Long Term Risk: An Operator Approach
AbstractWe create an analytical structure that reveals the long run risk-return relationship for nonlinear continuous time Markov environments. We do so by studying an eigenvalue problem associated with a positive eigenfunction for a conveniently chosen family of valuation operators. This family forms a semigroup whose members are indexed by the elapsed time between payoff and valuation dates. We represent the semigroup using a positive process with three components: an exponential term constructed from the eigenvalue, a martingale and a transient eigenfunction term. The eigenvalue encodes the risk adjustment, the martingale alters the probability measure to capture long run approximation, and the eigenfunction gives the long run dependence on the Markov state. We establish existence and uniqueness of the relevant eigenvalue and eigenfunction. By showing how changes in the stochastic growth components of cash flows induce changes in the corresponding eigenvalues and eigenfunctions, we reveal a long-run risk return tradeoff.
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Date of creation: Oct 2006
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- Hansen, Lars Peter & Scheinkman, José A., 2008. "Long Term Risk : An Operator Approach," Open Access publications from UniversitÃ© Paris-Dauphine urn:hdl:123456789/2282, Université Paris-Dauphine.
- Lars Peter Hansen & Jose A Sheinkman, 2007. "Long-term Risk: An Operator Approach," Levine's Bibliography 122247000000001669, UCLA Department of Economics.
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
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- Breeden, Douglas T., 1979. "An intertemporal asset pricing model with stochastic consumption and investment opportunities," Journal of Financial Economics, Elsevier, vol. 7(3), pages 265-296, September.
- Lars Peter Hansen & Jose Alexandre Scheinkman, 1993.
"Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes,"
NBER Technical Working Papers
0141, National Bureau of Economic Research, Inc.
- Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
- Xiaohong Chen & Lars Peter Hansen & Jose A. Scheinkman, 2009.
"Principal components and the long run,"
CeMMAP working papers
CWP07/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Ravi Bansal & Amir Yaron, 2004.
"Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles,"
Journal of Finance,
American Finance Association, vol. 59(4), pages 1481-1509, 08.
- Ravi Bansal & Amir Yaron, 2000. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," NBER Working Papers 8059, National Bureau of Economic Research, Inc.
- Stutzer, Michael, 2003. "Portfolio choice with endogenous utility: a large deviations approach," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 365-386.
- Schroder, Mark & Skiadas, Costis, 1999. "Optimal Consumption and Portfolio Selection with Stochastic Differential Utility," Journal of Economic Theory, Elsevier, vol. 89(1), pages 68-126, November.
- Lettau, Martin & Wachter, Jessica, 2005.
"Why is Long-Horizon Equity Less Risky? A Duration-based Explanation of the Value Premium,"
CEPR Discussion Papers
4921, C.E.P.R. Discussion Papers.
- Martin Lettau & Jessica A. Wachter, 2007. "Why Is Long-Horizon Equity Less Risky? A Duration-Based Explanation of the Value Premium," Journal of Finance, American Finance Association, vol. 62(1), pages 55-92, 02.
- Martin Lettau & Jessica Wachter, 2005. "Why is Long-Horizon Equity Less Risky? A Duration-Based Explanation of the Value Premium," NBER Working Papers 11144, National Bureau of Economic Research, Inc.
- Jessica Wachter & Martin Lettau, 2005. "Why is Long-Horizon Equity Less Risky? A Duration-Based Explanation of the Value Premium," 2005 Meeting Papers 302, Society for Economic Dynamics.
- David K. Backus & Stanley E. Zin, 1994.
"Reverse Engineering the Yield Curve,"
94-09, New York University, Leonard N. Stern School of Business, Department of Economics.
- repec:cup:macdyn:v:1:y:1997:i:2:p:333-54 is not listed on IDEAS
- Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
- Evan W. Anderson & Lars Peter Hansen & Thomas J. Sargent, 2003. "A Quartet of Semigroups for Model Specification, Robustness, Prices of Risk, and Model Detection," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 68-123, 03.
- Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-94, March.
- Nina Boyarchenko & Sergei Levendorski&icaron;, 2007. "The Eigenfunction Expansion Method In Multi-Factor Quadratic Term Structure Models," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 503-539.
- Kreps, David M & Porteus, Evan L, 1978.
"Temporal Resolution of Uncertainty and Dynamic Choice Theory,"
Econometric Society, vol. 46(1), pages 185-200, January.
- David M Kreps & Evan L Porteus, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Levine's Working Paper Archive 625018000000000009, David K. Levine.
- Fernando Alvarez & Urban J. Jermann, 2005. "Using Asset Prices to Measure the Persistence of the Marginal Utility of Wealth," Econometrica, Econometric Society, vol. 73(6), pages 1977-2016, November.
- Bansal, Ravi & Lehmann, Bruce N., 1997. "Growth-Optimal Portfolio Restrictions On Asset Pricing Models," Macroeconomic Dynamics, Cambridge University Press, vol. 1(02), pages 333-354, June.
- Lars Peter Hansen, 2008. "Modeling the Long Run: Valuation in Dynamic Stochastic Economies," NBER Working Papers 14243, National Bureau of Economic Research, Inc.
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