# 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.

**December 19, 2023** - Technical Trading, Volatility Effects

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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**October 26, 2023** - Momentum Investing, Volatility Effects

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

**October 13, 2023** - Strategic Allocation, Volatility Effects

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

**September 19, 2023** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

Are equity multifactor strategies, as implemented by exchange-traded funds (ETF), attractive? To investigate, we consider seven 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.

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

**August 29, 2023** - Investing Expertise, Volatility Effects

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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**August 17, 2023** - Volatility Effects

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

**August 15, 2023** - Strategic Allocation, Technical Trading, Volatility Effects

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

- Ivy 5 EW: Assign equal weight (EW), meaning 20%, to each of the five positions and rebalance annually.
- 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).
- 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.
- 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)

iShares MSCI EAFE ETF (EFA)

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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**July 11, 2023** - Equity Premium, Volatility Effects

Is the ability of the VIX percentile threshold rule described in “Using VIX and Investor Sentiment to Explain Stock Market Returns” to explain future stock market excess return in-sample readily exploitable out-of-sample? To investigate, we test a strategy (VIX Percentile Strategy) that each month holds SPDR S&P 500 ETF Trust (SPY) or 3-month U.S. Treasury bills (T-bills) according to whether a recent end-of-month level of the CBOE Volatility Index (VIX) is above or below a specified inception-to-date (not full sample) percentage threshold. To test sensitivities of the strategy to settings for its two main features, we consider:

- Each of 70th, 75th, 80th, 85th or 90th percentiles as the VIX threshold for switching between T-bills and SPY.
- Each of 0, 1, 2 or 3 skip months between VIX measurement and strategy response.

We focus on compound annual growth rate (CAGR) and maximum drawdown (MaxDD) as essential performance metrics and use buy-and-hold SPY as a benchmark. We do not quantify frictions due to switching between SPY and T-bills for the VIX Percentile Strategy. Using end-of-month VIX levels since January 1990 and dividend-adjusted SPY prices and T-bill yields since January 1993 (SPY inception), all through May 2023, *we find that:* Keep Reading

**July 10, 2023** - Sentiment Indicators, Volatility Effects

Do stock market return volatility (as a measure of risk) and aggregate investor sentiment (as a measure of risk tolerance) work well jointly to explain stock market returns? In their June 2023 paper entitled “Time-varying Equity Premia with a High-VIX Threshold and Sentiment”, Naresh Bansal and Chris Stivers investigate the in-sample power an optimal CBOE Volatility Index (VIX) threshold rule and a linear Baker-Wurgler investor sentiment relationship to explain future variation in U.S. stock market excess return (relative to U.S. Treasury bill yield). They skip one month between VIX/sentiment measurements and stock market returns to accommodate investor digestion of new information. They consider return horizons of 1, 3, 6 and 12 months. They also extend this 2-factor model to include the lagged Treasury implied-volatility index (ICE BofAML MOVE Index) as a third explanatory variable. Using monthly excess stock market return and VIX during January 1990 through December 2022, monthly investor sentiment during January 1990 through June 2022 and monthly MOVE index during October 1997 through December 2022, *they find that:*

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**June 9, 2023** - Calendar Effects, Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

What characteristics of U.S. equity factor return series are most relevant to respective factor performance? In his May 2023 paper entitled “The Cross-Section of Factor Returns” David Blitz explores long-term average returns and market alphas, 60-month market betas and factor performance cyclicality for U.S. equity factors. He also assesses potentials of three factor rotation strategies: low-beta, seasonal and return momentum. Using monthly returns for 153 published U.S. equity market factors, classified statistically into 13 groups, during July 1963 through December 2021, *he finds that:*

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