Summary

Here, we bring together and apply optimization principles using Excel as our platform, solving and analyzing four distinct optimization schemes for the purpose of highlighting the impact imposed by constraints. The purpose was to illustrate the impact that constraints have on the optimized solution and in particular to assess the cost of constraints in the form of portfolio risk and return. We study three constraints in particular—a targeted portfolio return, no short sales (no negative weights), and capped allocations to specific assets. Our results show that while constraints may be imposed on the portfolio for institutional reasons or to cap exposure to certain asset classes, the result is that they always restrict the space in which our optimizer can search for the optimal portfolio. That suggests that constraints have costs, and in particular, we find that two costs are higher risk (for sure) and possibly lower returns. We then take a fresh look at performance statistics, again, in the form of marginal contributions to risk and allocative risk, along with a fresh look at the efficient frontier.