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STAT 400
(Chapter 5.3)
Spring 2012
1.
Models of the pricing of stock options often make the assumption of a normal
distribution.
An investor believes that the price of an
Burger Queen
stock
option is a normally distributed random variable with mean $18 and standard
deviation $3.
He also believes that the price of an
Dairy King
stock option is
a normally distributed random variable with mean $14 and standard deviation $2.
Assume the stock options of these two companies are independent.
The investor
buys 8shares of
Burger Queen
stock option and 9 shares of
Dairy King
stock
option.
What is the probability that the value of this portfolio will exceed $300?
BQ has Normal distribution,
BQ
= $18,
BQ
= $3.
DK has Normal distribution,
DK
= $14,
DK
= $2.
Value of the portfolio
VP = 8
BQ + 9
DK.
Then VP has Normal distribution.
VP
= 8
BQ
+ 9
DK
= 8
18 + 9
14 =
$270.
2
VP
= 8
2
2
BQ
+ 9
2
2
DK
= 64
9 + 81
4 = 900.
VP
=
$30.
P( VP > 300 ) =
30
270
300
Z
P
= P( Z > 1.00 ) = 1 – 0.8413 =
0.1587
.

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