IDEAS home Printed from https://ideas.repec.org/p/bfi/wpaper/2012-008.html
   My bibliography  Save this paper

Risk Pricing over Alternative Investment Horizons

Author

Listed:
  • Lars Peter Hansen

    () (The University of Chicago)

Abstract

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.

Suggested Citation

  • Lars Peter Hansen, 2012. "Risk Pricing over Alternative Investment Horizons," Working Papers 2012-008, Becker Friedman Institute for Research In Economics.
  • Handle: RePEc:bfi:wpaper:2012-008
    as

    Download full text from publisher

    File URL: https://econresearch.uchicago.edu/sites/econresearch.uchicago.edu/files/BFI_2012-008.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Narayana R. Kocherlakota & Luigi Pistaferri, 2007. "Household Heterogeneity and Real Exchange Rates," Economic Journal, Royal Economic Society, vol. 117(519), pages 1-25, March.
    2. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-673, September.
    3. Constantinides, George M & Duffie, Darrell, 1996. "Asset Pricing with Heterogeneous Consumers," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 219-240, April.
    4. Jules van Binsbergen & Michael Brandt & Ralph Koijen, 2012. "On the Timing and Pricing of Dividends," American Economic Review, American Economic Association, vol. 102(4), pages 1596-1618, June.
    5. Abel, Andrew B, 1990. "Asset Prices under Habit Formation and Catching Up with the Joneses," American Economic Review, American Economic Association, vol. 80(2), pages 38-42, May.
    6. Abel, Andrew B., 2002. "An exploration of the effects of pessimism and doubt on asset returns," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1075-1092, July.
    7. Lars Peter Hansen & Jose A. Scheinkman, 2012. "Recursive utility in a Markov environment with stochastic growth," Working Papers 1380, Princeton University, Department of Economics, Econometric Research Program..
    8. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-262, April.
    9. YiLi Chien & Hanno Lustig, 2010. "The Market Price of Aggregate Risk and the Wealth Distribution," Review of Financial Studies, Society for Financial Studies, vol. 23(4), pages 1596-1650, April.
    10. Fernando Alvarez & Urban J. Jermann, 2000. "Efficiency, Equilibrium, and Asset Pricing with Risk of Default," Econometrica, Econometric Society, vol. 68(4), pages 775-798, July.
    11. Jaroslav Borovička & Mark Hendricks & José A. Scheinkman, 2011. "Risk-Price Dynamics," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(1), pages 3-65, Winter.
      • Jaroslav Borovička & Lars Peter Hansen & Mark Hendricks & José A. Scheinkman, 2009. "Risk Price Dynamics," NBER Working Papers 15506, National Bureau of Economic Research, Inc.
      • Jaroslav Borovicka & Lars Peter Hansen & Mark Hendricks & Jose A. Scheinkman, 2009. "Risk Price Dynamics," Working Papers 1393, Princeton University, Department of Economics, Econometric Research Program..
      • Lars Peter Hansen & Jaroslav BoroviÄ ka & Mark Hendricks & José A. Scheinkman, 2010. "Risk Price Dynamics," Working Papers 2010-004, Becker Friedman Institute for Research In Economics.
    12. Lars Peter Hansen & José A. Scheinkman, 2009. "Long-Term Risk: An Operator Approach," Econometrica, Econometric Society, vol. 77(1), pages 177-234, January.
    13. Sundaresan, Suresh M, 1989. "Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth," Review of Financial Studies, Society for Financial Studies, vol. 2(1), pages 73-89.
    14. Lior Menzly & Tano Santos & Pietro Veronesi, 2004. "Understanding Predictability," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 1-47, February.
    15. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    16. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
    17. Narayana Kocherlakota & Luigi Pistaferri, 2009. "Asset Pricing Implications of Pareto Optimality with Private Information," Journal of Political Economy, University of Chicago Press, vol. 117(3), pages 555-590, June.
    18. Cogley, Timothy, 2002. "Idiosyncratic risk and the equity premium: evidence from the consumer expenditure survey," Journal of Monetary Economics, Elsevier, vol. 49(2), pages 309-334, March.
    19. Cosmin L. Ilut & Martin Schneider, 2014. "Ambiguous Business Cycles," American Economic Review, American Economic Association, vol. 104(8), pages 2368-2399, August.
    20. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-969, July.
    21. Fernando Alvarez & Andrew Atkeson & Patrick J. Kehoe, 2002. "Money, Interest Rates, and Exchange Rates with Endogenously Segmented Markets," Journal of Political Economy, University of Chicago Press, vol. 110(1), pages 73-112, February.
    22. David Backus & Mikhail Chernov & Stanley Zin, 2014. "Sources of Entropy in Representative Agent Models," Journal of Finance, American Finance Association, vol. 69(1), pages 51-99, February.
    23. Alvarez, Fernando & Jermann, Urban J, 2001. "Quantitative Asset Pricing Implications of Endogenous Solvency Constraints," Review of Financial Studies, Society for Financial Studies, vol. 14(4), pages 1117-1151.
    24. Fernando Alvarez & Andrew Atkeson & Patrick J. Kehoe, 2009. "Time-Varying Risk, Interest Rates, and Exchange Rates in General Equilibrium," Review of Economic Studies, Oxford University Press, vol. 76(3), pages 851-878.
    25. Borovička, Jaroslav & Hansen, Lars Peter, 2014. "Examining macroeconomic models through the lens of asset pricing," Journal of Econometrics, Elsevier, vol. 183(1), pages 67-90.
    26. 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, August.
    27. Andrew Atkeson & Robert E. Lucas, 1992. "On Efficient Distribution With Private Information," Review of Economic Studies, Oxford University Press, vol. 59(3), pages 427-453.
    28. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    29. Alon Brav & George M. Constantinides & Christopher C. Geczy, 2002. "Asset Pricing with Heterogeneous Consumers and Limited Participation: Empirical Evidence," Journal of Political Economy, University of Chicago Press, vol. 110(4), pages 793-824, August.
    30. Pok-sang Lam & Stephen G. Cecchetti & Nelson C. Mark, 2000. "Asset Pricing with Distorted Beliefs: Are Equity Returns Too Good to Be True?," American Economic Review, American Economic Association, vol. 90(4), pages 787-805, September.
    31. Heaton, John, 1995. "An Empirical Investigation of Asset Pricing with Temporally Dependent Preference Specifications," Econometrica, Econometric Society, vol. 63(3), pages 681-717, May.
    32. He, Hua & Modest, David M, 1995. "Market Frictions and Consumption-Based Asset Pricing," Journal of Political Economy, University of Chicago Press, vol. 103(1), pages 94-117, February.
    33. Lars Peter Hansen & John C. Heaton & Nan Li, 2008. "Consumption Strikes Back? Measuring Long-Run Risk," Journal of Political Economy, University of Chicago Press, vol. 116(2), pages 260-302, April.
    34. 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, February.
    35. Matthew Shapiro & Mark Watson, 1988. "Sources of Business Cycles Fluctuations," NBER Chapters,in: NBER Macroeconomics Annual 1988, Volume 3, pages 111-156 National Bureau of Economic Research, Inc.
    36. Constantinides, George M, 1990. "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 519-543, June.
    37. Lars Peter Hansen & Thomas J. Sargent & Thomas D. Tallarini, 1999. "Robust Permanent Income and Pricing," Review of Economic Studies, Oxford University Press, vol. 66(4), pages 873-907.
    38. Hansen, Lars Peter & Heaton, John & Lee, Junghoon & Roussanov, Nikolai, 2007. "Intertemporal Substitution and Risk Aversion," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 61 Elsevier.
    39. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    40. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
    41. Lars Peter Hansen, 2012. "Dynamic Valuation Decomposition Within Stochastic Economies," Econometrica, Econometric Society, vol. 80(3), pages 911-967, May.
    42. Lars Hansen & José Scheinkman, 2012. "Pricing growth-rate risk," Finance and Stochastics, Springer, vol. 16(1), pages 1-15, January.
    43. Timothy J. Kehoe & David K. Levine, 1993. "Debt-Constrained Asset Markets," Review of Economic Studies, Oxford University Press, vol. 60(4), pages 865-888.
    44. Garcia, Rene & Renault, Eric & Semenov, Andrei, 2006. "Disentangling risk aversion and intertemporal substitution through a reference level," Finance Research Letters, Elsevier, vol. 3(3), pages 181-193, September.
    45. 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, March.
    46. Zhang, Harold H, 1997. " Endogenous Borrowing Constraints with Incomplete Markets," Journal of Finance, American Finance Association, vol. 52(5), pages 2187-2209, December.
    47. Hansen, Lars Peter & Heaton, John & Luttmer, Erzo G J, 1995. "Econometric Evaluation of Asset Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 8(2), pages 237-274.
    48. Sims, Christopher A, 1972. "Money, Income, and Causality," American Economic Review, American Economic Association, vol. 62(4), pages 540-552, September.
    49. Dybvig, Philip H & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1996. "Long Forward and Zero-Coupon Rates Can Never Fall," The Journal of Business, University of Chicago Press, vol. 69(1), pages 1-25, January.
    50. Mark Rubinstein, 1976. "The Valuation of Uncertain Income Streams and the Pricing of Options," Bell Journal of Economics, The RAND Corporation, vol. 7(2), pages 407-425, Autumn.
    51. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    52. 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.
    53. Luttmer, Erzo G J, 1996. "Asset Pricing in Economies with Frictions," Econometrica, Econometric Society, vol. 64(6), pages 1439-1467, November.
    54. Hengjie Ai & Mariano Massimiliano Croce & Kai Li, 2013. "Toward a Quantitative General Equilibrium Asset Pricing Model with Intangible Capital," Review of Financial Studies, Society for Financial Studies, vol. 26(2), pages 491-530.
    55. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Likuan Qin & Vadim Linetsky, 2014. "Positive Eigenfunctions of Markovian Pricing Operators: Hansen-Scheinkman Factorization, Ross Recovery and Long-Term Pricing," Papers 1411.3075, arXiv.org, revised Sep 2015.
    2. Likuan Qin & Vadim Linetsky, 2014. "Long Term Risk: A Martingale Approach," Papers 1411.3078, arXiv.org, revised Oct 2016.
    3. repec:oup:revfin:v:21:y:2017:i:3:p:945-985. is not listed on IDEAS
    4. John H. Cochrane, 2017. "Macro-Finance," Review of Finance, European Finance Association, vol. 21(3), pages 945-985.

    More about this item

    Keywords

    risk pricing; dynamic value decomposition;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bfi:wpaper:2012-008. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Toni Shears). General contact details of provider: http://edirc.repec.org/data/mfichus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.