# 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.

**July 5, 2017** - Volatility Effects

Does unusual behavior of the distribution of stock betas predict overall market behavior? In her March 2017 paper entitled “Beta Dispersion and Market-Timing”, Laura-Chloé Kuntz investigates the attractiveness of stock market timing strategies based on the dispersion of stock betas. She calculates betas using rolling windows of three or 12 months of daily returns. She considers two potential predictors derived from the distribution of betas: Beta Dispersion (BD), specified as the average of the top 5% of betas minus the average of the bottom 5% of betas; and, High Beta (HB), specified as the average of the top 5% of betas. Using S&P 500 stocks and the S&P 500 Index, she constructs a distribution of stock market return forecasts based on BD or HB for horizons of one, three or 12 months based on regressions relating past beta indicator to future stock market returns. She then tests three stock market timing strategies on the S&P 500 Index:

- Basic – each month hold the S&P 500 Index (1-month U.S. Treasury bills) if next-period forecasted returns are likely positive (negative).
- Unweighted – each month go long (short) the S&P 500 Index if next-period forecasted returns are likely positive (negative).
- Weighted – each month go long (short) the S&P 500 Index according to the probability of positive (negative) index return based on the historical forecast distribution, with the balance in 1-month U.S. Treasury bills.

Using monthly returns of S&P 500 Index stocks and the S&P 500 Index and monthly 1-month U.S. Treasury bill yield (as the risk-free rate, or cash yield) during September 1989 through September 2016,* she finds that:* Keep Reading

**June 27, 2017** - Volatility Effects

Does the options-based expected volatility of the expected volatility of the S&P 500 Index (expected volatility of VIX, or VVIX) convey useful information about future returns of related assets? In their April 2017 paper entitled “The Volatility-of-Volatility Term Structure”, Nicole Branger, Hendrik Hülsbusch and Alexander Kraftschik investigate the VVIX term structure via principal component analysis. They interpret the first, second and third principal components of the term structure as its level, slope and curvature, respectively. They examine relationships between the VVIX term structure and returns on S&P 500 Index option straddles and VIX option straddles. Using groomed daily prices for S&P 500 Index options and VIX options with maturities 1, 2, 3, 4 and 5 months, and daily excess returns of at-the-money delta-neutral S&P 500 Index straddles with maturities 1, 2, 3, 6, 9 and 12 months and VIX straddles with maturities 1, 2, 3, 4 and 5 months during September 2007 through August 2014, *they find that:* Keep Reading

**June 12, 2017** - Equity Premium, Strategic Allocation, Volatility Effects

Can investors predict the return of a stock from its relationship with the dispersion of returns across all stocks? In their May 2017 paper entitled “Building Efficient Portfolios Sensitive to Market Volatility”, Wei Liu, James Kolari and Jianhua Huang examine a 2-factor model which predicts the return on a stock based on its sensitivity to (1) the value-weighted stock market return (beta risk) and (2) the standard deviation of value-weighted returns for all stocks (zeta risk). They first each month estimate zeta for each stock via regressions of daily data over the past year. They then rank stocks by zeta into quantile portfolios and calculate next-month equal-weighted returns across these portfolios and various long-short combinations of these portfolios (hedge portfolios) to measure dependence of future returns on zeta. Finally, they generate performance data for aggregate zeta risk portfolios by adding value-weighted market index returns to returns for each of the long-short zeta-sorted portfolios. Using daily and monthly returns for a broad sample of U.S. stocks in the top 90% of market capitalizations for that year, monthly equity market returns and monthly U.S. Treasury bill yields as the risk-free rate during January 1965 through December 2015, *they find that:* Keep Reading

**May 26, 2017** - Strategic Allocation, Volatility Effects

What modifications must investors make to minimum variance portfolios to make them more attractive than equal weighting? In their April 2017 paper entitled “Asset Allocation with Correlation: A Composite Trade-Off”, Rachael Carroll, Thomas Conlon, John Cotter and Enrique Salvador assess conditions under which a minimum variance portfolio (requiring only estimates of asset covariances) beats an equally weighted portfolio. In particular, they test minimum variance portfolios that:

- Employ one of three ways (one constant and two dynamic) to estimate future asset return correlations.
- Consider a range of correlation forecasting horizons.
- Do and do not have shorting restrictions.
- Limit turnover by rebalancing only when: (1) any weight drifts outside a fixed percentage band; or, (2) any asset drifts outside a no-trade range based on its volatility, such that each asset has the same probability of triggering (allowing riskier assets more latitude).
- Have rebalancing frictions of either 0.2% or 0.5% of traded value.

These variations enable analyses of trade-offs among parameter estimation error, correlation forecasting horizon, turnover and rebalancing frictions. Their key portfolio performance metrics are volatility, Sharpe ratio and turnover. They consider seven asset universes for forming minimum variance portfolios: 10, 30 or 48 U.S. industry portfolios during January 1970 through December 2013; 20 portfolios of U.S. stocks sorted by size and book-to-market ratio during January 1970 through December 2013; stock indexes for nine developed countries during January 1980 through December 2013; the 30 stocks in the Dow Jones Industrial Average during January 2003 through December 2012; and, the 197 stocks continuously listed in the S&P 500 Index during January 1996 through December 2012. Using daily returns in excess of the risk-free rate for the assets in these universes, *they find that:* Keep Reading

**May 3, 2017** - Volatility Effects

Is there a reliable way to forecast spikes in U.S. stock market expected volatility, as measured by the CBOE Volatility Index (VIX), and thereby avoid or exploit associated market declines? In his April 2017 paper entitled “Forecasting a Volatility Tsunami”, Andrew Thrasher examines several calm-before-the-storm signals for predicting spikes in VIX, which he defines as a 30% advance from a close to an intraday high within five trading days. The signals considers are:

- VIX at a 4-week low.
- Decline in VIX by at least 15% over three trading days.
- Standard deviation (volatility) of VIX during the last 20 trading days at or below the 15th percentile of the full-sample distribution of its 20-day standard deviations for the first time in at least 10 trading days.
- Standard deviation (volatility) of CBOE VVIX (expected volatility of VIX during the next month) during the last 20 trading days at or below the 15th percentile of the full-sample distribution of its 20-day standard deviations for the first time in at least 10 trading days.
- Both signals 3 and 4.

Using daily VIX and VVIX levels during late May 2006 through June 2016, *he finds that:* Keep Reading

**April 20, 2017** - Strategic Allocation, Volatility Effects

What are the ins and outs of crash risk measurement via Value at Risk (VaR)? In their March 2017 paper entitled “A Gentle Introduction to Value at Risk”, Laura Ballotta and Gianluca Fusai provide an introduction to VaR in financial markets, with examples mainly from commodity markets. They address problems related to VaR estimation and backtesting at single asset and portfolio levels. Based largely on mathematics and empirical considerations, *they conclude that:* Keep Reading

**April 17, 2017** - Commodity Futures, Volatility Effects

Is option-implied volatility a useful predictor of returns for commodity futures? In her March 2017 paper entitled “Commodity Option Implied Volatilities and the Expected Futures Returns”, Lin Gao tests the power of option-implied volatilities (with 12-month detrending) for commodities to predict commodity futures returns. Specifically, she each month buys (sells) the fourth of commodities with the lowest (highest) detrended implied volatilities at of the end of the preceding month. To generate continuous return series for liquid commodity futures contracts, she rolls contracts when time-to-expiration decreases to one month. She further compares the implied volatility hedge strategy to five other commodity futures hedge strategies (specified below): (1) momentum; (2) basis; (3) basis-momentum; (4) hedging pressure; and, (5) growth in open interest expressed indollars. Using options data for 25 commodities to calculate end-of-month implied volatilities and contemporaneous commodity futures price and open interest data as available during January 1990 through October 2014, *she finds that:* Keep Reading

**April 6, 2017** - Equity Premium, Size Effect, Volatility Effects

Does disentangling measures of stock illiquidity and market capitalization (size) support belief in an illiquidity premium (a reward for holding illiquid assets)? In the December 2016 version of their paper entitled “The Value of True Liquidity”, Robin Borcherding and Michael Stein investigate this question by controlling the most widely used stock illiquidity metric for size. Specifically they define and calculate true stock liquidities by:

- Calculating for each stock the conventional Amihud monthly measure of illiquidity (average absolute price impact of dollar trading volume during a month).
- Capture unexplained residuals from a regression that controls for the linear relationship (negative correlation) between this conventional illiquidity metric and size.
- Sorting stocks by size and capturing more detail regression residuals within size ranges to control for the non-linear relationship between conventional illiquidity and size.

They then form double-sorted portfolios to compare interactions of conventional and true liquidity with stock volatility and size. Using daily returns, trading data and characteristics for 4,739 U.S. common stocks during January 1990 through September 2015, *they find that:* Keep Reading

**March 24, 2017** - Momentum Investing, Value Premium, Volatility Effects

Are widely used stock factor premiums amenable to timing based on the ratio of aggregate valuation of stocks in the long side to aggregate valuation of stocks in the short side of the factor portfolio (the value spread)? In their March 2017 paper entitled “Contrarian Factor Timing is Deceptively Difficult”, Clifford Asness, Swati Chandra, Antti Ilmanen and Ronen Israel test a strategy that times factor portfolios based on the value spread, in single-factor or multi-factor portfolios. They consider three annually rebalanced factor hedge portfolios: (1) value (High Minus Low book-to-market ratio, or HML); (2) momentum (Up Minus Down, or UMD); and, (3) low beta (Betting Against Beta, or BAB). Their main measure for calculating the value spread is book-to-market ratio, so that a high (low) value spread implies a cheap (expensive) factor. To standardize the value spread, they use z-scores (number of standard deviations above or below the historical average, with positive values indicating undervalued). They use the first 120 months of data to calculate the first z-score. They compare performances of factor portfolios without timing to performances of the same portfolios with a timing overlay that varies capital weights for a factor between 50% and 150% of its passive weight according to the factor’s value spread (scaled to total portfolio weight 100%). They consider variants that are and are not industry neutral. Using factor and return data for large-capitalization U.S. stocks during 1968 through 2016, *they find that:* Keep Reading

**March 22, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

How diversifying are different equity factors within and across country stock markets? In his January 2016 paper entitled “The Power of Equity Factor Diversification”, Ulrich Carl analyzes diversification properties of six equity factors (market excess return, size, value, momentum, low-beta and quality) across 20 developed stock markets. He defines each factor conventionally as returns to a portfolio that is each month long (short) stocks with the highest (lowest) expected returns based on that factor. He considers: (1) cross-country correlations for each factor; (2) cross-factor correlations for each country; (3) cross-country, cross-factor correlations; (4) dynamics of cross-country correlations for each factor based on rolling 36-month windows of returns; and, (5) cross-country correlations for each factor for the 30% lowest and 30% highest market excess returns (tail events). He also applies principal component analysis as another way to evaluate how diverse the 120 country-factor return streams are. Finally, he constructs cross-factor and cross-country portfolios to assess economic value of diversification properties. Using monthly returns in U.S. dollars for the six factors in each of the 20 countries during January 1991 through April 2015, *he finds that:* Keep Reading