Question: 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:

The broker plans to exercise her option lust 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:

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?

Draw the decision tree. What action should she take to maximize her expected utility?

How would this answer differ if she elected to pursue a pure expected monetary value approach? Why?