- TITLE: Portfolio optimization
with linear and fixed transaction costs
- AUTHOR: M. Lobo,
M. Fazel, and S. Boyd
- ABSTRACT: We consider the problem of portfolio selection,
with transaction costs and constraints on exposure to risk.
Linear transaction costs, bounds on the variance of the return,
and bounds on different shortfall probabilities
are efficiently handled by
convex optimization methods. For such problems, the globally
optimal portfolio can be computed very rapidly.
Portfolio optimization problems with
transaction costs that include a fixed fee, or discount breakpoints,
cannot be directly solved by convex optimization.
We describe a relaxation method which yields an easily computable
upper bound via convex optimization.
We also describe a heuristic method for finding a suboptimal
portfolio, which is based on solving a small number of convex
optimization problems (and hence can be done efficiently).
Thus, we produce a suboptimal solution, and also an upper bound on
the optimal solution.
Numerical experiments suggest that for practical problems the gap
between the two is small, even for large problems involving hundreds
The same approach can be used for related problems,
such as that of tracking an index with a portfolio
consisting of a small number of assets.
- STATUS: Annals of Operations Research, special
issue on financial optimization, 152(1):376-394, July 2007.
- Final paper: pdf file