A Two-State Capital Asset Pricing Model with Unobservable States
We derive theoretical discrete time asset pricing restrictions on the within state conditional mean equations for the market portfolio and for individual assets under the assumptions: (1) the conditional CAPM holds; (2) asset returns are driven by an underlying unobserved two-state discrete Markov process. We show that the market risk-premiums in the two states can be decomposed into a standard CAPM volatility-level premium plus an additional volatility-uncertainty premium. The latter premium is increasing in the market price of risk, the uncertainty about the next period's state and the difference in volatility between the two states. In an empirical application the model is estimated for the U.S. stock market 1836-2003. We apply a discrete mixture of two Normal Inverse Gaussian (NIG) distributions to represent the return characteristics in the unobservable states. Our results show that the high-risk regime has a volatility of 36.28 % on an annual basis while the low-risk regime has just 14.42%, and the latter is much more frequent. Stock returns display characteristics that support our specification of within state NIG distributions as an alternative to Normal distributions. The risk premiums for the two regimes are 2.79% and 17.86% on an annual basis, but the volatility-uncertainty premium for the two states are shown to give an unimportant contribution to the estimated risk premium. The most striking result, from a practical point of view, is that the average sample risk premium of 4% belongs to the highest quintiles of the estimated conditional risk premiums.
|Date of creation:||06 Dec 2004|
|Contact details of provider:|| Postal: Department of Economics, School of Economics and Management, Lund University, Box 7082, S-220 07 Lund,Sweden|
Phone: +46 +46 222 0000
Fax: +46 +46 2224613
Web page: http://www.nek.lu.se/en
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Adrian R. Pagan & G. William Schwert, 1989.
"Alternative Models For Conditional Stock Volatility,"
NBER Working Papers
2955, National Bureau of Economic Research, Inc.
- Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290.
- Pagan, A.R. & Schwert, G.W., 1989. "Alternative Models For Conditional Stock Volatility," Papers 89-02, Rochester, Business - General.
- Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993.
" On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks,"
Journal of Finance,
American Finance Association, vol. 48(5), pages 1779-1801, December.
- Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
- Lubos Pastor & Robert F. Stambaugh, "undated".
"The Equity Premium and Structural Breaks,"
Rodney L. White Center for Financial Research Working Papers
11-00, Wharton School Rodney L. White Center for Financial Research.
- Luboš Pástor & Robert F. Stambaugh, 2000. "The Equity Premium and Structural Breaks," CRSP working papers 519, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
- Lubos Pastor & Robert F. Stambaugh, 2000. "The Equity Premium and Structural Breaks," NBER Working Papers 7778, National Bureau of Economic Research, Inc.
- Lubos Pástor & Robert F. Stambaugh, "undated". "The Equity Premium and Structural Breaks," Rodney L. White Center for Financial Research Working Papers 21-98, Wharton School Rodney L. White Center for Financial Research.
- L. Ingber, 1996. "Adaptive simulated annealing (ASA): Lessons learned," Lester Ingber Papers 96as, Lester Ingber.
- Scott Mayfield, E., 2004. "Estimating the market risk premium," Journal of Financial Economics, Elsevier, vol. 73(3), pages 465-496, September.
- Morten B. Jensen & Asger Lunde, 2001. "The NIG-S&ARCH model: a fat-tailed, stochastic, and autoregressive conditional heteroskedastic volatility model," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-10.
- French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
- Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
- Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
- Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
- Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
- Hamilton, James D., 1988. "Rational-expectations econometric analysis of changes in regime : An investigation of the term structure of interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 385-423.
- L. Ingber, 1993. "Simulated annealing: Practice versus theory," Lester Ingber Papers 93sa, Lester Ingber.
- Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 65-99.
When requesting a correction, please mention this item's handle: RePEc:hhs:lunewp:2004_028. 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: (David Edgerton)
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 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.