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Optimal Investment With Default Risk

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  • Yuanfeng Hou

    (Yale University)

  • Xiangrong Jin

    (FAME and University of Lausanne)

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    Abstract

    In this paper, we investigate how investors who face both equity risk and credit risk would optimally allocate their financial wealth in a dynamic continuous-time setup. We model credit risk through the defaultable zero-coupon bond and solve the dynamics of its price after pricing it. Using stochastic control methods, we obtain a closed-form solution to this investment problem and characterize its variation with respect to different factors in the economy. We find that non-zero recovery rate of the credit-risky bond affects investors' decision in a fundamental way. Because of this, investors try to time the market conditions in their decision making process. It also induces hedging term in this setup of otherwise deterministic investment opportunity set. Through numerical examples, we show that the inclusion of credit market is shown to be able to enhance investors' welfare.

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    Bibliographic Info

    Paper provided by International Center for Financial Asset Management and Engineering in its series FAME Research Paper Series with number rp46b.

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    Date of creation: Mar 2002
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    Handle: RePEc:fam:rpseri:rp46b

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    Related research

    Keywords: Default Risk; Corporate Bond; Asset Allocation; Welfare Analysis;

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    References

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    1. Ammer, John & Campbell, John, 1993. "What Moves the Stock and Bond Markets? A Variance Decomposition for Long-Term Asset Returns," Scholarly Articles 3382857, Harvard University Department of Economics.
    2. Longstaff, Francis A & Schwartz, Eduardo S, 1995. " A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
    3. John Y. Campbell & Luis M. Viceira, 1998. "Who Should Buy Long-Term Bonds?," NBER Working Papers 6801, National Bureau of Economic Research, Inc.
    4. Philip H. Dybvig & Chi-fu Huang, 1988. "Nonnegative Wealth, Absence of Arbitrage, and Feasible Consumption Plans," Cowles Foundation Discussion Papers 860, Cowles Foundation for Research in Economics, Yale University.
    5. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    6. Pierre Collin-Dufresne, 2001. "Do Credit Spreads Reflect Stationary Leverage Ratios?," Journal of Finance, American Finance Association, vol. 56(5), pages 1929-1957, October.
    7. Kwan, Simon H., 1996. "Firm-specific information and the correlation between individual stocks and bonds," Journal of Financial Economics, Elsevier, vol. 40(1), pages 63-80, January.
    8. Jarrow, Robert A & Turnbull, Stuart M, 1995. " Pricing Derivatives on Financial Securities Subject to Credit Risk," Journal of Finance, American Finance Association, vol. 50(1), pages 53-85, March.
    9. Duffee, Gregory R, 1999. "Estimating the Price of Default Risk," Review of Financial Studies, Society for Financial Studies, vol. 12(1), pages 197-226.
    10. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
    11. Leland, Hayne E & Toft, Klaus Bjerre, 1996. " Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, vol. 51(3), pages 987-1019, July.
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    Cited by:
    1. Tomasz Bielecki & Inwon Jang, 2006. "Portfolio optimization with a defaultable security," Asia-Pacific Financial Markets, Springer, vol. 13(2), pages 113-127, June.
    2. Kraft, Holger & Steffensen, Mogens, 2008. "How to invest optimally in corporate bonds: A reduced-form approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 348-385, February.

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