Volatility Effects

Are machine learning predictions for both stock returns and return volatilities attractively exploitable? In their March 2025 paper entitled “Deep Learning of Conditional Volatility and Negative Risk-Return Relation”, Qi Wu, Xing Yan and Wenxuan Ma apply non-linear deep learning models (neural networks of one to five layers) and likelihood estimation to forecast next-month stock returns and volatilities. They select model settings and hyperparameters based on established practices from the literature and common experience, without extensive searching. They apply the neural network models to 153 firm-specific variables for U.S. stocks annually during 1991 through 2020 using 11-year rolling windows (seven years of training, three years of validation and one year of testing) for a total of 20 years of out-of-sample testing. Specifically, they each month for each model variation:

• Double sort stocks first on next-month predicted volatility and then on next-month predicted return.
• Reform portfolios that are long (short) the tenth, or decile, of stocks with the best (worst) expected returns.

They also consider single-variable sorts for benchmarking. They focus on gross Sharpe ratio of resulting portfolios as the key performance statistic. Using monthly data as specified for a broad sample of U.S. stocks, excluding those priced under $1.00 or with market capitalizations below $5 million, during January 1991 through December 2020 (18,916 stocks, with some data grooming), they find that:

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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:

1. Buy and Hold – buy an initial amount of SVXY and let this position ride indefinitely. This is a long-term investment strategy.
2. 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 2025, we find that: Keep Reading

Do leveraged exchange-traded funds (LETF) with daily leverage resets reliably fall behind portfolios with the same initial leverage but no resets? In his February 2025 paper entitled “Multi-day Return Properties of Leveraged Index ETFs”, Baolian Wang compares the multi-day return properties of leveraged, daily reset LETFs to those of matched initial leverage positions with no resets. He estimates reset costs for the former and margin financing costs (based on the overnight Effective Federal Funds Rate) for the latter. Specifically, he considers LETFs for different combinations of:

• S&P 500 Index, Nasdaq 100 Index, Bloomberg U.S. Treasury 7-10 Year Index, MSCI EAFE Index and MSCI Emerging Markets Index as underlying assets.
• Holding intervals of 5, 10, 21, 63 and 252 trading days.
• Leverage multiples of 2x, 3x, -1x, -2x and -3x.

For each combination, he simulates 1,000 paths of daily returns using random draws of historical returns. For each path, he calculates holding interval returns for the daily reset and no reset alternatives, and their difference. Using daily total return data for the specified indexes and the overnight Effective Federal Funds Rate from respective index inceptions through June 2023, he finds 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 February 2025, we find that: Keep Reading

How might an investor construct a portfolio of very risky assets? To investigate, we revisit ideas first considered five years ago:

• First, diversify with monthly rebalancing of (the GBTC portfolio):
  1. Grayscale Bitcoin Trust ETF (GBTC), an indirect Bitcoin holding.
  2. SPDR Gold Shares (GLD), an indirect gold holding.
  3. ProShares Short VIX Short-Term Futures ETF (SVXY), to capture part of the U.S. stock market volatility risk premium by shorting short-term VIX futures.
• Second, capturing upside volatility and managing drawdown of this portfolio via gain-skimming to a cash position.

We assume equal initial allocations of $10,000 to each of the three assets. We perform a monthly skim as follows: (1) if the risky assets have month-end combined value less than combined initial allocations ($30,000), we rebalance to equal weights for next month; or, (2) if the risky assets have combined month-end value greater than combined initial allocations, we rebalance to initial allocations and move the excess permanently (skim) to cash. We very conservatively assume monthly portfolio reformation frictions of 1% of month-end combined value of risky assets. We assume accrued skimmed cash earns the 3-month U.S. Treasury bill (T-bill) yield. Using monthly prices of GBTC, GLD and SVXY adjusted for splits/dividends and contemporaneous T-bill yield during May 2015 (limited by GBTC) through January 2025, we find that:

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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