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Tempering effects of (dependent) background risks: A mean-variance analysis of portfolio selection

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  • Eichner, Thomas
  • Wagener, Andreas

Abstract

In a mean variance framework, we analyse risk taking in the presence of a (possibly) dependent background risk, exemplified in a linear portfolio selection problem. We first characterise the comparative statics of changes in the distribution and dependence structure of the background risk. For unfair, undesirable and loss-aggravating increases in background risks (both dependent and independent), we then present necessary and sufficient restrictions on preferences such that greater background uncertainty leads to reduced risk taking. With mean-variance preferences, these restrictions boil down to simple conditions on the marginal rate of substitution between risk and return. They can be easily related to familiar notions such as risk vulnerability, properness or standardness.

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  • Eichner, Thomas & Wagener, Andreas, 2012. "Tempering effects of (dependent) background risks: A mean-variance analysis of portfolio selection," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 422-430.
    • Handle: RePEc:eee:mateco:v:48:y:2012:i:6:p:422-430
    DOI: 10.1016/j.jmateco.2012.09.001
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    1. Steven J. Davis & Paul Willen, 2013. "Occupation-Level Income Shocks and Asset Returns: Their Covariance and Implications for Portfolio Choice," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03n04), pages 1-53.
    2. Patrick L. Brockett & Yehuda Kahane, 1992. "Risk, Return, Skewness and Preference," Management Science, INFORMS, vol. 38(6), pages 851-866, June.
    3. Guiso, Luigi & Jappelli, Tullio & Terlizzese, Daniele, 1996. "Income Risk, Borrowing Constraints, and Portfolio Choice," American Economic Review, American Economic Association, vol. 86(1), pages 158-172, March.
    4. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini & Marco Taboga, 2009. "Portfolio Selection With Monotone Mean‐Variance Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 487-521, July.
    5. Epstein, Larry G, 1985. "Decreasing Risk Aversion and Mean-Variance Analysis," Econometrica, Econometric Society, vol. 53(4), pages 945-961, July.
    6. Mayers, David, 1973. "Nonmarketable Assets and the Determination of Capital Asset Prices in the Absence of a Riskless Asset," The Journal of Business, University of Chicago Press, vol. 46(2), pages 258-267, April.
    7. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
    8. Luc Arrondel & Hector Calvo Pardo & Xisco Oliver, 2010. "Temperance in Stock Market Participation: Evidence from France," Economica, London School of Economics and Political Science, vol. 77(306), pages 314-333, April.
    9. Luigi Guiso & Tullio Jappelli, 1998. "Background Uncertainty and the Demand for Insurance Against Insurable Risks," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 23(1), pages 7-27, June.
    10. Peter C. Fishburn & R. Burr Porter, 1976. "Optimal Portfolios with One Safe and One Risky Asset: Effects of Changes in Rate of Return and Risk," Management Science, INFORMS, vol. 22(10), pages 1064-1073, June.
    11. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    12. Wagener, Andreas, 2002. "Prudence and risk vulnerability in two-moment decision models," Economics Letters, Elsevier, vol. 74(2), pages 229-235, January.
    13. Ilia Tsetlin & Robert L. Winkler, 2005. "Risky Choices and Correlated Background Risk," Management Science, INFORMS, vol. 51(9), pages 1336-1345, September.
    14. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    15. Massimo Massa & Andrei Simonov, 2006. "Hedging, Familiarity and Portfolio Choice," Review of Financial Studies, Society for Financial Studies, vol. 19(2), pages 633-685.
    16. K. Borch, 1969. "A Note on Uncertainty and Indifference Curves," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(1), pages 1-4.
    17. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    18. Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-430, June.
    19. Thomas Eichner, 2008. "Mean Variance Vulnerability," Management Science, INFORMS, vol. 54(3), pages 586-593, March.
    20. Ormiston, Michael B & Quiggin, John, 1993. "Two-Parameter Decision Models and Rank-Dependent Expected Utility," Journal of Risk and Uncertainty, Springer, vol. 7(3), pages 273-282, December.
    21. Heaton, John & Lucas, Deborah, 2000. "Portfolio Choice in the Presence of Background Risk," Economic Journal, Royal Economic Society, vol. 110(460), pages 1-26, January.
    22. Solnik, Bruno H., 1978. "Inflation and Optimal Portfolio Choices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(5), pages 903-925, December.
    23. Fatma Lajeri-Chaherli, 2002. "More on Properness: The Case of Mean-Variance Preferences," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 27(1), pages 49-60, June.
    24. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.
    25. Bottazzi, Laura & Pesenti, Paolo & van Wincoop, Eric, 1996. "Wages, profits and the international portfolio puzzle," European Economic Review, Elsevier, vol. 40(2), pages 219-254, February.
    26. Lajeri-Chaherli, Fatma, 2003. "Partial derivatives, comparative risk behavior and concavity of utility functions," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 81-99, August.
    27. Luisa Tibiletti, 1995. "Beneficial changes in random variables via copulas: An application to insurance," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 20(2), pages 191-202, December.
    28. Chamberlain, Gary, 1983. "A characterization of the distributions that imply mean--Variance utility functions," Journal of Economic Theory, Elsevier, vol. 29(1), pages 185-201, February.
    29. Brito, Ney O, 1977. "Marketability Restrictions and the Valuation of Capital Assets under Uncertainty," Journal of Finance, American Finance Association, vol. 32(4), pages 1109-1123, September.
    30. Thomas Eichner & Andreas Wagener, 2003. "Variance Vulnerability, Background Risks, and Mean-Variance Preferences," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 28(2), pages 173-184, December.
    31. Fatma Lajeri-Chaherli, 2004. "Proper and Standard Risk Aversion in Two-Moment Decision Models," Theory and Decision, Springer, vol. 57(3), pages 213-225, November.
    32. Ormiston, Michael B & Schlee, Edward E, 2001. "Mean-Variance Preferences and Investor Behaviour," Economic Journal, Royal Economic Society, vol. 111(474), pages 849-861, October.
    33. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
    34. Patrick L. Brockett & James R. Garven, 1998. "A Reexamination of the Relationship Between Preferences and Moment Orderings by Rational Risk-Averse Investors," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 23(2), pages 127-137, December.
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