Date of Award

January 2012

Document Type


Degree Name

Master of Science (MS)


Economics & Finance

First Advisor

Daniel Biederman


The implementation of constraints are standard practice for a portfolio manager.

The eect, mathematical and practical, is a study still in development. This

thesis oers a standardized approach to finding a potential explanation of these

constraints. It considers this approach in both the MVO and CVaR settings both

theoretically by providing a mathematical proof, and practically by simulating

portfolio optimizations with both generated and actual market data. In the MVO

setting an MVO with constraints is equivalent to an unconstrained MVO with

perturbed covariance matrix. With regards to CVaR, the CVaR optimization with

constraints is equivalent to an unconstrained CVaR optimization with a perturbed

asset returns matrix. While this study clarifies how this process can be applied to

other portfolio optimizations under constraint it leaves room for a deeper study of

how the adjustment of particular individual constraints can eect portfolio optimization.