Portfolio optimization and mixed integer quadratic programming
We begin with the well-known Markowitz model of risk and return fora portfolio of stocks. This model is used to choose a minimum risk portfolio from a universe of stocks that achieves a specified level of expected return subject to a budget constraint and possibly other (linear) constraints. This model is a convex quadratic programming model over continuous variables. As such, many of the variables may have small and unrealistic values in an optimal solution. In addition, a minimum risk portfolio may contain far too many stocks for an investor to hold. Eliminating these unwanted characteristics of minimum risk solutions can be accomplished using binary decision variables. We discuss an implementation of branch-and-bound for convex quadratic programming using the Optimization Subroutine Library. We then discuss how the structure of these particular types of additional constraints can be used to obtain a more efficient implementation. We present some computational experience with instances from the finance industry.
- OSTI ID:
- 36165
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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