Profits at Bangor Finestkind Power, Light, and Fishmarket (PFPL&F) for the winter of 2020-21 are expected to be -84.5+0.23H-0.00012H², where H is the number of heating degree days in Bangor. H as a a normal distribution with a mean of 980 and a standard deviation of 230.

A: What is the probability that PFPL&F will lose money next winter?

B: You want to adopt a hedging strategy so that the probability of losing money because H is too low is 1.5 percent, while the probability of losing money because H is too high is 2 percent. What levels of H do you have to hedge to?

C: Unhedged, what are the losses if H equals the levels you solved for in part B?

D: Puts and calls are available at strike prices 0.7 standard deviations away from the mean, with a markup of 10 percent. How much will they cost?

E: How many calls and puts will you purchase to hedge your position, as outlined in Part B?

F: Graph your unhedged and hedged profits as H goes from 300 to 1600.

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