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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.

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Making Minimum Variance Stock Portfolios Work

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

Forecasting VIX Spikes

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:

  1. VIX at a 4-week low.
  2. Decline in VIX by at least 15% over three trading days.
  3. 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.
  4. 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.
  5. Both signals 3 and 4.

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

Value-at-Risk Estimation Tutorial

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

Implied Volatility Trading Strategy for Commodity Futures

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

True Iliquidity and Future Stock Returns

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

Valuation-based Factor Timing

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

Equity Factor Diversification Benefits

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

Which Equity Factors Are Predictable?

Are the returns of factors widely used to predict the cross-section of stock returns themselves predictable? In the January 2016 draft of his paper entitled “Equity Factor Predictability”, Ulrich Carl analyzes predictability of market, size (market capitalization), value (book-to-market ratio), momentum (returns from 12 months ago to one month ago), low beta (betting against beta) and quality factor returns. All factor returns derive from hedge portfolios that are long (short) stocks with high (low) expected returns based on their factor values. He employs a broad range of economic and financial variables in four sets and multiple ways of testing predictability to ensure robustness of findings and limit model/data snooping bias. Predictability tests he applies include: combinations of simple forecasts (mean or median of single-variable regression forecasts); principal component analysis to distill forecasting variables into a few independent predictive factors; and, methods that adjust variable emphasis according to their respective past performances. He considers several predictability evaluation metrics, including: mean squared error compared to that of the historical average return; utility gain of timing based on predictability; and, information ratio (difference in return divided by difference in risk) relative to the historical average return. He mostly examines next-month forecasts with a one-month gap between predictive variable measurement and forecasted return over two test periods: 1975-2013 and 1950-2013. Using monthly returns for the six factors (start dates ranging from 1928 to 1958), a large set of financial variables since 1928 and a large set of economic variables since 1962, all through November 2013, he finds that: Keep Reading

Purified Factor Portfolios

How attractive are purified factor portfolios, constructed to focus on one factor by avoiding exposures to other factors? In their January 2017 paper entitled “Pure Factor Portfolios and Multivariate Regression Analysis”, Roger Clarke, Harindra de Silva and Steven Thorley explore a multivariate regression approach to generating pure factor portfolios. They consider five widely studied factors: value (earnings yield); momentum (cumulative return from 12 months ago to one month ago); size (market capitalization); equity market beta; and, profitability (gross profit margin). They also consider bond beta (regression of stock returns on 10-year U.S. Treasury note returns) to examine interest rate risk. They each month reform two types of factor portfolios:

  1. Primary – a factor portfolio with weights that deviate simply from market weights based on analysis of just one factor, with differences from market portfolio weights scaled by market capitalization.
  2. Pure – a factor portfolio derived from a multiple regression that isolates each factor, ensuring that it has zero exposures to all other factors.

They measure factor portfolio performance based on: average difference in monthly returns between each factor portfolio and the market portfolio; annualized standard deviation of the underlying monthly return differences; 1-factor (market) alpha; and, information ratio (alpha divided by incremental risk to the market portfolio). Using return and factor data for the 1,000 largest U.S. stocks during 1967 through 2016, they find that: Keep Reading

Simple Test of ‘Option-implied Correlation as Stock Market Return Predictor’

“Option-implied Correlation as Stock Market Return Predictor” finds that implied correlation for a broad stock market index relative to its components may be useful for predicting equity market returns. To corroborate, we look at the readily available CBOE S&P 500 Implied Correlation Indexes. The indexes are a series of three based on sequential pairings of December S&P 500 Index options and January options for the 50 largest S&P 500 stocks with maturities of about one and two years, so two of the three are active at any time. CBOE discontinues calculation of the “near” series as the options approach maturity in November and starts a new “far” series. Presumably, investors are overly pessimistic (optimistic) about future opportunity for diversification when the indexes are high (low). Using daily levels of the available 12 implied correlation index two-year series and daily returns of the S&P 500 Index during January 2007 through mid-February 2017, we find that: Keep Reading

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