Handout I
Risk
Throughout this class, the risk of any asset will be de…ned as its variance. Thus, an asset with variance
¾
2
1
is riskier than an asset with variance
¾
2
2
if and only if
¾
2
1
> ¾
2
2
. Where
¾
2
i
is the variance of the ith asset.
An investor is riskaverse if he or she has preferences over consumption represented by a concave utility
function. That is, if an investor’s utility function
u
(
c
)
exhibits diminishing marginal utility (
u
0
(
c
)
>
0
and
u
00
(
c
)
<
0)
as c increases we say this investor is riskaverse.
As the name implies, a riskaverse investor views risk as a “bad” and is willing to pay to avoid it.
For Example, suppose I were to o¤er the following game to a riskaverse investor.
We will ‡ip a fair
coin. If the coin comes up heads, I will pay
x
=
®
dollars. If the coin comes up tails, I will pay
x
=
¯
dollars.
® > ¯:
The expected payout of this game is
E
[
x
] =
:
5
E
[
x
j
h
]+
:
5
E
[
x
j
t
] =
:
5
®
+
:
5
¯
. If the investor
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 Fall '08
 CHABOT
 Economics, Variance, Utility, Probability theory, St. Petersburg paradox, riskaverse investor

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