switch to the short (long) side  of the premium.
3. Momentum – When the premium over the last year becomes relatively high (low), switch to the long (short) side of the premium.

To measure historical premium distributions, they consider an expanding window of initial length 10 years or a rolling 10-year window. For switching to the short side of premiums, they consider historical distribution thresholds of top 10%, 20% or 50% (bottom 10%, 20% or 50%) for valuation ratio and mean reversion (momentum). For switching to the long side of premiums, they consider thresholds of bottom 10%, 20% or 50% (top 50%) for valuation ratio and mean reversion (momentum). They consider  monthly or annual portfolio rebalancing. The number of timing strategies tested is thus 720. For the U.S. sample, monthly returns start in July 1963 for profitability and July 1927 for the other three premiums. For the developed ex-U.S. (emerging markets) sample, premium returns start in July 1990 (July 1994). Benchmarks are returns to strategies that continuously hold just the long side of each premium portfolio. Using monthly data as specified through December 2022, they find that: Keep Reading

The number of published factors significantly explaining variation in individual stock returns has grown steadily over time into the hundreds, inviting the term “factor zoo.” Are all these factors important when applied in combination? In their October 2023 paper entitled “Factor Zoo”, Alexander Swade, Matthias Hanauer, Harald Lohre and David Blitz assess compressibility of the factor zoo by starting with the market factor and then adding one-at-a-time via iterative regressions the factor explaining the largest amount of residual (unexplained) alpha, until the incremental alpha explained by adding a factor is no longer significant. For each factor in their main analysis, they each month calculate its return by: (1) sorting stocks based on the factor; (2) forming a portfolio that is long (short) the third of stocks with the the highest (lowest) expected returns; and, (3) holding the portfolio for one month. They weight stocks in these portfolios based on market valuation capped at the 80th percentile of NYSE valuations (but consider simple value-weighted and equal-weighted portfolios in robustness tests). Using monthly returns for 153 known U.S. equity factors during November 1971 through December 2021, they find that:

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Do conventional market capitalization-weighted stock indexes suffer from a long-term buy-high/sell-low performance drag when adding and deleting stocks? In their October 2023 paper entitled “Reimagining Index Funds”, Robert Arnott, Chris Brightman, Xi Liu and Que Nguyen construct alternative indexes that select stocks based on fundamental measures of underlying firm size and then weight them by market capitalization (Fundamental-selection Cap-weighted, FS-CW). Specifically, the each March:

• For each firm, calculate four fundamental measures of firm size as percentages of aggregate values for all U.S. firms:
  1. Current book value adjusted for intangibles.
  2. 5-year trailing average sales adjusted for the equity-to-asset ratio.
  3. 5-year trailing average cash flow plus R&D expenses.
  4. 5-year trailing average dividend plus share repurchases.
• For each firm, average these four measures.
• Rank stocks of these firms based on their respective averages.
• Reform equal-weighted indexes of the top 500 (FS-CW 500) or the top 1000 (FS-CW 1000) stocks.

For perspective, they also reform at the end of each June a portfolio of the top 500 stocks selected purely based on market capitalization (True CW 500). They then compare returns and 4-factor (adjusting for market, size, book-to-market and momentum) alphas of the Russell 1000, True CW 500, FS-CW 500 and FS-CW 1000 measured relative to the S&P 500. Using monthly data as described above for all publicly traded U.S. stocks, S&P 500, Russell 1000 and the four stock factors to support backtesting from July 1991 through December 2022, they find that: Keep Reading

Is the the conventional retirement portfolio glidepath as recommended by many financial advisors, away from stocks and toward bonds over time, really optimal? In their October 2023 paper entitled “Beyond the Status Quo: A Critical Assessment of Lifecycle Investment Advice”, Aizhan Anarkulova, Scott Cederburg and Michael O’Doherty present a lifecycle income/wealth model using stationary block bootstrap simulations (average block length 120 months to preserve long-term behaviors) with labor income uncertainty, Social Security income, longevity uncertainty and historical monthly returns for stock indexes, government bonds and government bills across developed countries. They apply this model to estimate outcomes for several age-dependent, monthly rebalanced portfolios of stocks and bonds, including a representative target-date fund (TDF), as well as some fixed-percentage allocation strategies. They focus on a U.S. couple (a female and a male) who save during working years starting at age 25 and consume Social Security income and savings starting at age 65 with constant real 4% annual withdrawals. They evaluate four outcomes: (1) wealth at retirement; (2) retirement income; (3) conservation of savings; and, (4) bequest at death. Using monthly (local) real returns for domestic stock indexes, international stock indexes, government bonds and government bills as available for 38 developed countries during 1890 through 2019, they find that:

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Do target retirement date funds, offering glidepaths that shift asset allocations away from equities and toward bonds as target dates approach, safely generate attractive returns? To investigate, we consider seven such mutual funds offered by Vanguard, as follows:

• • Vanguard Target Retirement 2020 Fund (VTWNX)
  • Vanguard Target Retirement 2025 Fund (VTTVX)
  • Vanguard Target Retirement 2030 Fund (VTHRX)
  • Vanguard Target Retirement 2035 Fund (VTTHX)
  • Vanguard Target Retirement 2040 Fund (VFORX)
  • Vanguard Target Retirement 2045 Fund (VTIVX)
  • Vanguard Target Retirement 2050 Fund (VFIFX)

We consider as benchmarks SPDR S&P 500 ETF Trust (SPY), iShares iBoxx $ Investment Grade Corporate Bond ETF (LQD) and both 80-20 and 60-40 monthly rebalanced SPY-LQD combinations. We look at monthly and annual return statistics, including compound annual growth rate (CAGR) and maximum drawdown (MaxDD). Using monthly total returns for SPY, LQD, three target retirement date funds since October 2003 and four target retirement date funds since June 2006 (limited by Vanguard inception dates), all through September 2023, we find that:

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The “Simple Asset Class ETF Value Strategy” (SACEVS) seeks diversification across a small set of asset class exchanged-traded funds (ETF), plus a monthly tactical edge from potential undervaluation of three risk premiums:

1. Term – monthly difference between the 10-year Constant Maturity U.S. Treasury note (T-note) yield and the 3-month Constant Maturity U.S. Treasury bill (T-bill) yield.
2. Credit – monthly difference between the Moody’s Seasoned Baa Corporate Bonds yield and the T-note yield.
3. Equity – monthly difference between S&P 500 operating earnings yield and the T-note yield.

Premium valuations are relative to historical averages. How might this strategy react to changes in the Effective Federal Funds Rate (EFFR)? Using end-of-month values of the three risk premiums, EFFR, total 12-month U.S. inflation and core 12-month U.S. inflation during March 1989 (limited by availability of operating earnings data) through September 2023, we find that: Keep Reading

How do exchange-traded-funds (ETF) focused on supplying renewable energy perform? To investigate, we consider nine of the largest renewable energy ETFs, all currently available, as follows:

• • iShares Global Clean Energy (ICLN)
  • Invesco Solar (TAN)
  • First Trust NASDAQ Clean Edge Green Energy Index (QCLN)
  • Invesco WilderHill Clean Energy (PBW)
  • ALPS Clean Energy (ACES)
  • Invesco Global Clean Energy (PBD)
  • SPDR S&P Kensho Clean Power (CNRG)
  • First Trust Global Wind Energy (FAN)
  • Global X Renewable Energy Producers (RNRG)

We use SPDR S&P 500 (SPY) as a benchmark, assuming investors look at renewable energy stocks to beat the market and not to beat the energy sector. We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly returns for the nine renewable energy ETFs and SPY as available through September 2023, we find that: Keep Reading

Prior research indicates that stocks of firms with high direct and indirect carbon dioxide emissions tend to beat the market (offer a carbon premium). Does high-emissions stock outperformance derive from surprisingly high earnings? In their September 2023 paper entitled “Does the Carbon Premium Reflect Risk or Mispricing?”, Yigit Atilgan, Ozgur Demirtas, Alex Edmans and Doruk Gunaydin examine relationships between firm carbon dioxide emissions and future earnings surprises. They consider three levels of emissions from S&P Global Trucost: Scope 1 directly from firm operations; Scope 2 from firm consumption of purchased heat/electricity/steam; and, Scope 3 from upstream supply chain operations. They consider level of emissions (natural logarithm of emissions measured in tons) and annual change in level of emissions, with the latter winsorized at the 2.5% level. They consider several measures of earnings surprises, all comparing analyst forecasts to actual earnings. They calculate market reactions to earnings announcements as 3-day cumulative abnormal returns (CAR) relative to a 3-factor (market, size, book-to-market) model the day before through the day after earnings announcements. Using carbon dioxide emissions data, stock returns, market valuations, book values and analyst earnings forecasts for a broad sample of U.S. stocks during 2002 through 2021, they find that: Keep Reading