IDEAS home Printed from https://ideas.repec.org/a/eee/ecofin/v26y2013icp177-196.html
   My bibliography  Save this article

Portfolio selection and portfolio frontier with background risk

Author

Listed:
  • Huang, Hung-Hsi
  • Wang, Ching-Ping

Abstract

This study analyzes individual portfolio selection in the presence of background risk. Under the expected utility framework, this study determines necessary and sufficient conditions of utility functions for two-fund monetary separation with independently additive and multiplicative background risks, respectively. Under a mean–variance framework, this study analyzes the portfolio frontier characteristic given dependently additive background risk. The main findings include the two-fund separation property, portfolio frontier shapes, and a portfolio variance comparison between situations with and without background risk and Zero-Beta CAPM. In particular, the portfolio frontier constructed from n risky assets plus one riskless asset is analogous with only n risky assets.

Suggested Citation

  • Huang, Hung-Hsi & Wang, Ching-Ping, 2013. "Portfolio selection and portfolio frontier with background risk," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 177-196.
    • Handle: RePEc:eee:ecofin:v:26:y:2013:i:c:p:177-196
    DOI: 10.1016/j.najef.2013.09.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1062940813000752
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.najef.2013.09.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lintner, John, 1969. "The Aggregation of Investor's Diverse Judgments and Preferences in Purely Competitive Security Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 4(4), pages 347-400, December.
    2. Cardak, Buly A. & Wilkins, Roger, 2009. "The determinants of household risky asset holdings: Australian evidence on background risk and other factors," Journal of Banking & Finance, Elsevier, vol. 33(5), pages 850-860, May.
    3. Gollier Christian & Schlee Edward E, 2006. "Increased Risk-Bearing with Background Risk," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-31, March.
    4. Wenan Fei & Harris Schlesinger, 2008. "Precautionary Insurance Demand With State‐Dependent Background Risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(1), pages 1-16, March.
    5. Guenter Franke & Richard Stapleton & Marti Subrahmanyam, 2004. "Background risk and the demand for state-contingent claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 321-335, January.
    6. Detemple, Jerome & Sundaresan, Suresh, 1999. "Nontraded Asset Valuation with Portfolio Constraints: A Binomial Approach," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 835-872.
    7. Weil, Philippe, 1992. "Equilibrium asset prices with undiversifiable labor income risk," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 769-790.
    8. Lutz, Stefan, 2013. "Risk premia in multi-national enterprises," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 293-305.
    9. Günter Franke & Harris Schlesinger & Richard C. Stapleton, 2006. "Multiplicative Background Risk," Management Science, INFORMS, vol. 52(1), pages 146-153, January.
    10. Menoncin, Francesco, 2002. "Optimal portfolio and background risk: an exact and an approximated solution," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 249-265, October.
    11. Franke, Guenter & Schlesinger, Harris & Stapleton, Richard C., 2011. "Risk taking with additive and multiplicative background risks," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1547-1568, July.
    12. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    13. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2011. "Effects of background risks on cautiousness with an application to a portfolio choice problem," Journal of Economic Theory, Elsevier, vol. 146(1), pages 346-358, January.
    14. Luis M. Viceira, 2001. "Optimal Portfolio Choice for Long‐Horizon Investors with Nontradable Labor Income," Journal of Finance, American Finance Association, vol. 56(2), pages 433-470, April.
    15. Ilia Tsetlin & Robert L. Winkler, 2005. "Risky Choices and Correlated Background Risk," Management Science, INFORMS, vol. 51(9), pages 1336-1345, September.
    16. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    17. Telmer, Chris I, 1993. "Asset-Pricing Puzzles and Incomplete Markets," Journal of Finance, American Finance Association, vol. 48(5), pages 1803-1832, December.
    18. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    19. Henderson, Vicky, 2005. "Explicit solutions to an optimal portfolio choice problem with stochastic income," Journal of Economic Dynamics and Control, Elsevier, vol. 29(7), pages 1237-1266, July.
    20. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373, October.
    21. John Quiggin, 2003. "Background risk in generalized expected utility theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(3), pages 607-611, October.
    22. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    23. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    24. Jiang, Chonghui & Ma, Yongkai & An, Yunbi, 2010. "An analysis of portfolio selection with background risk," Journal of Banking & Finance, Elsevier, vol. 34(12), pages 3055-3060, December.
    25. Fanny Demers & Michel Demers, 1991. "Multivariate Risk Aversion and Uninsurable Risks: Theory and Applications," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 16(1), pages 7-43, June.
    26. Baptista, Alexandre M., 2012. "Portfolio selection with mental accounts and background risk," Journal of Banking & Finance, Elsevier, vol. 36(4), pages 968-980.
    27. 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.
    28. 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.
    29. 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.
    30. Baptista, Alexandre M., 2008. "Optimal delegated portfolio management with background risk," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 977-985, June.
    31. Akuzawa, Toshinao & Nishiyama, Yoshihiko, 2013. "Implied Sharpe ratios of portfolios with options: Application to Nikkei futures and listed options," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 335-357.
    32. Bai, Zhidong & Phoon, Kok Fai & Wang, Keyan & Wong, Wing-Keung, 2013. "The performance of commodity trading advisors: A mean-variance-ratio test approach," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 188-201.
    33. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
    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. Huang, Hung-Hsi & Lin, Shin-Hung & Wang, Ching-Ping & Chiu, Chia-Yung, 2014. "Adjusting MV-efficient portfolio frontier bias for skewed and non-mesokurtic returns," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 59-83.
    2. Marrero, Gustavo A. & Puch, Luis A. & Ramos-Real, Francisco J., 2015. "Mean-variance portfolio methods for energy policy risk management," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 246-264.
    3. Huang, Xiaoxia & Di, Hao, 2016. "Uncertain portfolio selection with background risk," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 284-296.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jiang, Chonghui & Ma, Yongkai & An, Yunbi, 2013. "International portfolio selection with exchange rate risk: A behavioural portfolio theory perspective," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 648-659.
    2. Moawia Alghalith & Xu Guo & Wing-Keung Wong & Lixing Zhu, 2016. "A General Optimal Investment Model In The Presence Of Background Risk," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-8, March.
    3. Jiang, Chonghui & Ma, Yongkai & An, Yunbi, 2010. "An analysis of portfolio selection with background risk," Journal of Banking & Finance, Elsevier, vol. 34(12), pages 3055-3060, December.
    4. Huang, Xiaoxia & Di, Hao, 2016. "Uncertain portfolio selection with background risk," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 284-296.
    5. Guo, Xu & Wong, Wing-Keung & Zhu, Lixing, 2013. "An analysis of portfolio selection with multiplicative background risk," MPRA Paper 51331, University Library of Munich, Germany.
    6. Lin, Wen-chang & Lu, Jin-ray, 2012. "Risky asset allocation and consumption rule in the presence of background risk and insurance markets," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 150-158.
    7. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    8. John H. Cochrane, 2014. "A Mean-Variance Benchmark for Intertemporal Portfolio Theory," Journal of Finance, American Finance Association, vol. 69(1), pages 1-49, February.
    9. Alghalith, Moawia, 2012. "The impact of background risk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6506-6508.
    10. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    11. Huang, Xiaoxia & Yang, Tingting, 2020. "How does background risk affect portfolio choice: An analysis based on uncertain mean-variance model with background risk," Journal of Banking & Finance, Elsevier, vol. 111(C).
    12. Xu, Guo & Wing-Keung, Wong & Lixing, Zhu, 2013. "Comparisons and Characterizations of the Mean-Variance, Mean-VaR, Mean-CVaR Models for Portfolio Selection With Background Risk," MPRA Paper 51827, University Library of Munich, Germany.
    13. Andrew Grant & Steve Satchell, 2019. "Endogenous divorce risk and investment," Journal of Population Economics, Springer;European Society for Population Economics, vol. 32(3), pages 845-876, July.
    14. James Huang & Richard Stapleton, 2017. "Higher-order risk vulnerability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 387-406, February.
    15. Guiso, Luigi & Sodini, Paolo, 2013. "Household Finance: An Emerging Field," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1397-1532, Elsevier.
    16. Xu Guo & Raymond H. Chan & Wing-Keung Wong & Lixing Zhu, 2019. "Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk," Risk Management, Palgrave Macmillan, vol. 21(2), pages 73-98, June.
    17. Li, Ting & Zhang, Weiguo & Xu, Weijun, 2015. "A fuzzy portfolio selection model with background risk," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 505-513.
    18. Gregory Phelan & Alexis Akira Toda, 2015. "On the Robustness of Theoretical Asset Pricing Models," Department of Economics Working Papers 2015-10, Department of Economics, Williams College.
    19. John Y. Campbell & Yeung Lewis Chanb & M. Viceira, 2013. "A multivariate model of strategic asset allocation," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part II, chapter 39, pages 809-848, World Scientific Publishing Co. Pte. Ltd..
    20. Christensen, Peter Ove & Larsen, Kasper & Munk, Claus, 2012. "Equilibrium in securities markets with heterogeneous investors and unspanned income risk," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1035-1063.

    More about this item

    Keywords

    Background risk; Portfolio selection; Portfolio frontier; Two-fund separation; Zero-Beta CAPM;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    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:eee:ecofin:v:26:y:2013:i:c:p:177-196. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/620163 .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.