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Comparisons between expected monetary approach and expected utility approach
A broker at Merrill Lynch is convinced that the price of ING's stock will rise in the next six months. ING is currently trading at $57/share. Upon inspecting the latest quotes on the options market, the broker discovers that she can purchase an option of ING for $5/share allowing her to buy ING at $55/share in two months. She could also purchase an option to buy ING within a six month period; this option, which has a cost of $10/Share, also has an exercise price of $55/share. She has estimated the following probability distributions for the stock price on the days the options expire:
Price
$50
$55
$60
$65
$70
$75
Probability at 2 months
0.05
0.15
015
0.25
0.35
Probability at 6 months
0
005
0.20
0.30
0.40
The broker plans to exercise her option just before its expiration if ING is selling for more than $55/share an immediately sell it at that market price. Of course, if ING is selling for less than $55/share on the expiration date then she will lose the entire purchase cost of the option. Before weighing her option she consults the latest update from the Risk
Management department:
Profit
$1,500
$1,000
$500
($750)
($2,000)
Utility
1.0
0.9
0.7
01
0.0
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