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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

Do Federal Funds Rate (FFR) actions taken by the Federal Reserve open market operations committee reliably predict stock market and U.S. Treasuries yield reactions? To investigate, we use the S&P 500 Index (SP500) as a proxy for the stock market and the yield for the 10-Year U.S. Constant Maturity Treasury note (T-note). We look at index returns and changes in T-note yield during the one and two months after FFR actions, separately for FFR increases and FFR decreases. Using data for the three series during January 1990 through December 2023, we find that:

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U.S. Academic Research Extinguishing Global Stock Anomalies?

Does publication of academic studies on stock return anomalies in the U.S. tend to extinguish these anomalies in global markets? In their November 2023 paper entitled “Does U.S. Academic Research Destroy the Predictability of Global Stock Returns?”, Guohao Tang, Yuwei Xie and Lin Zhu compare out-of-sample (post-research sample) and post-publication global returns to research-sample global returns for 87 factors described in U.S. journals. The global sample includes 38 country markets (22 developed and 16 developing). The 87 factors include those based on momentum, value, investment, profitability, intangibles and trading frictions. For each factor each month, they reform a portfolio that is long (short) the fifth of stocks expected to have the highest (lowest) next-month returns. They weight stocks in each portfolio either equally or by market capitalization according to the approach used in the associated published paper. Using data required to compute monthly returns for 87 anomalies across 38 countries with research sample end dates after 2000 during January 1990 through December 2020, they find that: Keep Reading

How Are Robotics-AI ETFs Doing?

How do exchange-traded-funds (ETF) focused on development of robotics-artificial intelligence (AI), an arguably hot area of technology, perform? To investigate, we consider five of the largest such ETFs, all currently available, as follows:

We use Invesco QQQ Trust (QQQ) as a benchmark, assuming investors look at robotics-AI stocks as a way to beat other technology stocks. We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly total returns for the five robotics-AI ETFs and QQQ as available through December 2023, we find that: Keep Reading

Focus on Global Factors?

Should investors focus on global equity factors or local (country) equity factors when trying to predict their local market returns? In their November 2023 paper entitled “How Global is Predictability? The Power of Financial Transfer Learning”, Oliver Hellum, Lasse Heje Pedersen and Anders Rønn-Nielsen compare the importance of global factors versus local factors for predicting local stock market returns in 35 countries. They generate optimal local and global factor models using the generalized elastic net usually trained in an early subsample and tested in a later subsample. They perform an array of tests:

  • For each country, they compare predictive powers of local and global factor models optimized pre-2000 and tested during 2000-2021.
  • For each country, they compare predictive powers of local and U.S. factor models optimized pre-2000 and tested during 2000-2021.
  • They check the predictive power of a non-U.S. factor model optimized during 1982-2021 and tested in the U.S. during 1926-1981.

Using trimmed monthly returns in U.S. dollars and most of the 153 firm characteristics (inputs) used in prior research for broad samples of firms/stocks since 1926 for the U.S. and since 1982 as available for 34 other countries, all through 2021, they find that:

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Volatility-adjusted Retirement Income Streams

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

Super Model?

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

Exhaustively Timing Equity Factor Premiums

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

Compressing the Equity Factor Zoo

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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Using Firm Fundamentals to Build Better Stock Indexes

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

All Stocks All the Time?

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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