A representative investor does not know which member of a set of well-defined parametric "structured models'' is best. The investor also suspects that all of the structured models are misspecified. These uncertainties about probability distributions of risks give rise to components of...

In this paper we develop alternative ways to compare asset pricing models when it is understood that their implied stochastic discount factors do not price all portfolios correctly. Unlike comparisons based on x2 statistics associated with null hypothesis that models are correct, our measures of...

Continuous-time Markov processes can be characterized conveniently by their infinitesimal generators. For such processes there exist forward and reverse-time generators. We show how to use these generators to construct moment conditions implied by stationary Markov processes. Generalized method...

Sparked by the recent "great recession" and the role of financial markets, considerable interest exists among researchers within both the academic community and the public sector in modeling and measuring systemic risk. In this essay I draw on experiences with other measurement agendas to place...

We present a novel approach to depicting asset pricing dynamics by characterizing shock exposures and prices for alternative investment horizons. We quantify the shock exposures in terms of elasticities that measure the impact of a current shock on future cash-flow growth. The elasticities are...

We must infer what the future situation would be without our interference, and what changes will be wrought by our actions. Fortunately, or unfortunately, none of these processes is infallible, or indeed ever accurate and complete. Knight (1921)

Asset prices contain information about the probability distribution of future states and the stochastic discounting of these states. Without additional assumptions, probabilities and stochastic discounting cannot be separately identified. Ross (2013) introduced a set of assumptions that restrict...

We construct shock elasticities that are pricing counterparts to impulse response functions. Recall that impulse response functions measure the importance of next-period shocks for future values of a time series. Shock elasticities measure the contributions to the price and to the expected...

Dynamic economic models make predictions about impulse responses that characterize how macroeconomic processes respond to alternative shocks over different horizons. From the perspective of asset pricing, impulse responses quantify the exposure of macroeconomic processes and other cash flows to...

We characterize and measure a long-run risk return tradeoff for the valuation of financial cash flows that are exposed to fluctuations in macroeconomic growth. This tradeoff features components of financial cash flows that are only realized far into the future but are still reflected in current...