45 Pages Posted: 23 Nov 2019
Date Written: November 12, 2019
We consider an approach to derive the conditional expectation of return quantities under the real-world probability measure, exploiting the form of the projected stochastic discount factor. Our treatment is formulaic in that the expectation can be synthesized from the prices of the risk-free bond, the asset, and options on the asset. The method is free of distributional assumptions, and we use it to study empirical questions related to (i) conditional probability of a disaster and return upside and (ii) spanning hypothesis in the Treasury market. We examine the empirical consistency of our approach and show that our treatment is relevant.
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