Portfolio Optimization

36 The Efficient Frontier Chap. 2

σ

µ

←

-

Figure 2.8 Plot of the Efficient Frontier: EfficFrontPlot.m.

2.3 Exerc i ses

2.1 Show β

2

= 0 if and only if µ is a multiple of l.

2.2 Verify equation (2.15) (β

1

= 0).

2.3 Verify equation (2.17) (β

2

= α

1

).

2.4 The purpose of this exercise is to establish relationships b etween

the optimal solutions f or (2.1), (2.2) and (2.3) and their respective

parameters µ

p

, σ

2

p

and t.

(a) Write out the optimality conditions for (2.1 ) and solve them

in terms of Σ

−1

. Show that these efficient portfolios are iden-

tical to those of (2.7)–(2.8). Assume µ is not a multiple of

Sec. 2.3 Exercises 37

l. Hints: (i) (2.1) has two linear constraints