Portfolio Optimization

46 The Capital Asset Pricing Model Chap. 3

µ

σ

α

β

←

→

Figure 3.1 Capital Market Line.

Consider the fo llowing implication of this model. Suppose in an

economy that everyo ne is mean-variance efficient and everyone “sees”

the same covariance matrix Σ and the same vector of expected returns

µ. Let two typical investors be Mr. X and Ms. Y and suppose their t

va lues are t

x

and t

y

, respectively. Note that t

x

and t

y

could be obtained

from the amounts Mr. X and Ms. Y invest in the risk free asset by means

of (3.6). Let Mr. X and Ms. Y’s holdings in the risky assets be denoted

by x a nd y, respectively. From (3.13),

x =

t

x

t

m

x

m

, and, y =

t

y

t

m

x

m

.

This implies that their