Portfolio Optimization

26 The Efficient Frontier Chap. 2

It can be shown (Exercise 2.3) that

β

2

= α

1

. (2.17)

Using (2.17) and eliminating t in (2.16) gives

σ

2

p

− β

0

= (µ

p

− α

0

)

2

/α

1

. (2.18)

Equation (2.18) shows the relationship between the variance (σ

2

p

)

and expected return (µ

p

) for efficient portfolios and is called the effi-

cient fro ntier. Two of the constants, α

0

and β

0

, in (2.18) can be in-

terpreted as follows. When t = 0 in (2.3), the problem becomes that

of minimizing the variance subject to the budget constraint. The ex-

pected return plays no role. The resulting portfo lio is called the globa l

minimum variance portfolio or simply the mi nimum variance portfolio.

From (2.8)