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Volatility Effects

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.

SACEMS with Inverse VIX-based Lookback Intervals

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 and top 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 equally weighted top two (EW Top 2) and the equally 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 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 January 2024, we find that: Keep Reading

Using SVXY to Capture the Volatility Risk Premium

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 more 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 switching frictions of 0.25% for movements of funds from SVXY to BIL in scenario 2. Using monthly adjusted closing prices for SVXY and BIL during October 2011 through December 2023, we find that: Keep Reading

Simple Ways to Beat Equal-weighted Stock Portfolios

Academic studies of stock portfolio optimization often use an equal-weighted (EW) strategy as benchmark. Are there simple EW enhancements that researchers ought to consider instead? In their December 2023 paper entitled “Outperforming Equal Weighting”, Antonello Cirulli and Patrick Walker test three sets of enhanced long-only EW portfolios relying solely on past returns:

  1. Momentum-enhanced EW – sort stocks into tenths (deciles) from lowest to highest average weekly return over the last 12 months.
  2. Volatility-enhanced EW – sort stocks into deciles from highest t0 lowest standard deviation of weekly returns over the last five years.
  3. Sharpe ratio-enhanced EW – sort stocks into deciles from lowest to highest Sharpe ratio calculated with weekly returns over the last years.

For each set, they then exclude the bottom 1, 2, 3, 4 or 5 deciles and weight stocks in retained deciles equally for a total of 15 enhanced EW portfolios. They reform all portfolios on the first Wednesday of each month. They then compare net performances of these portfolios to those of simple EW and capitalization-weighted portfolios of all stocks in the universe after debiting 0.1% frictions for turnover. They focus on large-capitalization/liquid stocks and check robustness of findings to subperiods, lookback intervals, level of frictions and rebalancing frequency. Using weekly returns in U.S. dollars, adjusted for splits and dividends, of MSCI USA, Europe, Emerging Markets and Developed Markets stocks starting five years before the test period of April 2002 through March 2022, they find that:

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Effects of Market Volatility on Market Trend Strategies

Does market volatility predictably affect returns to simple moving average (SMA) trend-following strategies? In their November 2023 paper entitled “Market Volatility and the Trend Factor”, Ming Gu, Minxing Sun, Zhitao Xiong and Weike Xu investigate how stock market volatility affects multi-SMA trend factor profitability. They first assess significance of the trend factor premium, as follows:

  • For each stock at the close on the last trading day of each month:
    • Compute SMAs of prices for lookback intervals of 3, 5, 10, 20, 50, 100, 200, 400, 600, 800 and 1000 trading days, and divide each SMA by the end price.
    • Starting five years into the sample period (1931), regress next-month stock returns on corresponding monthly SMA ratios over the past 60 months.
    • Average the SMA ratio regression coefficients separately over the past 12 months to estimate next-month coefficients and apply these coefficients to estimate next-month return.
  • At the end of each month, sort all stocks into tenths, or deciles, based on estimated next-month returns and form a trend factor hedge portfolio that is long (short) the equal-weighted top (bottom) decile. The trend factor premium is the monthly gross return for this portfolio.

They then assess how trend factor hedge portfolio returns interact with monthly stock market return volatility (standard deviation of monthly value-weighted market returns over the past 12 months) by specifying volatility has high or low when its prior-month value is above or below the full-sample median. Using data for all listed U.S. common stocks, excluding those priced below $5 or in the lowest tenth of NYSE market capitalizations, during January 1926 through December 2022, they find that:

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Sector Rotation Based on Relative Rotation Graphs

Do Relative Rotation Graphs (RRG), which visually segregate assets into leading, weakening, lagging or improving quadrants by relative performance, effectively identify equity sectors with relatively strong future returns? In his September 2023 paper entitled “Dynamic Sector Rotation”, John Rothe tests an RRG-based sector relative momentum strategy with stop-loss risk management based on volatility. Specifically, he:

  • Selects a universe of 31 sector sector/subsector exchange-traded funds (ETFs) based on daily trading volume, years in existence, overlap with other sector/subsectors, assets under management and liquidity.
  • Each week, holds the equal-weighted top 5 ETFs crossing into the RRG improving quadrant.
  • Manages the risk of each holding continuously via a Wilder Volatility Stop with a 5-day range.
  • Assumes a 2% annual management fee.

His benchmark is the S&P 500 Momentum Index. Using weekly returns for the selected ETF universe during a test period spanning January 2013 through mid-2023, he finds that: Keep Reading

Classic Stocks-Bonds Portfolios with Leveraged ETFs

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 2023, we find that: Keep Reading

Are Equity Multifactor ETFs Working?

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

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 2023, we find that: Keep Reading

Machine Stock Return Forecast Disagreement and Future Return

Is dispersion of stock return forecasts from different machine learning models trained on the same history (as a proxy for variation in human beliefs) a useful predictor of stock returns? In their August 2023 paper entitled “Machine Forecast Disagreement”, Turan Bali, Bryan Kelly, Mathis Moerke and Jamil Rahman relate dispersion in 100 monthly stock return predictions for each stock generated by randomly varied versions of a machine learning model applied to 130 firm/stock characteristics. They measure machine return forecast dispersion for each stock as the standard deviation of predicted returns. They then each month sort stocks into tenths (deciles) based on this dispersion, form either a value-weighted or an equal-weighted portfolio for each decile and compute average next-month portfolio return. Their key metric is average next-month return for a hedge portfolio that is each month long (short) the stocks in the lowest (highest) decile of machine return forecast dispersions. Using the 130 monthly firm/stock characteristics and associated monthly stock returns for a broad sample of U.S. common stocks (excluding financial and utilities firms and stocks trading below $5) during July 1966 through December 2022, they find that:

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Asset Class ETF Interactions with VIX

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 July 2023, we find that: Keep Reading

Comparing Ivy 5 Allocation Strategy Variations

A subscriber requested comparison of four variations of an “Ivy 5” asset class allocation strategy, as follows:

  1. Ivy 5 EW: Assign equal weight (EW), meaning 20%, to each of the five positions and rebalance annually.
  2. Ivy 5 EW + SMA10: Same as Ivy 5 EW, but take to cash any position for which the asset is below its 10-month simple moving average (SMA10).
  3. Ivy 5 Volatility Cap: Allocate to each position a percentage up to 20% such that the position has an expected annualized volatility of no more than 10% based on daily volatility over the past month, recalculated monthly. If under 20%, allocate the balance of the position to cash.
  4. Ivy 5 Volatility Cap + SMA10: Same as Ivy 5 Volatility Cap, but take completely to cash any position for which the asset is below its SMA10.

To perform the tests, we employ the following five asset class proxies:

iShares 7-10 Year Treasury Bond ETF (IEF)
SPDR S&P 500 ETF Trust (SPY)
Vanguard Real Estate Index Fund (VNQ)
Invesco DB Commodity Index Tracking Fund (DBC)

We consider monthly performance statistics, annual performance statistics, and full-sample compound annual growth rate (CAGR) and maximum drawdown (MaxDD). Annual Sharpe ratio uses average monthly yield on 3-month U.S. Treasury bills (T-bills) as the risk-free rate. The DBC series in combination with the SMA10 rule are limiting with respect to sample start date and the first return calculations. Using daily and monthly dividend-adjusted closing prices for the five asset class proxies and T-bill yield as return on cash during February 2006 through July 2023, we find that:

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