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Risk, Uncertainty, and Expected Returns∗
, 2011
"... NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff o ..."
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NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.
Risk, Uncertainty, and Expected Returns—Internet Appendix A Variance Risk Premium and Empirical Measurement
"... The central empirical variable of this paper, as a proxy for economic uncertainty, is the market variance risk premium (VRP)—which is not directly observable but can be estimated from the difference between modelfree optionimplied variance and the conditional expectation of realized variance. A.1 ..."
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The central empirical variable of this paper, as a proxy for economic uncertainty, is the market variance risk premium (VRP)—which is not directly observable but can be estimated from the difference between modelfree optionimplied variance and the conditional expectation of realized variance. A.1 Variance Risk Premium: Definition and Measurement In order to define the modelfree implied variance, let Ct(T,K) denote the price of a European call option maturing at time T with strike price K, and B(t, T) denote the price of a time t zerocoupon bond maturing at time T. As shown by Carr and Madan (1998) and BrittenJones and Neuberger (2000), among others, the market’s riskneutral Q expectation of the return variance σ2t+1 conditional on the information set Ωt, or the implied variance IVt at timet, can be expressed in a “modelfree ” fashion as a portfolio of European calls,