# 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.

**October 5, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

Do broad (capitalization-weighted) stock market indexes exhibit factor tilts that may indicate concentrations in corresponding risks? In their August 2017 paper entitled “What’s in Your Benchmark? A Factor Analysis of Major Market Indexes”, Ananth Madhavan, Aleksander Sobczyk and Andrew Ang examine past and present long-only factor exposures of several popular market capitalization indexes. Their analysis involves (1) estimating the factor characteristics of each stock in a broad index; (2) aggregating the characteristics across all stocks in the index; and (3) matching aggregated characteristics to a mimicking portfolio of five indexes representing value, size, quality, momentum and low volatility styles, adjusted for estimated expense ratios. For broad U.S. stock indexes, the five long-only style indexes are:

- Value – MSCI USA Enhanced Value Index.
- Size – MSCI USA Risk Weighted Index.
- Quality – MSCI USA Sector Neutral Quality Index.
- Momentum – MSCI USA Momentum Index.
- Low Volatility – MSCI USA Minimum Volatility Index.

For broad international indexes, they use corresponding long-only MSCI World style indexes. Using quarterly stock and index data from the end of March 2002 through the end of March 2017, *they find that:* Keep Reading

**September 7, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

How many, and which, factors should investors include when constructing multi-factor smart beta portfolios? In their August 2017 paper entitled “How Many Factors? Does Adding Momentum and Volatility Improve Performance”, Mohammed Elgammal, Fatma Ahmed, David McMillan and Ali Al-Amari examine whether adding momentum and low-volatility factors enhances the Fama-French 5-factor (market, size, book-to-market, profitability, investment) model of stock returns. They consider statistical significance, economic sense and investment import. Specifically, they:

- Determine whether factor regression coefficient signs and values distinguish between several pairs of high-risk and low-risk style portfolios (assuming stock style portfolio performance differences derive from differences in firm economic risk).
- Relate time-varying factor betas across style portfolios to variation in economic and market risks as proxied by changes in U.S. industrial production and S&P 500 Index implied volatility (VIX), respectively.
- Test an out-of-sample trading rule based on extrapolation of factor betas from 5-year historical rolling windows to predict next-month return for five sets (book-to-market, profitability, investment, momentum, quality) of four style portfolios (by double-sorting with size) and picking the portfolio within a set with the highest predicted returns.

Using monthly factor return data during January 1990 through October 2016, *they find that:* Keep Reading

**August 15, 2017** - Momentum Investing, Volatility Effects

What aspect of momentum strategy volatility is best for risk management? In his July 2017 paper entitled “Risk-Managed Momentum: The Effect of Leverage Constraints”, Federico Nucera examines stock momentum strategy risk management via different aspects of realized strategy variance with and without latitude for leverage. Specifically, he considers the following stock momentum strategy variations:

- Conventional – each month long (short) the value-weighted tenth, or decile, of stocks that are the biggest winners (losers) last month per Kenneth French’s specifications.
- Full Variance Weighting – each month weighting the conventional momentum portfolio by 1.44% (12% annual volatility) divided by the full variance of daily conventional momentum strategy returns over the past six months.
- Positive Semi-variance Weighting – each month weighting the conventional momentum portfolio by 0.68% divided by the semi-variance of positive daily conventional momentum strategy returns over the past six months.
- Negative Semi-variance Weighting – each month weighting the conventional momentum portfolio by 0.76% divided by the semi-variance of negative daily conventional momentum strategy returns over the past six months.

For each variation, he considers full weights (leverage), weights limited to 1.5X leverage and weights limited to 1.0X (no leverage). He focuses on gross annualized Sharpe ratio as the key performance metric. Using daily and monthly value-weighted momentum decile portfolio returns for a broad sample of U.S. stocks during November 1926 through December 2016, *he finds that:* Keep Reading

**August 11, 2017** - Calendar Effects, Volatility Effects

Do the returns of iPath S&P 500 VIX Short-term Futures ETN (VXX) and VelocityShares Daily Inverse VIX Short-term ETN (XIV) vary systematically across days of the week? To investigate, we look at daily close-to-open, open-to-close and close-to-close returns for both. Using daily split-adjusted opening and closing prices for VXX during February 2009 through July 2017 and for XIV during December 2010 through July 2017, *we find that:*

Keep Reading

**July 10, 2017** - Equity Premium, Volatility Effects

Is the Capital Asset Pricing Model (CAPM), which relates the return of an asset to its non-diversifiable risk, called beta, worth learning? In his June 2017 paper (provocatively) entitled “Is It Ethical to Teach That Beta and CAPM Explain Something?”, Pablo Fernandez tackles this question. Based on the body of relevant research, *he concludes that:*

Keep Reading

**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