Review of Quantitative Finance and Accounting, 20: 207–243, 2003
2003 Kluwer Academic Publishers. Manufactured in The Netherlands.
Jumps and Dynamic Asset Allocation
Graduate School of Business, Fordham University, 113 West 60th Street, New York, NY 10023
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Abstract. This paper analyzes the optimal dynamic asset allocation problem in economies with infrequent events
and where the investment opportunities are stochastic and predictable. Analytical approximations are obtained,
with which a thorough comparative study is performed on the impacts of jumps upon the dynamic decision. The
model is then calibrated to the U.S. equity market. The comparative analysis and the calibration exercise both
show that jump risk not only makes the investor’s allocation more conservative overall but also makes her dynamic
portfolio rebalancing less dramatic over time.
Key words: asset allocation, jumps, non-normality, time-varying investment opportunities, predictability
JEL Classiﬁcation: G11
Traditional asset allocation theory and practice are challenged by two distinct features of
today’s ﬁnancial markets: (1) jumps: asset prices move discontinuously; (2) predictabil-
ity: investment opportunities are time varying and, more importantly, predictable. Jumps
generate more extreme realizations than implied by a normal distribution. Traditional mean-
variance analysis is hence no longer enough: higher moments also play important roles.
Predictability, on the other hand, implies the existence of an intertemporal hedging demand.
This paper investigates the dynamic asset allocation problem in economies with both
features. Analytical approximations are obtained to solutions of the problem, with which a
thorough comparative study is performed on the impacts of jumps upon both the myopic
demand and the intertemporal hedging demand, as well as their interactions with each other.
I then calibrate the model to the U.S. equity market and assess the quantitative impacts
of the jumps under such a dynamic environment. Both the comparative analysis and the
calibration exercises demonstrate that jump risk not only makes the investor’s allocation
more conservative overall but also makes her dynamic portfolio rebalancing less dramatic
The isolated impacts of jumps or predictability on asset allocation have been studied in
the literature a long while ago. Merton (1971), for example, considers the myopic asset
allocation problem when the risky asset has a probability of default. The default event is
captured by a Poisson jump equal to the negative of the current price. Das and Uppal (1998)
consider a similar static problem with multiple risky assets with perfectly correlated jumps.
On predictability, Kim and Omberg (1996) solve a dynamic problem analytically where the