ABSTRACT Asset prices contain information about the probability distribution of future states and the stochastic discounting of those states as used by investors. To better understand the challenge in distinguishing investors' beliefs from risk‐adjusted discounting, we use Perron–Frobenius Theory to isolate a positive martingale component of the stochastic discount factor process. This component recovers a probability measure that absorbs long‐term risk adjustments. When the martingale is not degenerate, surmising that this recovered probability captures investors' beliefs distorts inference about risk‐return tradeoffs. Stochastic discount factors in many structural models of asset prices have empirically relevant martingale components.

We characterize and measure a long-term risk-return trade-off for the valuation of cash flows exposed to fluctuations in macroeconomic growth. This trade-off features risk prices of cash flows that are realized far into the future but continue to be reflected in asset values. We apply this analysis to claims on aggregate cash flows and to cash flows from value and growth portfolios by imputing values to the long-run dynamic responses of cash flows to macroeconomic shocks. We explore the sensitivity of our results to features of the economic valuation model and of the model cash flow dynamics. (c) 2008 by The University of Chicago. All rights reserved.

. We develop models of robust decision-making and pricing when there are contemporaneous big and small shocks. We illustrate these models using a stochasticgrowth economy. Large shocks are infrequent changes in the technological growth rate, and small shocks are continuous movements in the technology process. Large shocks evolve as a Markov jump process whereas small shocks are a Brownian motion. Robust decision-making is formalized as a two-player game. In contrast to rational expectations agents, our investors are decision-makers who treat models as approximations and fear misspecication. As an algorithmic device to enforce robustness, investors imagine a second, malevolent player, who has the ability to perturb the baseline model. We study two economies, each of which decentralizes a robust resource allocation problem with hidden growth rates. The economies dier in the manner in which the the model is viewed as an approximation. We compare the pricing implications to those that em...

In this article we characterize and estimate the process for short-term interest rates using federal funds interest rate data. We presume that we are observing a discrete-time sample of a stationary scalar diffusion. We concentrate on a class of models in which the local volatility elasticity is constant and the drift has a flexible specification. To accommodate missing observations and to break the link between “economic time” and calendar time, we model the sampling scheme as an increasing process that is not directly observed. We propose and implement two new methods for estimation. We find evidence for a volatility elasticity between one and one-half and two. When interest rates are high, local mean reversion is small and the mechanism for inducing stationarity is the increased volatility of the diffusion process.

Abstract We use decision theory to confront uncertainty that is sufficiently broad to incorporate “models as approximations.” We presume the existence of a featured collection of what we call “structured models” that have explicit substantive motivations. The decision-maker confronts uncertainty through the lens of these models, but also views these models as simplifications, and hence, as misspecified. We extend the max–min analysis under model ambiguity to incorporate the uncertainty induced by acknowledging that the models used in decision making are simplified approximations. Formally, we provide an axiomatic rationale for a decision criterion that incorporates model misspecification concerns. We then extend our analysis beyond the max-min case allowing for a more general criterion that encompasses a Bayesian formulation.