The Pricing of Systematic and Idiosyncratic Variance Risk

We use equity options to examine how systematic and idiosyncratic variance risk are priced. The variances of both systematic and idiosyncratic stock returns comove countercyclically and command sizeable risk premia. Systematic variance risk exhibits a negative price of risk, whereas common idiosyncratic variance risk carries a large positive risk premium in the cross-section of options. This differential pricing of systematic and idiosyncratic variance risk explains several phenomena, (1) the relative prices of index and individual options, (2) the sizeable cross-sectional variation in stock option expensiveness, (3) the volatility mispricing puzzle documented by Goyal and Saretto (2009), and (4) the substantial returns earned on various option portfolio strategies. We find little evidence for ICAPMand liquidity-based explanations of the observed patterns, but find support for theories of financial intermediation under capital constraints that account for the positive market price of idiosyncratic variance risk. Systematic return (co)variances play a pivotal role in asset allocation and for the risk-return tradeoff in financial markets. There is now ample evidence that variances and correlations vary stochastically over time and exhibit several patterns. Andersen, Bollerslev, Diebold, and Ebens (2001) document that individual stock variances tend to move together and correlations are high when variance is high. Both variances and correlations tend to increase during crisis periods and when the stock market performs poorly.1 As a result, states of the economy in which aggregate consumption is low and state prices are high coincide with high stock variances and correlations. Equities may thus offer fewer diversification benefits and less consumption insurance than suggested by looking at their unconditional moments. Augmenting investors’ portfolios with traded instruments that allow hedging systematic variance risk therefore yields substantial welfare gains, and systematic variance risk carries a negative risk premium.2 How idiosyncratic variance risk is priced in financial markets remains, however, largely an open question. Equity options are the natural type of traded instruments to take positions on (co)variance risk. The market for equity options has been expanding dramatically over the past decades.3 Equity options are now among the most important derivative securities and are used by institutional and individual investors for a variety of purposes, ranging from speculative trading on stock price movements to the transfer of (co)variance risk between investors. An improved understanding of the pricing of the various sources of risk in options markets and the benefits of diverse options strategies is essential for educating investors and informed policy-making. Option prices exhibit a number of empirical regularities. First, as documented by Carr and Wu (2009) and Driessen, Maenhout, and Vilkov (2009), there are sizeable differences between the prices of index and stock options. Index options are “expensive,” that is, they carry a large negative variance risk premium (meaning that the future variance implicit in index option prices In a seminal study, Black (1976) shows that volatility rises in falling financial markets. Longin and Solnik (2001) document that correlations rise in periods of high volatility. Erb, Harvey, and Viskanta (1994) show that stock market correlations tend to be higher when several countries are simultaneously in recession. Campbell, Lettau, Malkiel, and Xu (2001) document that idiosyncratic variances are countercyclical and positively related to market variance. See Driessen, Maenhout, and Vilkov (2009), Egloff, Leippold, and Wu (2009), DaFonseca, Grasselli, and Ielpo (2009), and Buraschi, Porchia, and Trojani (2010). Exchange-listed options began trading in the U.S. when the CBOE started on April 26, 1973. A total of 911 calls on 16 stocks were listed initially. Put trading was introduced in 1977. Options volume was 1.1 million contracts in the first year and exceeded 100 million contracts by 1981. Trading topped 1 (2) billion in 2004 (2006) and reached 3.59 billion contracts in 2009. See www.cboe. com for a historical digest.