# 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.

**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

**March 15, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

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

**March 10, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

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:

- 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.
- 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

**March 3, 2017** - Volatility Effects

“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

**March 2, 2017** - Equity Options, Volatility Effects

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

**March 1, 2017** - Volatility Effects

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

**February 27, 2017** - Momentum Investing, Size Effect, Value Premium, Volatility Effects

Are there plenty of exchange-traded funds (ETF) offering positive or negative exposures to widely accepted factor premiums? In his February 2017 paper entitled “Are Exchange-Traded Funds Harvesting Factor Premiums?”, David Blitz analyzes the exposures of U.S. equity ETFs to market, size, value, momentum and volatility factors. Specifically, he calculates factor betas (exposures) from a multi-factor regression of monthly excess (relative to the risk-free rate) total returns for each ETF versus market, small-minus-big size (SMB), high-minus-low value (HML), winners-minus-losers momentum (WML) and low-minus-high volatility (LV-HV) factor returns during 2011 through 2015. His overall sample consists of 415 U.S. equity ETFs with least 36 months of return history as of the end of 2015. He also considers subsamples consisting of: (1) 103 smart beta ETFs that explicitly target factor premiums, including fundamentally weighted and high-dividend funds; and, (2) the remaining 312 conventional ETFs, including sector funds and funds with conflicting factor exposures. He includes lists of the 10 ETFs with the most positive and the 10 ETFs with the most negative exposures to each factor from among the 100 largest ETFs. Using monthly Assets under Management (AuM) and total returns for the specified 415 ETFs, along with the monthly risk-free rate and the selected factor premiums during January 2011 through December 2015, *he finds that:* Keep Reading

**February 9, 2017** - Bonds, Volatility Effects

“Equity Market and Treasuries Variance Risk Premiums as Return Predictors” reports a finding, among others, that the variance risk premium for 10-year U.S. Treasury notes (T-note) predicts near-term returns for those notes (as manifested via futures). However, the methods used to calculate the variance risk premium are complex. Is there a simple way to exploit the predictive power found? To investigate, we test whether a simple measure of the volatility risk premium (VRP) for T-notes predicts returns for the iShares 7-10 Year Treasury Bond (IEF) exchange-traded fund. Specifically we:

- Calculate daily realized volatility of IEF as the standard deviation of daily total returns over the past 21 trading days, multiplied by the square root of 252 to annualize.
- Use daily closes of CBOE/CBOT 10-year U.S. Treasury Note Volatility Index (TYVIX) as annualized implied volatility.
- Calculate the daily T-note VRP as TYVIX minus IEF realized volatility.

VRP here differs from that in the referenced research in three ways: (1) it is a volatility premium rather than a variance premium based on standard deviation rather than the square of standard deviation; (2) it is implied volatility minus expected realized volatility, rather than the reverse, and so should be mostly positive; and, (3) estimation of expected realized volatility is much simpler. When TYVIX has daily closes on non-market days, we ignore those closes. When TYVIX does not have daily closes on market days, we reuse the most recent value of TYVIX. These exceptions are rare. Using daily IEF dividend-adjusted prices since December 2002 and daily closes of TYVIX since January 2003 (earliest available), both through January 2017, *we find that:* Keep Reading

**February 8, 2017** - Bonds, Equity Premium, Volatility Effects

Do bonds, like equity markets, offer a variance risk premium (VRP)? If so, does the bond VRP predict bond returns? In their January 2017 paper entitled “Variance Risk Premia on Stocks and Bonds”, Philippe Mueller, Petar Sabtchevsky, Andrea Vedolin and Paul Whelan examine and compare the equity VRP (EVRP) via the S&P 500 Index and U.S. Treasuries VRP (TVRP) via 5-year, 10-year and 30-year U.S. Treasuries. They specify VRP generally as the difference between the variance indicated by past values of variance (realized) and that indicated by current option prices (implied). Their VRP calculation involves:

- To forecast daily realized variances at a one-month horizon, they first calculate high-frequency returns from intra-day price data of rolling futures series for each of 5-year, 10-year and 30-year Treasury notes and bonds and for the S&P 500 Index. They then apply a fairly complex regression model that manipulates squared inception-to-date returns (at least one year) and accounts for the effect of return jumps.
- To calculate daily implied variances for Treasuries at a one-month horizon, they employ end-of-day prices on cross-sections of options on Treasury futures. For the S&P 500 Index, they use the square of VIX.
- To calculate daily EVRP and TVRPs with one-month horizons, subtract respective implied variances from forecasted realized variances.

When relating VRPs to future returns for both Treasuries and the S&P 500 Index, they calculate returns from fully collateralized futures positions. Using the specified futures, index and options data during July 1990 through December 2014, *they find that:* Keep Reading

**February 3, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

Does suppressing unrelated risks from stock factor portfolios improve performance? In their January 2017 paper entitled “Diversify and Purify Factor Premiums in Equity Markets”, Raul Leote de Carvalho, Lu Xiao, François Soupé and Patrick Dugnolle investigate how to improve the capture of four types of stock factor premiums: value (12 measures); quality (16 measures); low-risk (two measures); and, momentum (10 measures). They standardize the different factor measurement scales based on respective medians and standard deviations, and they discard outliers. Their baseline factors portfolios employ constant leverage (CL) by each month taking 100% long (100% short) positions in stocks with factor values associated with the highest (lowest) expected returns. They strip unrelated risks from baseline portfolios by:

- SN – imposing sector neutrality by segregating stocks into 10 sectors before ranking them for assignment to long and short sides of the factor portfolio.
- CV – replacing constant leverage by each month weighting each stock in the portfolio to target a specified volatility based on its actual volatility over the past three years.
- HB – hedging the market beta of the portfolio each month based on market betas of individual stocks calculated over the past three years by taking positions in the capitalization-weighted market portfolio and cash.
- HS – hedging the size beta of the portfolio each month based on size betas of individual stocks calculated over the past three years by taking positions in the equal-weighted market portfolio and the capitalization-weighted market portfolio.

They examine effects of combining measures within factor types, combining types of factors and excluding short sides of factor portfolios. They also look at U.S., Europe and Japan separately. Their portfolio performance metric is the information ratio, annualized average return divided by annualized standard deviation of returns. Using data for stocks in the MSCI World Index since January 1997, in the S&P 500 Index since January 1990, in the STOXX Europe 600 Index since January 1992 and in the Japan Topix 500 Index since August 1993, all through November 2016, *they find that:* Keep Reading