Portfolio Optimization

74 Sharpe Ratios and Implied Risk Free Returns Chap. 4

and σ

2

p0

= β

0

+ t

2

0

β

2

. But then (1) µ

p0

is the optimal solution fo r the

problem of maximizing the portfolio’s expected return with the portfo-

lio variance being held at σ

2

p0

; i.e., (2.2) with σ

2

p

= σ

2

p0

. Furthermore, (2)

σ

2

p0

is the minimum variance of the portfolio with the expected return

being held at µ

p0

; i.e., (2.1) with µ

p

= µ

p0

.

Table 4.1 shows these pairs for a variety of values of t for the problem

of Example 2.1. For example, for t = 0.10, the minimum portfolio vari-

ance is 0.0134043 when the expected return is required to be 1.19574.

Conversely, the maximum expected return is 1.19 574 when ...