Title: Relative performance approach to robust portfolio selection
Abstract:
Recent interest in the general topic of ``robust portfolio selection" in
the finance, economics, and optimization communities, has been motivated
largely by the observation that the solutions of classical optimal
portfolio selection problems (such as ``mean-variance optimization") are
sensitive to statistical errors that can arise during calibration, and
that the ``real world" performance of such portfolios can be poor if
these errors are ignored. The commonly proposed method for addressing
this problem has been ``worst case" optimization (which has it roots in
statistics as well as electrical engineering). This has led in turn to
methodologies such as ``robust mean-variance portfolio selection" and
``robust utility maximization". The primary criticism of this approach to
optimal investment, however, is that it gives rise to extremely
conservative solutions.

In this talk, we propose and analyze an alternative measure of ``robust
performance". This alternative measure differs from the typical ``worst
case expected utility" and ``worst case mean-variance" formulations in
that the ``robust performance" of a (dynamic) portfolio is evaluated not
only on the basis of its performance when there is an adversarial
opponent (``nature"), but also by its performance relative to a fully
informed `benchmark investor" who behaves optimally given complete
knowledge of the otherwise ambiguous model. This ``relative performance"
approach has several important properties: (i) decisions arising from
this approach are less pessimistic than the portfolios obtained from the
typical ``worst case expected utility" and ``worst case mean-variance"
formulations, and (ii) the dynamic ``relative performance" problem
reduces to a convex static optimization problem under reasonable choices
of the benchmark portfolio. This static problem is interesting in its own
right: it can be interpreted as a less pessimistic alternative to the
single period ``worst case mean-variance" problem.

Joint work with George Shanthikumar and Thaisiri Watewai.