We study asset pricing when agents face risk and uncertainty and empirically demonstrate that uncertainty has a substantial effect on asset prices. We measure risk with past volatility and uncertainty with the degree of disagreement of professional forecasters, attributing different weights to each forecaster. We run regressions representing the typical risk-return trade-off and augment these regressions with a measure of uncertainty. We find stronger empirical evidence for a uncertainty-return trade-off than for the traditional risk-return trade-off. We investigate the performance of a two-factor model with risk and uncertainty in the cross-section. * Evan Anderson: Northern Illinois University, Department of Economics, Zulauf 515, DeKalb, IL 60115, phone: (630) 450-0533, email: ewanderson@niu.edu. Eric Ghysels: Department of Finance, Kenan-Flagler Business School, and Department of Economics, University of North Carolina -Chapel Hill, Chapel Hill, NC 27599-3305, phone: (919) 966-5325, email: eghysels@unc.edu. Jennifer L. Juergens: Arizona State University, W.P. Carey School of Business, Department of Finance, Tempe, AZ 85287, phone: (480) 965-3131, email: Jennifer.Juergens@asu.edu. We would like to thank Lars Hansen, Peter Hansen, Chris Jones, Leonid Kogan, Jianjun Miao, Athanasios Orphanides, Simon Potter, Eric Renault, Robert Rich, Tom Sargent and Raman Uppal for very helpful comments. This paper was presented at Northern Illinois University, SAMSI Opening Workshop, 2006 EFA meetings, 2006 Winter Meetings of the Econometric Society, the SAMSI Conference on Model Uncertainty, 2006 NBER Summer Institute Asset Pricing Workshop, 2007 AFA meetings, UC Santa Cruz, University of Illinois at Urbana-Champaign, and University of Wisconsin-Madison. Early versions of the ideas in this paper were also presented at the Board of Governors, the FDIC, the Federal Reserve Bank of New York, Simon Fraser University and Stanford University. We thank seminar participants for helpful comments.Electronic copy of this paper is available at: http://ssrn.com/abstract=890621One of the most studied theoretical relationships in empirical finance is that the expected excess return of the market over a risk-free bond should vary positively and proportionally to the volatility of the market return. This risk-return trade-off is so fundamental that it could well be described as the "first fundamental law of finance." Merton (1973) derived this theoretical relationship in a continuous time model in which all agents have power preferences and hedging concerns are negligible, and it is sometimes referred to as Merton's ICAPM or simply the ICAPM.The empirical evidence for a risk-return trade-off is mixed. Many studies have run versions of the following regression:where r et+1 is the excess return of the market over a risk-free bond, γ is a risk aversion coefficient, and V t is (market) risk. 1 The goal has been to find a significantly positive γ coefficient that captures the trade-off between risk and return. Baillie and DeGennaro (199...

A representative agent fears that his model, a continuous time Markov process with jump and diffusion components, is misspecified and therefore uses robust control theory to make decisions. Under the decision maker's approximating model, cautious behavior puts adjustments for model misspecification into market prices for risk factors. We use a statistical theory of detection to quantify how much model misspecification the decision maker should fear, given his historical data record. A semigroup is a collection of objects connected by something like the law of iterated expectations. The law of iterated expectations defines the semigroup for a Markov process, while similar laws define other semigroups. Related semigroups describe (1) an approximating model; (2) a model misspecification adjustment to the continuation value in the decision maker's Bellman equation; (3) asset prices; and (4) the behavior of the model detection statistics that we use to calibrate how much robustness the decision maker prefers. Semigroups 2, 3, and 4 establish a tight link between the market price of uncertainty and a bound on the error in statistically discriminating between an approximating and a worst case model. (JEL: C00, D51, D81, E1, G12)

* We thank Stan Levine (previously of First Call) and First Call/Thomson for providing the earnings data used in this study. We express our appreciation to Campbell Harvey and anonymous referees for providing invaluable comments and suggestions. This paper is a substantially revised version of an earlier paper by the last two authors, Ghysels and Juergens (2001). We also like to thank Günter Franke, Raman Uppal and Fernando Zapatero for their comments as well as participants at the 2002

This paper is a revised version of my University of Chicago Ph.D. thesis which was completed under the supervision of Lars Peter Hansen. I thank the other members of my committee, Robert E. Lucas, Jr. and Thomas J. Sargent, for their support. I thank Thomas J. Sargent and most of all Lars Peter Hansen for encouragement, guidance, many conversations and comments. I thank Fernando

This paper catalogues formulas that are useful for estimating dynamic linear economic models. We describe algorithms for computing equilibria of an economic model and for recursively computing a Gaussian likelihood function and its gradient with respect to parameters. We display an application to Rosen, Murphy, and Scheinkman's (1994) model of cattle cycles.

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