Portfolio Optimization

Chapter 8

Determination of the Entire

Efficient Frontier

8.1 The Entire Efficient Frontier

The model problem we shall address in this chapter is

minimize : −tµ

′

x +

1

2

x

′

Σx

subj ect t o : a

′

i

x ≤ b

i

, i = 1, 2, . . . , m,

a

′

i

x = b

i

, i = m + 1, m + 2, . . . , m + q,

(8.1)

which is identical to the model problem (7.2) used in Chapter 7. The-

orem 7.1 showed that the optimal solution for (8 .1 ) , was a piecewise

linear function of the risk aversion parameter t. The result was an exis-

tence result and did not tell us how to construct the optimal solution.

It is the purpose of this chapter to formulate an algor ithm for the so-

lution of (8.1) for all t ≥ 0. Throughout ...