文档介绍：Q UANTITATIVE F INANCE V OLUME 1 (2001) 45–72 RESEARCH PAPER
I NSTITUTE OF P HYSICS P UBLISHING quant.
Asset allocation and derivatives
Martin B Haugh and Andrew W Lo1
MIT Sloan School of Management and Operations Research Center,
50 Memorial Drive, E52–432, Cambridge, MA 02142–1347, USA
E-mail: ******@
Received 14 November 2000
Abstract
The fact that derivative securities are equivalent to specific dynamic trading
strategies plete markets suggests the possibility of constructing
buy-and-hold portfolios of options that mimic certain dynamic investment
policies, . asset-allocation rules. We explore this possibility by solving the
following problem: given an optimal dynamic investment policy, find a set of
options at the start of the investment horizon which e closest to the
optimal dynamic investment policy. We solve this problem for several
combinations of preferences, return dynamics and optimality criteria, and
show that under certain conditions, a portfolio consisting of just a few options
is an excellent substitute for considerably plex dynamic investment
policies.
1. plex securities at a single point in time to mimic the
properties of a dynamic trading strategy over a period of
It is now well known that under certain conditions, complex time. Specifically, we focus on dynamic investment policies,
financial instruments such as options and other derivative . asset-allocation rules, that arise from standard dynamic
securities can be replicated by sophisticated dynamic trading
optimization problems in which an investor maximizes the
strategies involving simpler securities such as stocks and
expected utility of his end-of-period wealth, and we pose
bonds. This ‘delta-hedging’ strategy—for which Robert
the following problem: given an investor’s optimal dynamic
Merton and Myron Scholes shared the Nobel Memorial
Prize in Economics in 1998—is largely responsible for the investment policy for two assets, stocks and bonds, construc