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Lecture 12
I.
The link between the Two Fund Theorem and “price of risk”.
Recall the Two Fund Theorem from Risk and Return I. The investor’s problem of choosing an optimal
portfolio given Given N assets with respective expected returns
r
1
; r
2
;:::;r
N
, variances
¾
2
1
; ¾
2
2
;:::;¾
2
N
,
¾
2
n
>
0
for all
n;
and covariances
¾
j;n
.
Markowitz portfolio theory implies that any riskaverse investor will choose a portfolio of these assets
that lies on the upward slopping portion of the e¢cient frontier. The optimal choice for each investor will
depend on their preferences over risk and return.
A)
RiskFree Asset
If we introduce a riskfree asset (
¾
2
= 0
) to the investors choice set, the variance of any portfolio
formed from a combination of
w
F
invested in the riskfree asset and
w
M
invested in a risky portfolio will be
w
2
M
¾
2
M
. Where
¾
2
M
is the variance of the risky portfolio.
Thus, as the investor alters
w
M
;
the proportion of wealth invested in the risky portfolio, the tradeo¤
between return and standard deviation is linear.
This has a remarkable e¤ect on investors’ optimal choices.
Given a set of risky assets and a riskfree
asset, each riskaverse investor will choose to hold the same risky portfolio, regardless of their preferences
over risk and return.
The investor’s optimal portfolio choice will be a linear combination of the riskfree asset and the “market
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 Winter '08
 CHABOT

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