Scandinavian Working Papers in Economics

Working Papers,
Copenhagen Business School, Department of Finance

No 2000-9: Optimal Consumption and Investment Strategies with Stochastic Interest Rates

Carsten Sørensen and Claus Munk
Additional contact information
Carsten Sørensen: Department of Finance, Copenhagen Business School, Postal: Department of Finance, Copenhagen Business School, Solbjerg Plads 3, A5, DK-2000 Frederiksberg, Denmark
Claus Munk: Dept. of Accounting, Finance & Law, SDU - Odense University, Postal: Dept. of Accounting, Finance & Law, SDU - Odense University, Campusvej 55, DK-5230 Odense M, Denmark

Abstract: We study the consumption and investment choice of a time-additive power utility investor and demonstrate how theinvestor should optimally hedge changes in the op- portunity set. The investor is allowed to invest in stocks and interest rate dependent assets in a continuous-time dynamically complete market. In particular, we demon- strate that under stochastic interest rates the investor optimally hedges changes in the term structure of interest rates by investing in acoupon bond, or portfolio of bonds, with a payment schedule that matches the forward-expected (i.e certainty equivalent) consumption pattern. This is of conceptual importance since the hedge portfolio does not depend on the speci c term structure dynamics (only through the consequences for the optimal consumption pattern). We consider two explicit examples where the dynamics of the term structure of interest rates are given by theVasicek-model and a three-factor non-Markovian Heath-Jarrow-Morton model.

Keywords: Investment; Strategies

JEL-codes: A00

42 pages, May 1, 2001

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