Volatility Effects

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 July 2002, before the sample period used for any 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 November 2024, we find that: Keep Reading

Can investors safely use leverage to squeeze incremental return from low-volatility/factor-tilted stocks, thereby avoiding underperformance of these stocks during bull markets? In their October 2024 paper entitled “Low-Risk Alpha Without Low Beta”, David Blitz, Clint Howard, Danny Huang and Maarten Jansen exploit the low-volatility anomaly by leveraging multifactor, low-risk, global stock portfolios to a beta of 1.0 while controlling tracking error relative to a capitalization-weighted benchmark. Their portfolio formation rules are:

• The portfolio is long only and fully invested in liquid (large-capitalization) stocks.
• Maximum individual stock weight is the lower of 1.5% or 20 times its benchmark weight.
• Exposure to countries, regions and sectors may deviate at most 10% from benchmark weights.
• Portfolio beta (portfolio-weighted sum of historical stock betas for the last 156 weekly returns) must be less than 0.8 relative to the benchmark.
• Portfolio optimization involves trading off expected returns, benchmark tracking error and turnover. Expected stock returns derive from a multifactor score with 50% for low-risk (equal-weighted combination of past 260-day volatility, 156-week volatility, 260-day beta and 156-week beta), 16.67% for value (net payout yield), 16.67% for quality (gross profits to assets) and 16.67% for momentum (return from 12 months ago to one month ago).
• Use synthetic positions (for example, via equity options) to achieve leverage, with no cash collateral and financing costs equal to the risk-free rate.
• Rebalance at the end of each month but ignore slight deviations from target weights.

They separately discuss impacts of portfolio rebalancing frictions and additional leverage costs/penalties. They focus on developed markets but also look at an emerging markets sample and North American, European and Asia Pacific subsamples. Using daily and monthly data for developed market stocks since December 1985 and emerging market stocks since December 1995, all through December 2023, along with contemporaneous spreads and interest/Treasury bill rates, they 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:

• Equities:
  • SPDR S&P 500 (SPY)
  • iShares Russell 2000 Index (IWM)
  • iShares MSCI EAFE Index (EFA)
  • iShares MSCI Emerging Markets Index (EEM)
• Bonds:
  • iShares Barclays 20+ Year Treasury Bond (TLT)
  • iShares iBoxx $ Investment Grade Corporate Bond (LQD)
  • iShares JPMorgan Emerging Markets Bond Fund (EMB)
• Real assets:
  • Vanguard REIT ETF (VNQ)
  • SPDR Gold Shares (GLD)
  • Invesco DB Commodity Index Tracking (DBC)

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 October 2024, we find that: Keep Reading

How can the low-volatility effect, whereby stocks with low past volatility tend to outperform the market on a risk-adjusted basis (but lag during long bull markets), help achieve common investment goals? In their October 2024 paper entitled “Leveraging the Low-Volatility Effect”, Lodewijk van der Linden, Amar Soebhag and Pim van Vliet test ways to use the low-volatility effect to support five distinct investment goals. Their low-volatility benchmark strategy each month holds the 100 of the 1,000 largest U.S. stocks with the lowest 36-month volatilities. They consider ways to exploit the effect in five ways:

1. To safely boost return, they integrate value (net payout yield) and momentum (return from 12 months ago to one month ago) with low-volatility by each month: (1) selecting the 500 of the 1,000 largest U.S. stocks with the lowest 36-month volatilities; and, (2) picking the 100 of these stocks with the highest combined net payout yield and momentum. 
2. To beat a conventional 60-40 stocks-bonds portfolio, they consider: (1) replacing 10% of stocks and 5% of bonds with a 15% allocation to Strategy 1; (2) assigning equal weights to stocks, bonds and Strategy 1; or, (3) allocating 70% to Strategy 1 and 30% to bonds.
3. To beat the stock market, they target a market beta of 1.00 via a 140% long position in Strategy 1, financed either by: (1) borrowing 40%, with credit spread plus the T-bill rate as the borrowing cost; or, (2) using equity market index futures, with annual return slippage and implicit costs 0.2%.
4. For absolute returns, they consider a 100% position in Strategy 1, offset by: (1) 48% short positions in speculative stocks (high volatility, low net payout yield and low momentum), assuming 2% annual shorting costs; or, (2) a 72% position in short equity market index futures, with 0.2% annual costs.
5. For crash protection compared to 5% out-of-the-money 1-month put options, they target a market beta of -0.50 by combining: (1) a 30% long position in the low-volatility benchmark with a 50% short position in speculative stocks, with credit spread over the T-bill rate as the borrowing cost; or, (2) a 70% long position in the low-volatility benchmark with a 100% short position in equity market index futures, with 0.2% annual costs.

In general, portfolio rebalancing is monthly. Using monthly data for the largest 1,000 U.S. stocks and for the other asset types specified above during 1990 through 2023, they find that: Keep Reading

Can investors reliably exploit the somewhat opaquely presented strategy summarized in “Using Wilder Volatility Stops to Time the U.S. Stock Market”, which employs Welles Wilder’s Average True Range (ATR) volatility metric to generate buy and sell signals for broad U.S. stock market indexes? To investigate, we each trading day for the SPDR S&P 500 ETF Trust (SPY):

1. Compute true range as the greatest of: (a) daily high minus low; (b) absolute value of daily high minus previous close; and, (c) absolute value of daily low minus previous close.
2. Calculate ATR as the simple average of the last five true ranges (including the current one).
3. Generate a Wilder Volatility Stop (WVS) by multiplying ATR by a risk factor of 2.5.
4. When out of SPY, buy when it closes above a dynamic trendline defined by a trend minimum plus current WVS (breakout). When in SPY, sell when it closes below a dynamic trendline defined by a trend maximum minus current WVS (breakdown).

We perform the above calculations using raw (not adjusted for dividends) daily SPY prices, but use dividend-adjusted prices to calculate returns. We assume any breakout/breakdown signal and associated SPY-cash switch occurs at the same close. We initially ignore SPY-cash switching frictions, but then test outcome sensitivity to different levels of frictions. We ignore return on cash due to frequency of switching. We further test outcome sensitivity to parameter choices and to an alternative definition of ATR. We use buy-and-hold SPY as a benchmark. Using daily raw and dividend-adjusted prices for SPY during January 1993 (inception) through most of October 2024, 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:

• 40% ProShares UltraPro QQQ (TQQQ)
• 20% Direxion Daily 20+ Year Treasury Bull 3X Shares (TMF)
• 40% iShares 20+ Year Treasury Bond ETF (TLT)

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 September 2024, we find that: Keep Reading

Some experts interpret stock market return volatility as an indicator of investor sentiment, with high (low) volatility indicating ascendancy of fear (greed). Volatility of volatility (VoV) would thus indicate uncertainty in investor sentiment. Does the risk associated with this uncertainty depress stock prices and thereby predict strong stock market returns? To investigate, we consider two measures of U.S. stock market volatility: (1) realized volatility, calculated as standard deviation of daily S&P 500 Index returns over the last 21 trading days (annualized); and, (2) implied volatility as measured by the Chicago Board Options Exchange Market Volatility Index (VIX). For both, we calculate VoV as the standard deviation of volatility over the past 21 trading days and test the ability of VoV to predict SPDR S&P 500 (SPY) returns. To avoid overlap in volatility and VoV calculations, we focus on monthly return intervals. Using daily values of the S&P 500 Index since December 1989 and VIX since inception in January 1990, and monthly dividend-adjusted SPY closes since inception in January 1993, all through August 2024, we find that: Keep Reading

Are equity multifactor strategies, as implemented by exchange-traded funds (ETF), attractive? To investigate, we consider eight multifactor ETFs, all currently available:

• iShares Edge MSCI Multifactor USA (LRGF) – holds large and mid-cap U.S. stocks with focus on quality, value, size and momentum, while maintaining a level of risk similar to that of the market. The benchmark is iShares Russell 1000 (IWB).
• iShares Edge MSCI Multifactor International (INTF) – holds global developed market ex U.S. large and mid-cap stocks based on quality, value, size and momentum, while maintaining a level of risk similar to that of the market. The benchmark is iShares MSCI ACWI ex US (ACWX).
• Goldman Sachs ActiveBeta U.S. Large Cap Equity (GSLC) – holds large U.S. stocks based on good value, strong momentum, high quality and low volatility. The benchmark is SPDR S&P 500 (SPY).
• John Hancock Multifactor Large Cap (JHML) – holds large U.S. stocks based on smaller capitalization, lower relative price and higher profitability, which academic research links to higher expected returns. The benchmark is SPY.
• John Hancock Multifactor Mid Cap (JHMM) – holds mid-cap U.S. stocks based on smaller capitalization, lower relative price and higher profitability, which academic research links to higher expected returns. The benchmark is SPDR S&P MidCap 400 (MDY).
• JPMorgan Diversified Return U.S. Equity (JPUS) – holds U.S. stocks based on value, quality and momentum via a risk-weighting process that lowers exposure to historically volatile sectors and stocks. The benchmark is SPY.
• Xtrackers Russell 1000 Comprehensive Factor (DEUS) – seeks to track, before fees and expenses, the Russell 1000 Comprehensive Factor Index, which seeks exposure to quality, value, momentum, low volatility and size factors. The benchmark is IWB.
• Vanguard U.S. Multifactor (VFMF) – uses a rules-based quantitative model to evaluate U.S. common stocks and construct a U.S. equity portfolio that seeks to achieve exposure to multiple factors across market capitalizations (large, mid and small). The benchmark is iShares Russell 3000 (IWV).

We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly returns for the seven equity multifactor ETFs and benchmarks as available through August 2024, we find that: Keep Reading

How do crypto-asset prices interact with conventional market risks, monetary policy and crypto-specific factors? In their July 2024 paper entitled “What Drives Crypto Asset Prices?”, Austin Adams, Markus Ibert and Gordon Liao investigate factors influencing crypto-asset returns using a sign-restricted, structural vector auto-regressive model. Specifically, they decompose daily Bitcoin returns into components reflecting:

• Monetary policy – estimated from effects of changes in the short-term risk-free rate on crypto-asset prices.
• Conventional risk premiums – estimated from daily interactions of 2-year zero coupon U.S. Treasury notes (T-notes) and the S&P 500 Index to account for changes in risk compensation required for holding traditional financial assets.
• Crypto risk premium – estimated from variations in the risk compensation demanded
  by investors for holding crypto assets as indicated by crypto-asset market liquidity and volatility.
• Level of crypto adoption – estimated from co-movements of Bitcoin and stablecoin market capitalizations to reflect crypto-asset innovation, regulatory changes and sentiment shifts.

Using daily data for the risk-free rate, S&P 500 Index, T-notes, Bitcoin and two stablecoins (USDT and USDC), during January 2019 through February 2024, they find that: Keep Reading

Does the CBOE Volatility Index (VIX) exhibit exploitable seasonality? To investigate, we calculate by calendar month and compare average monthly:

• Change in VIX.
• Return for ProShares VIX Short-Term Futures ETF (VIXY).
• Return for ProShares Short VIX Short-Term Futures ETF (SVXY).

Using monthly closes of VIX since January 1990, monthly split-adjusted closes for  for VIXY since inception in January 2011 and monthly split-adjusted closes for SVXY since inception in October 2011, all through June 2024, we find that: Keep Reading