# 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 12, 2014** - Momentum Investing, Volatility Effects

Is it possible to predict serial correlation (autocorrelation) of stock returns, and thereby enhance reversal and momentum strategies. In the January 2014 version of his paper entitled “The Information Content of Option Prices Regarding Future Stock Return Serial Correlation”, Scott Murray investigates the relationship between the variance ratio (the ratio of realized to implied stock return variance, a measure of the variance risk premium) to stock return serial correlation. He calculates realized variance at the end of each month from daily log stock returns over the prior three months. He calculates implied variance at the end of each month as the square of the volatility implied by at-the-money 0.5 delta call and put options one month from expiration. He first measures the power of the variance ratio to predict stock return serial correlation. He then tests the effectiveness of this predictive power to enhance reversal and momentum stock trading. Using the specified return and option data for all U.S. stocks with listed options during January 1996 through December 2012, *he finds that:* Keep Reading

**December 9, 2013** - Volatility Effects

Do upside (downside) market volatility surprises scare investors out of (draw investors into) the stock market? In the November 2013 version of his paper entitled “Dynamic Asset Allocation Strategies Based on Unexpected Volatility”, Valeriy Zakamulin investigates the ability of unexpected stock market volatility to predict future market returns. He calculates stock market index volatility for a month using daily returns. He then regresses monthly volatility versus next-month volatility to predict next-month volatility. Unexpected volatility is the series of differences between predicted and actual monthly volatility. He tests the ability of unexpected volatility to predict stock market returns via regression tests and two market timing strategies. One strategy dynamically weights positions in a stock index and cash (the risk-free asset) depending on the prior-month difference between actual and past average unexpected index volatility. The other strategy holds a 100% stock index (cash) position when the prior-month difference between actual and average past unexpected index volatility is negative (positive). His initial volatility prediction uses the first 240 months of data, and subsequent predictions use inception-to-date data. He ignores trading frictions involved in strategy implementation. Using daily and monthly (approximated) total returns of the S&P 500 Index and the Dow Jones Industrial Average (DJIA), along with the U.S. Treasury bill (T-bill) yield as the return on cash, during January 1950 through December 2012, *he finds that:* Keep Reading

**November 19, 2013** - Strategic Allocation, Volatility Effects

Are implied volatility futures good diversifiers of underlying indexes? Do implied volatility futures for different indexes represent a reliable pair trading opportunity? In their November 2013 paper entitled “Investment Strategies with VIX and VSTOXX Futures”, Silvia Stanescu and Radu Tunaru update the case for hedging conventional stock and stock-bond portfolios with near-term implied volatility futures for the S&P 500 Index (VIX) and the Euro STOXX 50 Index (VSTOXX). For this analysis, they use data for the U.S. and European stock market indexes, associated implied volatility futures and U.S. and European aggregate bond indexes from March 2004 for U.S. assets (VIX futures inception) and from May 2009 for European assets (VSTOXX futures inception), both through February 2012. They also investigate a statistical arbitrage (pair trading) strategy exploiting a regression-based prediction of the trend in the gap between VIX and VSTOXX during the last six months of 2012. Using daily data for the specified indexes and implied volatility futures contracts, *they find that:* Keep Reading

**November 13, 2013** - Volatility Effects

An array of leveraged exchange-traded funds (ETF) track short-term (daily) changes in popular indexes. Over longer holding periods, these ETFs tend to veer off track. The cumulative veer can be large. How do leveraged ETFs actually perform over a multi-year period? What factors contribute to their failure to achieve targeted leverage versus underlying indexes? To investigate, we consider:

- 46 ProShares 2X and -2X leveraged equity index ETFs (23 matched long-short pairs), with start date 4/23/07 (determined by the youngest of these funds), encompassing broad indexes, style indexes and sector indexes.
- 10 ProShares 3X and -3X leveraged equity index ETFs (five matched long-short pairs), with start date 2/11/10, encompassing broad indexes only.

We measure achieved average daily leverage by comparing the average daily return of each leveraged ETF to the average daily return of a 1X ETF designed to track the same index. We measure achieved long-term leverage by comparing the terminal return of each leveraged ETF to the terminal return of a 1X ETF designed to track the same index. Using daily adjusted prices for all these funds through 10/31/13, *we find that:* Keep Reading

**October 31, 2013** - Equity Options, Volatility Effects

Is there exploitable feedback between stock returns and behaviors of associated options due to concentration of informed traders in one market or the other? In the October 2013 version of their paper entitled “The Joint Cross Section of Stocks and Options”, Byeong-Je An, Andrew Ang, Turan Baliand and Nusret Cakici investigate lead-lag relationships between stock returns and changes in associated option-implied volatilities. In case there is some asymmetry, they examine call option and put option implied volatilities separately. They focus on near-term options with delta of 0.5 and expiration in 30 days. Using daily stock returns and associated call and put option implied volatilities (available from OptionMetrics), firm fundamentals and risk adjustment factors during January 1996 through December 2011, *they find that:* Keep Reading

**October 4, 2013** - Momentum Investing, Strategic Allocation, Volatility Effects

Has Modern Portfolio Theory failed to deliver over the past decade because users employ long-term averages for expected returns, volatilities and correlations that do not respond to changing market environments? Do short-term estimates of these key inputs work better? In their May 2012 paper entitled “Adaptive Asset Allocation: A Primer”, Adam Butler, Michael Philbrick and Rodrigo Gordillo backtest a progression of strategies culminating in an Adaptive Asset Allocation (AAA) strategy that incorporates return predictability from relative momentum (last 120 trading days, about six months), volatility predictability from recent volatility (last 60 trading days) and pairwise correlation predictability from recent correlations (last 250 trading days). Their tests employ nine asset class indexes (U.S. stocks, European stocks, Japanese stocks, U.S. real estate investment trusts (REIT), International REITs, intermediate-term U.S. Treasuries, long-term U.S. Treasuries and commodities) and a spot gold price series. They reform portfolios monthly based on evolving return, volatility and correlation forecasts. They ignore trading frictions as negligible for “intelligent retail or institutional investors” via mutual funds or Exchange Traded Funds. Using daily returns for the nine indexes and spot gold) to test six strategies during January 1995 through March 2012, *they find that:* Keep Reading

**September 20, 2013** - Bonds, Volatility Effects

Do low-risk bonds, like low-risk stocks, tend to outperform their high-risk counterparts? In their September 2013 paper entitled “Low-Risk Anomalies in Global Fixed Income: Evidence from Major Broad Markets”, Raul Leote de Carvalho, Patrick Dugnolle, Xiao Lu and Pierre Moulin investigate whether low-risk beats high-risk for different measures of risk and different bond segments. They consider only measures of risk that account for the fact that the risk of a bond inherently decreases as it approaches maturity, emphasizing duration-times-yield (yield elasticity). They focus on corporate investment grade bonds denominated in dollars, euros, pounds or yen, but also consider government and high-yield corporate bonds worldwide. Each month, they rank a selected category of bonds by risk into fifths (quintile portfolios). For calculation of monthly quintile returns, they weight individual bond returns by market capitalization. They reinvest coupons the end of the month. They focus on quintile portfolio Sharpe ratios to test the risk-performance relationship. Using monthly risk data and returns for 85,442 individual bonds during January 1997 through December 2012 (192 months), *they find that:* Keep Reading

**September 5, 2013** - Volatility Effects

Some experts interpret stock market return volatility as an indicator of investor sentiment, with high (low) volatility indicating ascendancy of fear (greed). Volatility of volatility (VoV) would thus indicate uncertainty in investor sentiment. Does the risk associated with this uncertainty depress stock prices and thereby predict relatively high future stock market returns? To investigate, we consider two measures of U.S. stock market volatility: (1) realized volatility, calculated as the standard deviation of daily S&P 500 Index return over the last 21 trading days (annualized); and, (2) *implied* volatility as measured by the Chicago Board Options Exchange Market Volatility Index (VIX). For both, we calculate VoV as the standard deviation of volatility over the past 21 trading days and test the ability of VoV to predict SPDR S&P 500 (SPY) returns. To avoid overlap in volatility and VoV calculations, we focus on monthly return intervals. Using daily values of the S&P 500 Index since December 1989 and VIX since inception in January 1990, and monthly dividend-adjusted SPY closes since inception in January 1993, all through July 2013, *we find that:* Keep Reading

**August 12, 2013** - Volatility Effects

Does exceptional (idiosyncratic) stock volatility exploitably predict future returns? In her April 2013 paper entitled “Revisiting Idiosyncratic Volatility and Stock Returns”, Fatma Sonmez re-examines the relationship between idiosyncratic volatility and future stock returns. She defines idiosyncratic volatility as the standard deviation of daily residuals from monthly regressions of returns (in excess of the risk-free rate) for each stock versus Fama-French model factors. Using daily returns and contemporaneous market, size and book-to-market factors for U.S. listed stocks during 1963 through 2008, *she finds that:* Keep Reading

**August 1, 2013** - Volatility Effects

Prior research (see “The Implied-Realized Volatility Gap as Return Predictor” and “Variance Risk Premium Predictive Power Worldwide”) indicates that the stock market volatility (or variance) risk premium, measured as the difference between the volatility implied by prices of stock index options and some measure of recent historical index volatility, significantly predicts future stock market returns. Does this finding support a trading strategy? To investigate, we consider a simple volatility risk premium (VRP) measured as S&P 500 Index option-implied volatility (VIX) minus S&P 500 Index historical volatility (standard deviation of daily returns over the past 21 trading days). Since VIX is an annualized percentage, we annualize historical daily volatility by multiplying by the square root of 252. We then relate this simple VRP to future S&P 500 Index returns and apply a VRP-related signal to time SPDR S&P 500 (SPY). Using daily levels of the S&P 500 Index and VIX since January 1990, and daily values of SPY and the 13-week U.S. Treasury bill (T-bill) yield as return on cash since the end of January 1993, all through mid-July 2013, *we find that:* Keep Reading