© 2009 Elsevier Limited All rights reserved. This chapter will appear simultaneously in: Sortino,
The Sortino Framework for Constructing Portfolios.
Doi:10.1016/B978-0-12-374952-9.00007-5.

2010

Optimization and portfolio selection

Hal Forsey and Frank Sortino

7

Executive Summary

Dr. Hal Forsey and Dr. Frank Sortino present a new Forsey – Sortino Optimizer

that generates a mean – downside risk efficient frontier. Part 2 develops a second-

ary optimizer that finds the best combination of active managers, to add value,

and passive indexes, to lower costs.

7.1 Introduction

It is important for the reader to understand the assumptions that apply to all
optimizers before I discuss the development of SIA’s portfolio selection routines.
Utility Theory 1 provides a backdrop for discussing the limitations of mathematics
with respect to finding an optimal solution to portfolio selection. The underlying
assumption of most people who use optimizers is that the probability distribu-
tion is known. Well, in portfolio management it is not known. It can only be
estimated, which means that the portfolios on the so-called efficient frontier

(^1) From Utility Theory:
(a) If the outcome from a choice of action is known with certainty, then the optimal choice of
action is the one with outcome of greatest utility.
(b) If the probability distribution of the outcomes from a choice of action is known, then the optimal
choice of action is the one with the greatest expected utility of its outcomes.
(c) If the probability distribution of the outcomes from a choice of action is only approximate, then
the action with the greatest expected utility may or may not be a reasonable choice of action.
Utility Theory applied to choosing an optimal portfolio:
(a) If the return from each possible investment is known with certainty, then the optimal investment
portfolio is a 100% allocation to the investment with the greatest return. This only assumes that
the utility function is an increasing function of return.
(b) If the joint probability of returns for the set of possible investments is known and if the utility
function for portfolios with a given variance increases as the expected return increases, then the
optimal portfolio is on the mean-variance efficient frontier.
(c) If the joint probability of returns is only approximate, then portfolios on the efficient frontier
may or may not be reasonable choices.