Is an Optimal Solution Always Best ?
(Second Quarter 2006)

Borrowing the concept of Utility from economics, asset managers are presented with the idea that all rational investors prefer to hold stocks with the highest expected returns at the lowest possible risk. To achieve this goal, managers first develop forecasts for stock returns, volatilities and correlations, and then turn to a sophisticated process called optimization to determine how many shares of a stock to hold. But the large number of stocks available, and the even larger number of combination of stocks, creates a mathematical problem that is only solvable with computer-based algorithms. It is in this last step, where the manager prepares all
the data and then pushes a button, that human intuition takes a back seat to the complexity and precision of a computer. The final portfolio is given back to the manager with no explanation other than to say the portfolio is optimal! So is a manager done? Well, not really since a manger will look over the portfolio to see if the positions make sense and hold a reasonable doubt that an optimal portfolio may not always be the best one.

Optimizers vary in form and sophistication, from linear methods to quadratic, conic and other non-linear methods with names such as nested benders decomposition and object oriented parallel solvers. As computers become more powerful, new methods become feasible and new features are added. For example, optimizers can offer tax-aware optimization and one step long-short, and can handle composite assets, non-linear transaction costs, penalty functions, soft constraints and round lotting.

While computers have taken many quips, such as “garbage in - garbage out” and “3.5 giga-mistakes per second,” the criticism of optimal portfolios has fallen mainly in two areas 1) the long-only constraint imposed by clients results in sub-optimal portfolios and 2 ) even if the mathematical formulation is correct, the validity of optimization is suspect when the input data has uncertainty or errors.


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