On Portfolio Separation Theorems with Heterogeneous Beliefs and Attitudes towards Risk
AbstractThe early work of Tobin (1958) showed that portfolio allocation decisions can be reduced to a two stage process: first decide the relative allocation of assets across the risky assets, and second decide how to divide total wealth between the risky assets and the safe asset. This so called twofund separation relies on special assumptions on either returns or preferences. Tobin (1958) analyzed portfolio demand in a mean-variance setting. We revisit the fund separation in settings that allow not only for heterogeneity of preferences for higher order moments, but also for heterogeneity of beliefs among agents. To handle the various sources of heterogeneity, beliefs, and preferences, we follow the framework of Samuelson (1970) and its recent generalization by Chabi-Yo, Leisen, and Renault (2006). This generic approach allows us to derive, for risks that are infinitely small, optimal shares of wealth invested in each security that coincide with those of a Mean-Variance-Skewness-Kurtosis optimizing agent. Besides the standard Sharpe-Lintner CAPM mutual fund separation we obtain additional mutual funds called beliefs portfolios, pertaining to heterogeneity of beliefs, a skewness portfolio similar to Kraus and Litzenberger (1976), beliefs about skewness portfolios with design quite similar to beliefs portfolios, a kurtosis portfolio, and finally portfolio heterogeneity of the preferences for skewness across investors in the economy as well as its covariation with heterogeneity of beliefs. These last two mutual funds are called cross-co-skewness portfolio and cross-co-skewness-beliefs portfolios. Under various circumstances related to return distribution characteristics, cross-agent heterogeneity and market incompleteness, some of these portfolios disappear.
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Bibliographic InfoPaper provided by Bank of Canada in its series Working Papers with number 08-16.
Length: 38 pages
Date of creation: 2008
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Financial markets; Market structure and pricing;
Find related papers by JEL classification:
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
- D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
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- Eric Jondeau & Michael Rockinger, 2006.
"Optimal Portfolio Allocation under Higher Moments,"
European Financial Management,
European Financial Management Association, vol. 12(1), pages 29-55.
- Massimo Guidolin & Allan Timmerman, 2006.
"International asset allocation under regime switching, skew and kurtosis preferences,"
2005-034, Federal Reserve Bank of St. Louis.
- Massimo Guidolin & Allan Timmermann, 2008. "International asset allocation under regime switching, skew, and kurtosis preferences," Review of Financial Studies, Society for Financial Studies, vol. 21(2), pages 889-935, April.
- Lars Peter Hansen & Thomas J. Sargent & Thomas D. Tallarini Jr., 1997.
"Robust Permanent Income and Pricing,"
Levine's Working Paper Archive
596, David K. Levine.
- Markus K. Brunnermeier & Jonathan A. Parker, 2002.
LSE Research Online Documents on Economics
24954, London School of Economics and Political Science, LSE Library.
- Markus K. Brunnermeier & Jonathan A. Parker, 2002. "Optimal Expectations," Working Papers 146, Princeton University, Woodrow Wilson School of Public and International Affairs, Discussion Papers in Economics..
- Brunnermeier, Markus K & Parker, Jonathan A, 2004. "Optimal Expectation," CEPR Discussion Papers 4656, C.E.P.R. Discussion Papers.
- Jonathan A. Parker & Markus K. Brunnermeier, 2004. "Optimal Expectations," Econometric Society 2004 North American Winter Meetings 426, Econometric Society.
- Jonathan Parker & Markus K Brunnermeier, 2002. "Optimal Expectations," FMG Discussion Papers dp434, Financial Markets Group.
- Markus K. Brunnermeier & Jonathan A. Parker, 2004. "Optimal Expectations," NBER Working Papers 10707, National Bureau of Economic Research, Inc.
- Chapman, D.A., 1996.
"Approximating the Asset Pricing Kernel,"
96-02, Rochester, Business - Financial Research and Policy Studies.
- Jennifer Juergens & Evan Anderson & Eric Ghysels, 2004. "Do Heterogeneous Beliefs Matter for Asset Pricing?," Econometric Society 2004 North American Summer Meetings 477, Econometric Society.
- Cass, David & Stiglitz, Joseph E., 1970. "The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds," Journal of Economic Theory, Elsevier, vol. 2(2), pages 122-160, June.
- Heckman, James & Scheinkman, Jose, 1987. "The Importance of Bundling in a Gorman-Lancaster Model of Earnings," Review of Economic Studies, Wiley Blackwell, vol. 54(2), pages 243-55, April.
- Sy-Ming Guu & Kenneth L. Judd, 2001.
"Asymptotic methods for asset market equilibrium analysis,"
Springer, vol. 18(1), pages 127-157.
- Kenneth L. Judd & Sy-Ming Guu, 2001. "Asymptotic Methods for Asset Market Equilibrium Analysis," NBER Working Papers 8135, National Bureau of Economic Research, Inc.
- Cunha, Flavio & Heckman, James J. & Navarro, Salvador, 2004.
"Separating Uncertainty from Heterogeneity in Life Cycle Earnings,"
IZA Discussion Papers
1437, Institute for the Study of Labor (IZA).
- Flavio Cunha & James Heckman & Salvador Navarro, 2005. "Separating uncertainty from heterogeneity in life cycle earnings," Oxford Economic Papers, Oxford University Press, vol. 57(2), pages 191-261, April.
- Flavio Cunha & James J. Heckman & Salvador Navarro, 2005. "Separating Uncertainty from Heterogeneity in Life Cycle Earnings," NBER Working Papers 11024, National Bureau of Economic Research, Inc.
- Cunha, Flavio & Heckman, James & Navarro, Salvador, 2004. "Separating uncertainty from heterogeneity in life cycle earnings," Working Paper Series 2005:6, IFAU - Institute for Evaluation of Labour Market and Education Policy.
- Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, 06.
- Constantinides,George & Duffie,Darrel, 1992.
"Asset pricing with heterogeneous consumers,"
Discussion Paper Serie A
381, University of Bonn, Germany.
- Lars Peter Hansen & Thomas J. Sargent, 2001. "Acknowledging Misspecification in Macroeconomic Theory," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(3), pages 519-535, July.
- Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-55, July.
- Miles S. Kimball, 1989.
"Precautionary Saving in the Small and in the Large,"
NBER Working Papers
2848, National Bureau of Economic Research, Inc.
- Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
- Ross, Stephen A., 1978. "Mutual fund separation in financial theory--The separating distributions," Journal of Economic Theory, Elsevier, vol. 17(2), pages 254-286, April.
- Heaton, John & Lucas, Deborah, 1995. "The importance of investor heterogeneity and financial market imperfections for the behavior of asset prices," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 42(1), pages 1-32, June.
- Evan W. Anderson & Eric Ghysels & Jennifer L. Juergens, 2005. "Do Heterogeneous Beliefs Matter for Asset Pricing?," Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 875-924.
- Robert F. Dittmar, 2002. "Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns," Journal of Finance, American Finance Association, vol. 57(1), pages 369-403, 02.
- Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
- Russell, Thomas, 1980. "Portfolio separation : The analytic case," Economics Letters, Elsevier, vol. 6(1), pages 59-66.
- Samuelson, Paul A, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances, and Higher Moments," Review of Economic Studies, Wiley Blackwell, vol. 37(4), pages 537-42, October.
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