March 2017

Stochastic Compounding and Uncertain Valuation

Lars Peter Hansen and Jose A. Scheinkman

Exploring long-term implications of valuation leads us to recover and use a distorted probability measure that reflects the long-term implications for risk pricing. This measure is typically distinct from the physical and the risk neutral measures that are well known in mathematical finance. We apply a generalized version of Perron-Frobenius theory to construct this probability measure and present several applications. We employ Perron-Frobenius methods to i) explore the observational implications of risk adjustments and investor beliefs as reflected in asset market data; ii) catalog alternative forms of misspecification of parametric valuation models; and iii) characterize how long-term components of growth-rate risk impact investor preferences implied by Kreps-Porteus style utility recursions.

Pages: 21-50|Title of book: After the Flood: How the Great Recession Changed Economic Thought |Publisher: The University of Chicago Press |Tags: Uncertainty and Valuation|Export BibTeX >

Author = {Hansen, Lars Peter and Scheinkman, Jose},
Booktitle = {After The Flood: How the Great Recession Changed Economic Thought},
Pages = {21-50},
Publisher = {The University of Chicago Press},
Title = {Stochastic Compounding and Uncertain Valuation},
Year = {2017}}

January 2017 | Article

Ambiguity Aversion and Model Misspecification: An Economic Perspective

Lars Peter Hansen, Massimo Marinacci

How to accommodate potential model misspecification is a challenging topic. On the one hand, if we have very precise information about the nature of the misspecification, then presumably we would fix or repair the model. On the other hand, if we allow for too large of a set of possible ways for a model to be misspecified, we may find that little can be said of value in confronting the decision problem. The interplay between tractability and conceptual appeal is a central consideration when producing tools that aid in statistical decision making. Our comment will describe other important advances in decision theory within the economics discipline that are designed to confront uncertainty conceived broadly to include an aversion to ambiguity and a concern about model misspecification. We will also delineate some special challenges for applications in the social sciences.

Journal: Statistical Science|Volume: 31|Pages: 511-515|Tags: Risk, Robustness and Ambiguity|Export BibTeX >
  title={Ambiguity Aversion and Model Misspecification: An Economic Perspective},
  author={Hansen, Lars Peter and Marinacci, Massimo},
  journal={Statistical Science},
January 2017 | Chapter

Term Structure of Uncertainty in the Macroeconomy

Lars Peter Hansen, Jaroslav Borovička

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 macroeconomic shocks. Financial markets provide compensations to investors who are exposed to these shocks. Adopting an asset pricing vantage point, we describe and apply methods for computing exposures to macroeconomic shocks and the implied compensations represented as elasticities over alternative payoff horizons. The outcome is a term structure of macroeconomic uncertainty.


You can find a verbal description of this research here.

Volume: 2B, Chapter 20|Pages: 1641-1694|Title of book: Handbook of Macroeconomics|Editor(s): John B. Taylor, Harald Uhlig|Place of Publication: Netherlands and Great Britain|Publisher: Elsevier|Tags: Financial Market Linkages to the Macroeconomy, Uncertainty and Valuation|Export BibTeX >
  title={Term Structure of Uncertainty in the Macroeconomy},
  author={Borovi{v{c}}ka, Jaroslav and Hansen, Lars Peter},
  journal={Handbook of Macroeconomics},
March 2016 | Article

Misspecified Recovery

Jaroslav Borovička, Lars Peter Hansen, José A. Scheinkman

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.

Journal: Journal of Finance|Tags: Econometrics, Uncertainty and Valuation|Export BibTeX >
  title={Misspecified Recovery},
  author={Borovi{v{c}}ka, Jaroslav and Hansen, Lars Peter and Scheinkman, Jos{'e} A},
  journal={The Journal of Finance},
  publisher={Wiley Online Library}
January 2015 | Article

Four Types of Ignorance

Lars Peter Hansen, Thomas J. Sargent

This paper studies alternative ways of representing uncertainty about a law of motion in a version of a classic macroeconomic targetting problem of Milton Friedman (1953). We study both “unstructured uncertainty” – ignorance of the conditional distribution of the target next period as a function of states and controls – and more “structured uncertainty” – ignorance of the probability distribution of a response coefficient in an otherwise fully trusted specification of the conditional distribution of next period׳s target. We study whether and how different uncertainties affect Friedman׳s advice to be cautious in using a quantitative model to fine tune macroeconomic outcomes.

Journal: Journal of Monetary Economics|Volume: 69|Issue Number: January|Pages: 97-113|Tags: Risk, Robustness and Ambiguity|Export BibTeX >
  title={Four Types of Ignorance},
  author={Hansen, Lars Peter and Sargent, Thomas J.},
  journal={Journal of Monetary Economics},
November 2014 | Article

Examining Macroeconomic Models Through the Lens of Asset Pricing

Jaroslav Borovička, Lars Peter Hansen

Dynamic stochastic equilibrium models of the macro economy are designed to match the macro time series including impulse response functions. Since these models aim to be structural, they also have implications for asset pricing. To assess these implications, we explore asset pricing counterparts to impulse response functions. We use the resulting dynamic value decomposition (DVD) methods to quantify the exposures of macroeconomic cash flows to shocks over alternative investment horizons and the corresponding prices or compensations that investors must receive because of the exposure to such shocks. We build on the continuous-time methods developed in Hansen and Scheinkman (2010), Borovicka et al. (2011) and Hansen (2011) by constructing discrete-time shock elasticities that measure the sensitivity of cash flows and their prices to economic shocks including economic shocks featured in the empirical macroeconomics literature. By design, our methods are applicable to economic models that are nonlinear, including models with stochastic volatility. We illustrate our methods by analyzing the asset pricing model of Ai et al. (2010) with tangible and intangible capital.

Journal: Journal of Econometrics|Volume: 183|Issue Number: 1|Pages: 67-90|Tags: Financial Market Linkages to the Macroeconomy, Uncertainty and Valuation|Export BibTeX >
  title={Examining Macroeconomic Models Through the Lens of Asset Pricing},
  author={Borovi{v{c}}ka, Jaroslav and Hansen, Lars Peter},
  journal={Journal of Econometrics},
September 2014 | Article

Shock Elasticities and Impulse Responses

Jaroslav Borovička, Lars Peter Hansen, Jose A. Scheinkman

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 future cash flow from changes in the exposure to a shock in the next period. They are elasticities because their measurements compute proportionate changes. We show a particularly close link between these objects in environments with Brownian information structures.

Journal: Mathematics and Financial Economics|Volume: 8|Issue Number: 4|Pages: 333-354|Tags: Financial Market Linkages to the Macroeconomy, Uncertainty and Valuation|Export BibTeX >
  title={Shock Elasticities and Impulse responses},
  author={Borovi{v{c}}ka, Jaroslav and Hansen, Lars Peter and Scheinkman, Jos{'e} A},
  journal={Mathematics and Financial Economics},
July 2014 | Article

Uncertainty Outside and Inside Economic Models (Nobel Lecture)

Lars Peter Hansen

“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)

Journal: Journal of Political Economy|Volume: 122|Issue Number: 5|Pages: 945-987|Tags: Econometrics, Financial Market Linkages to the Macroeconomy, Risk, Robustness and Ambiguity, Uncertainty and Valuation|Export BibTeX >

Author = {Hansen, Lars},
Date-Added = {2016-03-28 00:37:47 +0000},
Date-Modified = {2016-03-28 00:40:13 +0000},
Journal = {Journal of Political Economy},
Number = {5},
Pages = {945 – 987},
Title = {Nobel Lecture: Uncertainty Outside and Inside Economic Models},
Url = {},
Volume = {122},
Year = {2014},
Bdsk-Url-1 = {}}

January 2013 | Chapter

Risk Pricing over Alternative Investment Horizons

Lars Peter Hansen

I explore methods that characterize model-based valuation of stochastically growing cash flows. Following previous research, I use stochastic discount factors as a convenient device to depict asset values. I extend that literature by focusing on the impact of compounding these discount factors over alternative investment horizons. In modeling cash flows, I also incorporate stochastic growth factors. I explore dynamic value decomposition (DVD) methods that capture concurrent compounding of a stochastic growth and discount factors in determining risk-adjusted values. These methods are supported by factorizations that extract martingale components of stochastic growth and discount factors. These components reveal which ingredients of a model have long-term implications for valuation. The resulting martingales imply convenient changes in measure that are distinct from those used in mathematical finance, and they provide the foundations for analyzing model-based implications for the term structure of risk prices. As an illustration of the methods, I re-examine some recent preference based models. I also use the martingale extraction to revisit the value implications of some benchmark models with market restrictions and heterogenous consumers.

Pages: 1571-1611|Title of book: Handbook of the Economics of Finance|Editor(s): George M Constantinides, Milton Harris, and René M Stulz|Place of Publication: Amsterdam|Publisher: North Holland|Tags: Uncertainty and Valuation|Export BibTeX >
  title={Risk Pricing Over Alternative Investment Horizons},
  author={Hansen, Lars Peter},
November 2012 | Chapter

Challenges in Identifying and Measuring Systemic Risk

Lars Peter Hansen

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 in perspective the challenge of quantifying systemic risk, or more generally, of providing empirical constructs that can enhance our understanding of linkages between financial markets and the macroeconomy.

Title of book: Risk Topography: Systemic Risk and Macro Modeling|Editor(s): Markus Konrad Brunnermeier and Arvind Krishnamurthy|Place of Publication: Chicago|Publisher: University of Chicago Press|Tags: Financial Market Linkages to the Macroeconomy|Export BibTeX >
  title={Challenges in Identifying and Measuring Systemic Risk},
  author={Hansen, Lars Peter},
  institution={National Bureau of Economic Research}