Edwina, a commodities broker, has acquired an option to buy 1,000 oz of gold at

Question

Edwina, a commodities broker, has acquired an option to buy 1,000 oz of gold at $50/oz. If she takes the option and if Congress relaxes import quotas, she can sell the gold for $80/oz. If she takes the option and Congress does not relax the import quotas, however, the company will lose $10/oz. Edwina believes that there is a 50% chance that the government will relax the quota. She also has the option of waiting until Congress decides whether to relax the import quota. If she adopts this strategy, however, there is a 70% chance that some other broker will have already taken the option. a If Edwina is risk-neutral, what should she do? b If Edwina's utility function for a change x in her asset position is given by u(x) (10,000+ x)1/2, what should she do?

Explanation / Answer

a) Potential gain, if govt telaxes import quota = (80-50)*1000 = $ 30,000

Potential loss, if govt does not relax import quota = 10*1000 = $ 10,000

Expected value (EV) of the decision to buy the option = 50%*30000 + 50*(-10000) = $ 10,000

Expected value (EV) of the decision to wait till govt decision = 50%*(30%*30000 + 70%*0)+50%*0 = $ 4,500

EV of decision to buy the option is higher. Therefore Edmina should buy the option.

b) Utility of potential gain, if govt relaxes the import quotas = (10000+30000)/2 = 20000

Utility of potential loss, if govt does not relax the import quotas = (10000-10000)/2 = 0

Expected utility of decision to buy the option = 20000*0.5+0*0.5 = 10000

Expected utility of decision to wait till govt decision = 50%*(30%*20000 + 70%*0)+50%*0 = 5000

Expected utility of decision to buy the option is higher. Therefore, she should buy the option.

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