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Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets

Author

Listed:
  • George CHACKO

    (Harvard University)

  • Luis M. VICEIRA

    (Harvard University and NBER)

Abstract
This paper analyzes optimal portfolio choice and consumption with stochastic volatility in incomplete markets. Using the Duffie-Epstein (1992) formulation of recursive utility in continuous time, it shows that the optimal portfolio demand for stocks under stochastic volatility varies strongly with the investor's coefficient of relative risk aversion, but only slightly with her elasticity of intertemporal substitution;by contrast, optimal consumption relative to wealth depends on both preference parameters. This paper also shows that stochastic variation in volatility produces an optimal intertemporal heding demand for stocks which is negative when changes in volatility are instantaneously negatively correlated with excess stock returns and investors have coefficients of relative risk aversion larger than one. The absolute size of this demand increase with the size of this correlation, and also with the persistence of shocks to volatility. An application to the US stock market shows that empirically this correlation is negative and large, which implies a negative hedging demand for stocks. This application also shows that only low frequency shocks to volatility exhibit enough persistence to generate sizable hedging demands by long-term, risk averse investors. A comparative statics exercise shows that the size of hedging deamnds is considerably more sensitive to changes in correlation.

Suggested Citation

  • George CHACKO & Luis M. VICEIRA, 1999. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," FAME Research Paper Series rp11, International Center for Financial Asset Management and Engineering.
    • Handle: RePEc:fam:rpseri:rp11
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    References listed on IDEAS

    as
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    Keywords

    Intertemporal portfolio choice; continuous-time; stochastic volatility; long-term investors; recursive utility; characteristic function; spectral GMM.;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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