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
|
0.05
|
|
Probability at 6 months
|
0
|
005
|
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
|
0
|
($750)
|
($2,000)
|
|
Utility
|
1.0
|
0.9
|
0.9
|
0.7
|
01
|
0.0
|
She needs to decide to purchase a 2 month option on 100 shares, a 6 month option on 100 shares, or do nothing at all
Sketch the broker's utility curve and describe what it says about her risk profile?