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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.

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

Option-implied Correlation as Stock Market Return Predictor

Does option-implied correlation, a measure of the expected average correlation between a stock index and its components over a specified horizon, predict stock market behavior? In their January 2017 paper entitled “Option-Implied Correlations, Factor Models, and Market Risk”, Adrian Buss, Lorenzo Schoenleber and Grigory Vilkov examine option-implied correlation as a stock market return predictor. They consider expected average correlations between:

  • Major U.S. stock indexes (S&P 500, S&P 100 and Dow Jones Industrial Average) and their respective component stocks.
  • Major U.S. stock indexes the nine Select Sector SPDR exchange-traded funds (ETF).
  • The nine Select Sector SPDR ETFs and their respective component stocks.

They calculate a correlation risk premium (CRP) as the implied average correlation minus realized average correlation measured over the past month, quarter or year. For comparison, they also calculate variance risk premium (VRP) as the difference between option-implied and realized return variances. Using daily returns for the specified indexes and ETFs (and component stocks of all) and for associated near-the-money options with 30, 91 and 365 days to maturity since January 1996 for S&P 500 and S&P 100 index, since October 1997 for DJIA and since mid-December 1998 for sector ETFs, all through August 2015, they find that: Keep Reading

Betting Against Correlation

What drives the low-risk stock return anomaly, wherein low-risk stocks outperform high-risk stocks (contrary to a reward-for-risk view)? In their February 2017 paper entitled “Betting Against Correlation: Testing Theories of the Low-Risk Effect”, Clifford Asness, Andrea Frazzini, Niels Gormsen and Lasse Pedersen investigate several ways to select low-risk stocks and infer from findings what drives low-risk outperformance as represented by the Betting Against Beta (BAB) strategy that is long low-beta stocks and short high-beta stocks. Specifically, they consider the following stock sorting selection methods:

  • Betting Against Correlation (BAC) – each month: (1) rank stocks into fifths (quintiles) based on volatility; (2) within each volatility quintile, sort stocks into low-correlation and high-correlation halves weighted by correlation rank such that lower correlation stocks have larger weights in low-correlation half and larger correlation stocks have larger weights in the high-correlation half; (3) weight all halves to have market beta one; (4) within each volatility quintile, form a hedge portfolio that is long (short) the low-correlation (high-correlation) half; and (5) compute the BAC factor return as the equal-weighted average of the five hedge portfolio returns.
  • Betting Against Volatility (BAV) – similar to BAC, but switching the order and uses of correlation and volatility sorts.
  • Low MAX (LMAX) – each month, form a value-weighted portfolio that is long (short) the value-weighted large-capitalization and small-capitalization stocks with the lowest (highest) averages of the five highest daily returns over the last month.
  • Scaled MAX (SMAX) – same as LMAX, but adjusted for volatility, using ratios of average of the five highest daily returns over the last month divided by respective volatility over the last month.
  • Idiosyncratic Volatility (IVOL) – each month, regress each firm’s daily stock returns over the given month on the daily returns to the market, size and book-to-market factors. IVOL is the residual volatility of this regression (unexplained by factor betas).

They decompose BAB into correlation (BAC) and volatility (BAV) components to distinguish between financial (leverage constraints, swaying institutional investors away from low-beta stocks) and behavioral (return-chasing) forces, respectively. They then compare BAC and SMAX outputs to distinguish between financial and lottery-preference explanations. Using data as available for the U.S. since January 1926 and for 23 other countries since July 1990, all through December 2015, they find that: Keep Reading

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