Reward goes with risk, and volatility represents risk. Therefore, volatility means reward; investors/traders get paid for riding roller coasters. Right? These blog entries relate to volatility effects.
What are the costs of mitigating tail risk via exchange-traded funds (ETF) designed to manage it? To investigate, we consider seven such ETFs, three dead and four live, as follows:
VelocityShares Tail Risk Hedged Large Cap ETF (TRSK) – hedges against tail risk by allocating 85% (15%) of assets to ETFs that track the S&P 500 Index (a volatility component designed to hedge against extreme market declines). This ETF is dead.
Cambria Global Tail Risk ETF (FAIL) – invests at least 40% of assets in investment grade, intermediate U.S. treasuries and TIPS, at least 40% in non-U.S. sovereign bonds and about 1% per month in put options. This ETF is dead.
Cambria Tail Risk ETF (TAIL) – holds cash and U.S. government bonds and about 1% of assets per month in put options.
Global X NASDAQ 100 Tail Risk ETF (QTR) – invests at least 80% of assets in the securities of the Nasdaq-100 Quarterly Protective Put 90 Index, which holds NASDAQ 100 stocks and put options on the NASDAQ 100 Index.
Global X S&P 500 Tail Risk ETF (XTR) – invests at least 80% of assets in the S&P 500 and put options on the S&P 500 Index.
Simplify Tail Risk Strategy ETF (CYA) – invests 50%-90% of assets in income-generating ETFs and up to 20% in derivatives to hedge tail risk. This ETF is dead.
Note that TRSK, QTR, XTR and CYA are composite portfolios holding equities and embedded tail risk protection, while FAIL, TAIL and CAOS are pure tail risk protection usable as adjuncts to separate equity portfolios. We use SPDR S&P 500 ETF Trust (SPY), iShares MSCI EAFE ETF (EFA) and Invesco QQQ Trust (QQQ) over matched sample periods for reference. We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly total returns for the seven tail risk ETFs, SPY, EFA and QQQ as available through March 2026, we find that:
Will investors in passive index funds overwhelm the ability of active investors to keep prices near fundamental value? If so, what happens? In their March 2026 paper entitled “A Model for Passive That Breaks the Market”, Michael Green, Hari Krishnan and Stephan Sturm model the impact of passive share on equity market behavior. Their model has the following assumptions:
Passive fund managers ignore fundamental value.
Equity index volatility tends to be higher when prices are low.
The fundamental value of the broad stock market tends to increase over the long run.
Active investors historically tend to push prices toward some notion of fair value. However, they may stop resisting above some passive share threshold, shorten their investment horizons and make little use of fundamentals.
Strength of reversion to fair value decreases as passive share increases.
The model considers cases for which active investors either do or do not change their behavior when faced with increased passive share. Using the above modeling assumptions and data for the S&P 500 during 1926-1994 as a baseline for the U.S. equity market without passive investing, they conclude that:
In response to “Shorting VXX with Crash Protection”, which investigates shorting iPath S&P 500 VIX Short-Term Futures (VXX) to capture the equity volatility risk premium, a subscriber asked about instead using a long position in ProShares Short VIX Short-Term Futures (SVXY). To investigate, we consider two scenarios based on monthly measurements:
Buy and Hold – buy an initial amount of SVXY and let this position ride indefinitely. This is a long-term investment strategy.
Monthly Skim – buy the same initial amount of SVXY and move to SPDR Bloomberg 1-3 Month T-Bill ETF (BIL) any month-end gains over the initial investment (the beginning-of-month SVXY position may become smaller, but not larger, than the initial investment). This is an income-generating investment strategy.
The offeror changed the SVXY investment objective at the end of February 2018 (when short VIX strategies crashed), more conservatively targeting henceforth -0.5 times the daily performance of the S&P 500 VIX Short-Term Futures Index rather than -1.0 times as before. We therefore examine SVXY performance separately before and after that change. We assume o.2% SVXY-BIL switching frictions in scenario 2. Using monthly adjusted closing prices for SVXY and BIL during October 2011 through February 2026, we find that:Keep Reading
Can investors use leveraged exchange-traded funds (ETF) to construct attractive versions of simple 60%/40% (60/40) and 40%/60% (40/60) stocks-bonds portfolios? In their March 2020 presentation package entitled “Robust Leveraged ETF Portfolios Extending Classic 40/60 Portfolios and Portfolio Insurance”, flagged by a subscriber, Mikhail Smirnov and Alexander Smirnov consider several variations of classic stocks/bonds portfolios implemented with leveraged ETFs. They ultimately focus on a monthly rebalanced partially 3X-leveraged portfolio consisting of:
To validate findings, we consider this portfolio and several 60/40 and 40/60 stocks/bonds portfolios. We look at net monthly performance statistics, along with compound annual growth rate (CAGR), maximum drawdown (MaxDD) based on monthly data and annual Sharpe ratio. To estimate monthly rebalancing frictions, we use 0.5% of amount traded each month. We use average monthly 3-month U.S. Treasury bill yield during a year as the risk-free rate in Sharpe ratio calculations for that year. Using monthly adjusted prices for TQQQ, TMF, TLT and for SPDR S&P 500 ETF Trust (SPY) and Invesco QQQ Trust (QQQ) to construct benchmarks during February 2010 (limited by TQQQ inception) through January 2026, we find that:Keep Reading
How have different asset classes recently interacted with the CBOE Volatility Index (VIX)? To investigate, we look at lead-lag relationships between VIX and returns for each of the following 10 exchange-traded fund (ETF) asset class proxies:
We look also at average next-month performances of these ETFs across ranges of of a VIX 3-month simple moving average (SMA3). Using end-of-month levels of VIX since January 1990 and dividend-adjusted monthly closing prices for the asset class proxies as available since July 2002, all through January 2026, we find that:Keep Reading
Is there a way to amplify the MAX overpricing anomaly (measured as the average of the five highest daily returns for a stock over the past month), which is driven by the desire of some investors for a lottery-like payoff? In their January 2026 paper entitled “MAX on Steroids: A New Measure of Investor Attraction to Lottery Stocks”, Baris Ince, Turan Bali and Han Ozsoylev introduce MAXᵝ as a variable that distills lottery-seeking behavior by removing the systematic return component from MAX. Specifically, they each month:
Sort stocks into tenths (deciles) based on their market betas as measured by a rolling window of 252 daily returns.
Within each beta-sorted decile, sort stocks based on MAX.
They then focus on excess returns (relative to U.S. Treasury bills) and factor model alphas of the value-weighted extreme deciles of MAX aggregated across beta deciles, plus a hedge portfolio that is long (short) the stocks in the highest (lowest) decile. Using daily returns and ownership data for U.S. listed common stocks, excluding utility/financial stocks and stocks priced under $5, during January 1968 through December 2022, they find that:
One concern about simple momentum strategies is data snooping bias impounded in selection of the lookback interval(s) used to measure asset momentum. To circumvent this concern, we consider the following argument:
The CBOE Volatility Index (VIX) broadly indicates the level of financial markets distress and thereby the tendency of investors to act complacently (when VIX is low) or to act in panic (when VIX is high).
Complacency translates to resistance in changing market outlook (long memory and lookback intervals), while panic translates to rapid changes of mind (short memory and short lookback intervals).
The inverse of VIX is therefore indicative of the actual aggregate current lookback interval affecting investor actions.
We test this argument by:
Setting a range for VIX using monthly historical closes from January 1990 through December 2006, before the sample period used for most tests of the Simple Asset Class ETF Momentum Strategy (SACEMS).
Applying buffer factors to the bottom (0.9) and top (1.1) of this actual inverse VIX range to recognize that it could break above or below the historical range in the future.
Segmenting the buffer-extended inverse VIX range into 12 equal increments and mapping these increments by rounding into momentum lookback intervals of 1 month (lowest segment) to 12 months (highest segment).
Applying this same method to future end-of-month inverse VIX levels to select the SACEMS lookback interval for the next month.
We test the top one (Top 1), the equal-weighted top two (EW Top 2) and the equal-weighted top three (EW Top 3) SACEMS portfolios. We focus on compound annual growth rate (CAGR), maximum drawdown based on monthly measurements, annual returns and Sharpe ratio as key performance statistics. To calculate excess annual returns for the Sharpe ratio, we use average monthly yield on 3-month Treasury bills during a year as the risk-free rate for that year. Benchmarks are these same statistics for tracked (baseline) SACEMS. Using monthly levels of VIX since inception in January 1990 and monthly dividend-adjusted prices of SACEMS assets since February 2006 (initial availability of a commodities ETF), all through December 2025, we find that:Keep Reading
In response to our inquiry about Goldman Sachs Panic Index data, Grok responded that the data are proprietary and unavailable. However, Grok offered “several high-quality public proxies and near-replicas…built by traders and quants using only freely available data. These reconstructions correlate extremely closely (often 0.90–0.98) with the snippets Goldman has shown clients over the years.” For one of these proxies, the percentile rank of VIX within its trailing 2-year window (0-100 scale), Grok provided a Python script to generate an historical daily series. Is it predictive of U.S. stock market returns? To investigate, we run the script to generate daily Panic Index Proxy data from the end of 2015 through November 2025 and relate the series to contemporaneous daily S&P 500 Index (SP500) returns. Using these two series, we find that:Keep Reading
How can investors and fund managers best exploit premiums associated with value, momentum, profitability, investment and low volatility factors, either to generate absolute return or to beat a market benchmark? In his September 2025 paper entitled “Strategic Style Allocation: Absolute or Relative?”, Pim van Vliet examines strategic allocation across long-only, value-weighted versions of these equity factors, depending on objective: absolute return or benchmark outperformance. To assess absolute return, he evaluates Sharpe ratios of factor allocations. To assess benchmark outperformance, he evaluates information ratios of factor allocations. He also investigates dynamic allocation between low volatility and the other factors, with portfolio adjustment frictions. Using long-only U.S. value-weighted factor returns during July 1963 through May 2025 and global factor index returns during January 1999 through March 2025, he finds that:Keep Reading
Does the ICE BofAML MOVE Index, the implied volatility of U.S. Treasuries as derived from options on U.S. Treasuries with maturities 2, 5, 10 and 30 years, usefully predict U.S. stock market and U.S. Treasury bond returns? To investigate, we perform two sets of calculations using SPDR S&P 500 ETF (SPY) as a proxy for the U.S. stock market and iShares 20+ Year Treasury Bond ETF (TLT) as a proxy for U.S. Treasury bonds:
Lead-lag analyses using correlations between end-of-month MOVE Index or change in MOVE Index and monthly SPY or TLT returns.
Average next-month SPY or TLT returns by ranked fifth (quintile) of end-of-month MOVE Index or change in MOVE Index.
Using end-month MOVE Index levels and monthly dividend-adjusted SPY and TLT data during November 2002 (limited by MOVE Index data) through August 2025, we find that:Keep Reading
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