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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.

Bitcoin Trend Predicts U.S. Stock Market Return?

A subscriber asked about an assertion that bitcoin (BTC) price trend/return predicts return of the S&P 500 Index (SP500). To investigate, we relate BTC returns to SP500 returns at daily, weekly and monthly frequencies. We rationalize the different trading schedules for these two series by excluding BTC trading dates that are not also SP500 trading days. Most results are conceptual, but we test three versions of an SP500 timing strategy based on prior BTC returns focused on compound annual growth rate (CAGR) and maximum drawdown (MaxDD). Using daily SP500 levels and (pruned) BTC prices during 9/17/2014 (limited by the BTC series) through 12/21/2022, we find that:

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Revisiting Effects of S&P 500 Additions and Deletions

How has the price impact associated with stocks entering or leaving the S&P 500 evolved? In their December 2022 paper entitled “The Disappearing Index Effect”, Robin Greenwood and Marco Sammon revisit abnormal returns for S&P 500 additions and deletions and investigate five potential drivers of findings. Using announcement dates, implementation dates and daily returns for 752 S&P 500 additions and 749 S&P 500 deletions during 1980 through 2020, they find that:

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Exploit U.S. Stock Market Dips with Margin?

A subscriber requested evaluation of a strategy that seeks to exploit U.S stock market reversion after dips by temporarily applying margin. Specifically, the strategy:

  • At all times holds the U.S. stock market.
  • When the stock market closes down more than 7% from its high over the past year, augments stock market holdings by applying 50% margin.
  • Closes each margin position after two months.

To investigate, we assume:

  • The S&P 500 Index represents the U.S. stock market for calculating drawdown over the past year (252 trading days).
  • SPDR S&P 500 (SPY) represents the market from a portfolio perspective.
  • We start a margin augmentation at the same daily close as the drawdown signal by slightly anticipating the drawdown at the close.
  • 50% margin is set at the opening of each augmentation and there is no rebalancing to maintain 50% margin during the two months (42 trading days) it is open.
  • If S&P 500 Index drawdown over the past year is still greater than 7% after ending a margin augmentation, we start a new margin augmentation at the next close.
  • Baseline margin interest is U.S. Treasury bill (T-bill) yield plus 1%, debited daily.
  • Baseline one-way trading frictions for starting and ending margin augmentations are 0.1% of margin account value.
  • There are no tax implications of trading.

We use buying and holding SPY without margin augmentation as a benchmark. Using daily levels of the S&P 500 Index, daily dividend-adjusted SPY prices and daily T-bill yields from the end of January 1993 (limited by SPY) through November 2022, we find that: Keep Reading

U.S. Dollar Seasonal Strength/Weakness and Stock Market Returns

A subscriber asked whether currency exchange rates exhibit reliable seasonality that may be used to time equities (with a stronger currency implying lower asset prices). To investigate, we look for reliable calendar month effects for the U.S. dollar (USD)-euro exchange rate and for Invesco DB US Dollar Index Bullish Fund (UUP). We further look at how monthly returns for these variables relate to those for SPDR S&P 500 ETF Trust (SPY) as a proxy for the U.S. stock market. Using monthly data for the USD-euro exchange rate since January 1999 and for UUP since March 2007, and corresponding data for SPY, all through November 2022, we find that: Keep Reading

Machines Picking Emerging Market Stocks

Are models based on advanced machine learning adept at predicting returns for individual emerging market stocks? In the November 2022 version of their paper entitled “Machine Learning and the Cross-section of Emerging Market Stock Returns”, Matthias Hanauer and Tobias Kalsbach compare abilities of machine learning models to predict emerging market stock returns. They consider nine alternatives: two traditional linear models (ordinary least squares and elastic net); two tree-based models (gradient boosted regression trees and random forest); and, five neural networks (one to five layers). Tree-based methods and neural networks identify non-linearities and variable interactions. They further consider a combination of the five neural networks and a combination of all tree-based plus neural network methods. For each model at the end of each month, they rank stocks into country-neutral fifths, or quintiles, based on next-month expected returns and reform a portfolio that is long (short) the quintile with the highest (lowest) expected returns. For tests of long-only net performance, they assume 1-way trading frictions are half the estimated bid-ask spread and apply trading cost mitigation rules. Using returns and 36 accounting/trading variables for 15,152 unique stocks from 32 emerging market countries as included in the MSCI Emerging Markets Index during July 1995 through December 2021 (with out-of-sample testing starting January 2002), they find that:

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Reliable U.S. Equity Market Oscillations?

Do annual stock market swing returns swing around their average like a pendulum? In the November update of his 2022 paper entitled “Periodic Structure of Equity Market Annual Returns and Their Predictability”, Daniel Pinelis investigates whether annual returns of the S&P 500 Index and the NASDAQ Composite Index exhibit reliable periodicity. Specifically, he models an oscillator indicator that accumulates directional imbalances in annual stock index returns and applies the indicator, in combination with statistical, graphical and machine learning methods, to estimate extent and timing of further market declines from the current levels. Using annual returns for the S&P 500 Index since the mid-1960s and for the NASDAQ Composite Index since the early 1970s, both through late 2022, he finds that:

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Option Gamma and Associated Future Stock Returns

Is option gamma, which indicates how aggressively option market makers must trade underlying stocks to hedge their option positions, a systematic driver of those stock returns? In his October 2022 paper entitled “Option Gamma and Stock Returns”, Amar Soebhag investigates the relationship between option gamma for individual stocks and future returns of those stocks. He defines net gamma exposure of a stock as a hedge-adjusted, gamma-weighted sum of open interest for options written on the stock. He each month sorts stocks into value-weighted tenths (deciles) by net gamma for the previous month and calculates next-month returns on the decile portfolios, with focus on the difference in returns between extreme deciles. He then looks at behavior of net gamma across stocks, interactions of net gamma with other stock return predictors and time variation of aggregate net gamma. Using daily gamma, open interest, implied volatility and trading volume for each option contract on listed U.S. common stocks price over $5 as available during January 1996 through December 2021, as well as contemporaneous returns for underlying stocks and data for other widely accepted stock return predictors, he finds that:

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Federal Reserve Treasuries Holdings and Asset Returns

Is the level, or changes in the level, of Federal Reserve (Fed) holdings of U.S. Treasuries (bills, notes, bonds and TIPS, measured weekly as of Wednesday) an indicator of future stock market and/or Treasuries returns? To investigate, we take dividend-adjusted SPDR S&P 500 (SPY) and iShares Barclays 20+ Year Treasury Bond (TLT) as tradable proxies for the U.S. stock and Treasuries markets, respectively. Using weekly Fed holdings of Treasuries, and SPY and TLT total returns during mid-December 2002 through late October 2022, we find that: Keep Reading

Equity Factors Come and Go with Economic Regimes?

Are many accepted equity factors/return anomalies artifacts of the secular decline in interest rates during their discovery sample periods? In their September 2022 paper entitled “The Factor Multiverse: The Role of Interest Rates in Factor Discovery”, Jules van Binsbergen, Liang Ma and Michael Schwert study the role of the secular decline in interest rates since the early 1980s in the discovery of equity factors/return anomalies. They use value-weighted long-short portfolios and monthly reformation for all factors/anomalies. They apply duration-matched fixed income portfolio return adjustments to returns for each anomaly portfolio to model returns for the latter if there had been no interest rate decline. They then classify each anomaly as false positive (present for unadjusted returns, but not adjusted returns), false negative (present for adjusted returns, but not unadjusted returns) or robust to the effect of interest rates (present for both unadjusted and adjusted returns). Using monthly returns for 153 accepted factors/anomalies over respective original test periods and for 1,395 potential undiscovered factors/anomalies based on firm accounting variables during July 1962 through December 2020, along with contemporaneous yield data for zero coupon U.S. Treasury bonds and notes, they find that:

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VIX and Future Stock Market Returns

Market commentators sometimes cite a high Chicago Board Options Exchange (CBOE) Volatility Index (VIX), the options-implied volatility of the S&P 500 Index as an indicator of investor sentiment and therefore a contrarian signal for the stock market. Specifically, a relatively high (low) VIX indicates panic (complacency) and therefore pending stock market strength (weakness). Does evidence support such conventional wisdom? To check, we relate the level of VIX to S&P 500 Index returns over the next 5, 10, 21, 63 and 126 trading days. Using daily closes for VIX and the S&P 500 Index during January 1990 (limited by the VIX series) through September 2022, we find that: Keep Reading

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