Download Option Prices and the Cross Section of Equity Returns

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.
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VIX as an Equity Market Factor. 1986‐2000.
Ang, Hodrick, Xing and Zhang (JoF,2006). 6
CBOE SKEW Index
Option Implied (Negative of) Skewness
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Market SKEW as a Factor. 1996‐2007.
Chang, Christoffersen and Jacobs (JFE, 2013)
Regress returns on market skew. Sort on skew beta
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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?
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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)
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Cumulative Returns on Factor Portfolios (%)
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Are We Just Capturing Market, Size, Value and Momentum Factors? No!
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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.
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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