On Optimal Portfolio Choice Under Stochastic Interest Rates

Posted: 6 Mar 2001

See all articles by Abraham Lioui

Abraham Lioui

EDHEC Business School

Patrice Poncet

ESSEC Business School; Universite Paris I Pantheon Sorbonne

Abstract

In an economy where interest rates and stock price changes follow fairly general stochastic processes, we analyse the portfolio problem of an expected utility investor. When the investment opportunity set is driven by an arbitrary number of state variables, the optimal portfolio strategy is known to contain a speculative element and Merton-Breeden hedging terms against the fluctuations of each and every state variable. While the first component is well identified and easy to work out, the implementation of the last ones is problematic as the investor must identify all the relevant state variables and estimate their distribution characteristics. Using a new decomposition of the optimal wealth, we show that the optimal strategy can be simplified to include, in addition to the speculative component, only two Merton-Breeden type hedging elements, however large is the number of state variables. The first one is associated with interest rate risk and the second one with the risk brought about by the co-movements of the spot interest rate and the market prices of risk. The implementation of the optimal strategy is thus much easier, as it involves estimating the characteristics of the yield curve and the market prices of risk only rather than those of numerous (a priori unknown) state variables. Moreover, the investor's horizon is shown explicitly to play a crucial role in the optimal strategy design, in sharp contrast with the traditional decomposition.

Keywords: Hedging, predictability, market price of risk

Suggested Citation

Lioui, Abraham and Poncet, Patrice, On Optimal Portfolio Choice Under Stochastic Interest Rates. Journal of Economic Dynamics and Control, Available at SSRN: https://ssrn.com/abstract=257428

Abraham Lioui (Contact Author)

EDHEC Business School ( email )

France

Patrice Poncet

ESSEC Business School ( email )

Avenue Bernard Hirsch
BP 105 Cergy Cedex, 95021
France
33 1 3443 3000 (Phone)
33 1 3443 3001 (Fax)

Universite Paris I Pantheon Sorbonne ( email )

Finance Department, UFR 06
17 rue de la Sorbonne
75005 Paris
France
33 1 40 46 2783 (Phone)
33 1 40 46 33 66 (Fax)

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