# 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.

**February 10, 2015** - Calendar Effects, Volatility Effects

Does the S&P 500 Implied Volatility Index (VIX) exhibit exploitable seasonality? To check, we calculate average monthly change in VIX and and average iPath S&P 500 VIX Short-Term Futures ETN (VXX) monthly return by calendar month. Using monthly closes of VIX since January 1990 and monthly reverse split-adjusted closes for VXX since January 2009, both through December 2014, *we find that:* Keep Reading

**January 28, 2015** - Volatility Effects

Does the term structure of the the option-implied expected volatility of the S&P 500 Index (VIX, normally measured at a one-month horizon) predict future returns of variance assets such as variance swaps, VIX futures and S&P 500 Index option straddles? In his January 2015 paper entitled “Risk Premia and the VIX Term Structure”, Travis Johnson investigates the relationship between the VIX term structure slope and the variance risk premium as measured by future returns of such assets. He constructs the VIX term structure by each day calculating six values of VIX from prices of S&P 500 Index options with maturities of one, two, three, six, nine and 12 months. He measures the variance risk premium from daily returns of S&P 500 Index variance swaps, VIX futures and S&P 500 Index option straddles of various maturities. Using daily closing quotes for the specified S&P 500 index options and daily returns for the specified variance assets as available during 1996 through 2013, *he finds that:* Keep Reading

**January 26, 2015** - Volatility Effects

Do country stock markets act like individual stocks with respect to return for risk taken? In his December 2014 paper entitled “Is There a Low-Risk Anomaly Across Countries?”, Adam Zaremba relates country stock market performance to four market risk metrics: beta (relative to the capitalization-weighted world stock market), standard deviation of returns, value at risk (fifth percentile of observations) and idiosyncratic (unexplained by world market) volatility. He uses historical intervals of 12 to 24 months as available to estimate risk metrics. He then forms capitalization-weighted portfolios of country markets by ranking them into fifths (quintiles) based on risk metric sorts. He also investigates whether risk/size and risk/book-to-market ratio double-sorts enhance country-level size and value effects. Using monthly returns and accounting data for 78 existing and discontinued country stock market indexes in U.S. dollars during February 1999 through September 2014, *he finds that:* Keep Reading

**December 26, 2014** - Volatility Effects

Are stock betas calculated with price jumps (arguably derived from informed trading) more useful than those calculated conventionally (arguably dominated by noise trading)? In the December 2014 version of their paper entitled “Roughing Up Beta: Continuous vs. Discontinuous Betas, and the Cross-Section of Expected Stock Returns”, Tim Bollerslev, Sophia Zhengzi Li and Viktor Todorov compare the powers of standard or “smooth” stock betas and jumpy or “rough” stock betas to predict stock returns. They measure smooth beta in two ways: from 75-minute returns during normal trading hours; and, from daily close-to-close returns. They measure rough beta also in two ways: from unusual jumps among 75-minute returns during normal trading hours; and, from close-to-open (overnight) returns. For all beta measurements, they employ the past year as the measurement interval. Using intraday prices and firm characteristics for the 985 stocks included in the S&P 500 Index during 1993 through 2010 (an average of 738 stocks per month), *they find that:* Keep Reading

**December 8, 2014** - Volatility Effects

How diverse are the beliefs of experts on the Capital Asset Pricing Model (CAPM)? In his November paper entitled “CAPM: The Model and 233 Comments about It”, Pablo Fernandez reproduces 52 largely disagreeing and 181 largely agreeing comments solicited from professors, finance professionals and Ph.D. students regarding his prior paper entitled “CAPM: an Absurd Model” (summarized in “Forget CAPM Beta?”). The range of beliefs in the comments is extreme, from

“I was shocked at how horrible your paper is. It is without a doubt the worst excuse for an academic study I have ever seen (and believe me that is saying a lot).”

to

“I totally agree with the absurdity of CAPM model.”

After reflecting on the body of comments, *he concludes that:* Keep Reading

**November 11, 2014** - Calendar Effects, Momentum Investing, Size Effect, Value Premium, Volatility Effects

Are gains from tax-loss harvesting, the systematic taking of capital losses to offset capital gains, additive to or subtractive from premiums from portfolio tilts toward common factors such as value, size, momentum and volatility (smart beta)? In their October 2014 paper entitled “Factor Tilts after Tax”, Lisa Goldberg and Ran Leshem look at the effects on portfolio performance of combining factor tilts and tax-loss harvesting. They call the incremental return from tax-loss harvesting tax alpha, which (while investor-specific) is typically in the range 1%-2% per year for wealthy investors holding broad capitalization-weighted portfolios. They test six long-only factor tilts based on Barra equity factor models: (1) value (high earnings yield and book-to-market ratio); (2) momentum (high recent past return); (3) value/momentum; (4) small/value; (5) quality (value stocks with low earnings variability, leverage and volatility); and, (6) minimum volatility/value (low volatility with diversification constraint and value tilt). Their overall benchmark is the MSCI All Country World Index (ACWI). Their tax alpha benchmark derives from a strategy that harvests losses in a capitalization-weighted portfolio (no factor tilts) without deviating far from the overall benchmark. The rebalancing interval is monthly for all portfolios. Using monthly returns for stocks in the benchmark index during January 1999 through December 2013, *they find that:* Keep Reading

**November 6, 2014** - Volatility Effects

Is the market beta of a stock stable across measurement frequencies and measurement intervals? In their October 2014 paper entitled “Which Is the Right ‘Market Beta’?: 1,385 US Companies and 147 Betas/Company in a Single Date”, Jose Paulo Carelli, Pablo Fernandez, Isabel Fernandez Acín and Alberto Ortiz present calculations of 147 betas relative to the S&P 500 Index for each of the S&P 1500 stocks with at least five years of return data on March 31, 2014. They calculate different betas based on monthly, weekly or daily returns over past intervals of one to five years. They then look at the dispersion of each stock’s beta and beta ranking across calculation methods (see the chart below for an example). In assessing dispersion, they focus on the difference between maximum and minimum values by stock. Using daily, weekly and monthly returns for 1,385 stocks and the S&P 500 Index during April 2009 through March 2014, *they find that:* Keep Reading

**October 7, 2014** - Equity Options, Volatility Effects

S&P 500 Index options data imply expected S&P 500 Index volatility (VIX) over the next month. In turn, VIX futures options data imply expected volatility of VIX (VVIX) over the next month. Does VVIX predict stock index option and VIX option returns? In their September 2014 paper entitled “Volatility-of-Volatility Risk”, Darien Huang and Ivan Shaliastovich investigate whether VVIX represents a time-varying risk affecting: (1) S&P 500 Index option returns above and beyond the risk represented by VIX; and (2) VIX futures option returns. They measure risk effects via returns on S&P 500 Index options hedged daily by shorting the S&P 500 Index and VIX futures options hedged daily by shorting VIX futures. Using monthly S&P 500 Index returns, VIX futures returns, VIX, VVIX, S&P 500 Index option prices and VIX option prices during February 2006 through June 2013, *they find that:* Keep Reading

**September 30, 2014** - Volatility Effects

Is the return on CBOE S&P 500 Volatility Index (VIX) futures predictable? In his preliminary paper entitled “The Expected Return of Fear”, Ing-Haw Cheng investigates whether the relationship between VIX futures prices and VIX level predicts the return on VIX futures. He focuses on monthly returns to a continuously-invested position in the nearest available VIX futures contract. He considers several different explanations for the behavior of VIX futures prices. Using VIX futures daily settlement prices during March 2004 through July 2014 (125 months), *he finds that:* Keep Reading

**September 24, 2014** - Volatility Effects

Are there times when investors should avoid low-volatility stocks? In their August 2014 paper entitled “Tactical Timing of Low Volatility Equity Strategies”, Sanne De Boer and James Norman investigate which factors predict the performance of low-volatility stocks relative to a capitalization-weighted index globally since 1980. They focus on two concerns: (1) will low-volatility stocks perform poorly when they are relatively expensive compared to the rest of the market; and, (2) will low-volatility stocks, which tend to pay high dividends, underperform when interest rates rise. Their low-volatility portfolio is a capitalization-weighted collection of country sectors processed quarterly in three steps designed to achieve a balance of low risk and sufficient diversification. They do not account for quarterly portfolio reformation frictions in return calculations. Using weekly data for all country sectors included in the MSCI Developed Markets Index during January 1975 through March 2014, *they find that:* Keep Reading