Volatility Effects

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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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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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

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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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)
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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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

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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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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A subscriber requested review of a strategy that seeks to exploit “Sell in May” by switching between risk-on assets during November-April and risk-off assets during May-October, with assets specified as follows:

• Risk-on – SPDR S&P 500 (SPY), iShares Russell 2000 Index (IWM) and Invesco DWA Technical Leaders (PDP).
• Risk-off – iShares Barclays 20+ Year Treas Bond (TLT) and Invesco S&P 500 Low Volatility (SPLV).

On each portfolio switch date, assets receive equal weight with 0.25% overall penalty for trading frictions. We focus on compound annual growth rate (CAGR), maximum drawdown (MaxDD) measured at 6-month intervals and Sharpe ratio measured at 6-month intervals as key performance statistics. As benchmarks, we consider buying and holding SPY, IWM or TLT and a 60%-40% SPY-TLT portfolio rebalanced frictionlessly at the ends of April and October (60-40). Using April and October dividend-adjusted closes of SPY, IWM, PDP, TLT and SPLV as available during October 2002 (first interval with at least one risk-on and one risk-off asset) through April 2023, and contemporaneous 6-month U.S. Treasury bill (T-bill) yield as the risk-free rate, we find that: Keep Reading

Does an allocation to gold truly protect a portfolio from downside risk? In their April 2023 paper entitled “The Golden Rule of Investing”, Pim van Vliet and Harald Lohre examine downside risks for portfolios of stocks (value-weighted U.S. stock market) and bonds (10-year U.S. Treasury notes) with and without gold (bullion) based on real returns and a 1-year investment horizon. They also investigate substitution of low-volatility stocks for the broad stock market in search of further downside risk protection. Using monthly returns for the specified assets and U.S. inflation data during 1975 (when gold becomes truly tradable) through 2022, they find that:

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