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On Portfolio Separation Theorems with Heterogeneous Beliefs and Attitudes towards Risk

Author

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  • Fousseni Chabi-Yo
  • Eric Ghysels
  • Eric Renault

Abstract

The 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.

Suggested Citation

  • Fousseni Chabi-Yo & Eric Ghysels & Eric Renault, 2008. "On Portfolio Separation Theorems with Heterogeneous Beliefs and Attitudes towards Risk," Staff Working Papers 08-16, Bank of Canada.
  • Handle: RePEc:bca:bocawp:08-16
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    References listed on IDEAS

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    1. Markus K. Brunnermeier & Jonathan A. Parker, 2005. "Optimal Expectations," American Economic Review, American Economic Association, vol. 95(4), pages 1092-1118, September.
    2. Sy-Ming Guu & Kenneth L. Judd, 2001. "Asymptotic methods for asset market equilibrium analysis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(1), pages 127-157.
    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. Eric Jondeau & Michael Rockinger, 2006. "Optimal Portfolio Allocation under Higher Moments," European Financial Management, European Financial Management Association, vol. 12(1), pages 29-55.
    5. Stephen A. Ross, 2005. "Mutual Fund Separation in Financial Theory—The Separating Distributions," World Scientific Book Chapters,in: Theory Of Valuation, chapter 10, pages 309-356 World Scientific Publishing Co. Pte. Ltd..
    6. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," Review of Economic Studies, Oxford University Press, vol. 25(2), pages 65-86.
    7. 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.
    8. 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.
    9. 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.
    10. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    11. 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.
    12. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    13. 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.
    14. 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.
    15. Chapman, David A, 1997. " Approximating the Asset Pricing Kernel," Journal of Finance, American Finance Association, vol. 52(4), pages 1383-1410, September.
    16. 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.
    17. 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, February.
    18. 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.
    19. James Heckman & Jose Scheinkman, 1987. "The Importance of Bundling in a Gorman-Lancaster Model of Earnings," Review of Economic Studies, Oxford University Press, vol. 54(2), pages 243-255.
    20. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
    21. Paul A. Samuelson, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments," Review of Economic Studies, Oxford University Press, vol. 37(4), pages 537-542.
    22. Russell, Thomas, 1980. "Portfolio separation : The analytic case," Economics Letters, Elsevier, vol. 6(1), pages 59-66.
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    Keywords

    Financial markets; Market structure and pricing;

    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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