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Option Prices and the Cross Section of Equity Returns Peter Christoffersen [email protected] 1 Overview Is there information in option prices that is useful for equity portfolio managers? I will show you recent academic research that suggest the answer is: Yes. 1. Portfolio allocation with option implied estimates of equity volatility and skewness 2. CBOE’s VIX and SKEW as equity market risk factors 3. CBOE’s “Oil VIX” as an equity market factor 2 First Topic: Firm Specific Option Implied Moments (OIMs) • Each month, compute option implied volatility, skewness (tail asymmetry), and kurtosis (symmetric fat tails) from 3‐month equity options on the largest 800 US stocks. • For each moment, sort stock into three groups (terciles). Keep track of the stock returns the following month. • Repeat exercise each month from January, 1996 through 2005. OptionMetrics data. 3 Conrad, Dittmar, Ghysels (Journal of Finance, 2013). 4 Second Topic: VIX and SKEW as Market Risk Factors • For each stock i, run a time series regression on monthly data of the form • Then sort the stocks into quintiles based on the size of their regression coefficients vol • Finally compute the value‐weighted average return for each quintile in the following month. Roll through the sample. • Use change in VIX for VOL as a measure of unexpected volatility. 5 VIX as an Equity Market Factor. 1986‐2000. Ang, Hodrick, Xing and Zhang (JoF,2006). 6 CBOE SKEW Index Option Implied (Negative of) Skewness 7 Market SKEW as a Factor. 1996‐2007. Chang, Christoffersen and Jacobs (JFE, 2013) Regress returns on market skew. Sort on skew beta 8 Third Topic: Option‐Implied Oil Price Volatility (OVX) as an Equity Factor • Lots of evidence on the interrelation between the oil price and the macro‐economy • Some controversy over causality between oil price and growth. Kilian versus Hamilton. • Hamilton: “Nine out of ten of the U.S. recessions since World War II were preceded by a spike up in the oil price” • Evidence of nonlinear relationships • Financialization of commodities in 2004‐2005. • Effects on the cross‐section of equity returns? 9 10 Cross‐Sectional Sorts • At the end of each month we use daily stock returns, market returns, and option‐implied oil vol changes during the month to estimate • We sort stocks into quintiles based on the IVOil beta. • We form five value‐weighted portfolios at the end of each month and record the daily returns of each quintile portfolio for the following month. • We repeat the procedure by rolling the beta estimation window forward one month at a time. 11 Sorting Stocks Oil Vol Beta Christoffersen and Pan (WP, 2014) 12 Cumulative Returns on Factor Portfolios (%) 13 Are We Just Capturing Market, Size, Value and Momentum Factors? No! 14 Is Option‐Implied Oil Volatility a Plausible Stock Market Risk Factor? • During the pre‐financialization period (1990‐ 2004), lagged changes in IVOil did not forecast stock market returns nor the market level volatility. • In the post‐financialization period (2005‐2012) lagged changes in oil forecasts both the monthly stock market return and the monthly stock market volatility. 15 Summary – Portfolio allocation with higher moments estimated from individual equity options. – CBOE’s VIX and SKEW as equity market factors – CBOE’s oil VIX as an equity market factor 16