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Finance Assignment Question

Willingness to Pay for Insurance. Frank Black has finally quit playing guitar for the Pixies, and has decided to pursue a lifelong dream of his, generating power through small-scale electricity generation plants. Suppose Frank has acquired the rights to a technology that allows for the sustainable generation of electric power, and the license to sell it onto the Arizona electricity-grid (no small feat on its own). Table 1 shows his projections for the first 5 years of operating profit (in millions of dollars). Despite being a rock-star, however, Frank is relatively risk averse, so his coefficient of risk aversion is 0.4. Use the data in table 1 to answer the questions that follow.

Table 1. Expected Utility of Profit

Year

Profit

U(profit)

U(E[profit])

1

10

2

12

3

8

4

16

5

14

Average =

12

  1. Assume the coefficient of risk aversion given above. Find the missing values for the utility of profit, for each year, in the above table, and find the expected (average) utility of profit. Next, find the utility of expected (average) profit. Compare these two values to show how you know Frank is risk averse.
  2. Frank is a pretty shrewd businessman, and would be willing to sell his power-generation firm to a willing investor. Assume Frank would accept his certainty equivalent (CE) value as a fair price for his firm. Find the CE value, and interpret what the CE value means in intuitive terms.
  3. Now suppose Frank is shopping for an insurance company that would be willing to insure his profit stream over time. Suppose his expected loss, or the amount his profit falls below average, is $2.0 million. What is his total willingness to pay for insurance, including his expected loss and his risk premium? Explain how this relates to the Bernoulli Hypothesis.

Futures Hedging. It is a little known fact, but probably obvious when you think about it, that Santa Claus is Canadian. When we learn about Santa Claus as children, we are led to believe that he simply distributes gifts all around the world at will, without concern for the financial implications of his gift-giving decisions. However, the business of Christmas gift distribution has become a risk management nightmare, given the myriad of items that he has to make and distribute every year. Suppose it is June 1, and S. Claus, Inc. expects to deliver 1.0 million hockey sticks (made from aluminum) to kids throughout the world on December 25. He would like to limit his exposure to fluctuations in the price of aluminum by hedging his input price risk on the Chicago Mercantile Exchange (CME) using their physical aluminum contract. Help Santa lock in an aluminum price by answering the following questions based on the data in table 2 (all prices in $ / metric ton (MT)):

Table 2. Long Hedge by S. Claus, Inc.

Date

Cash Market

Futures Market

Price Data as of June 1

Cash Market = $2,000

December Futures = $2,200

Transactions:

June 1

December 25

Net Cost per MT =

  1. What is the current basis? Explain 3 factors that may influence changes in the basis for aluminum, given that the delivery point is Chicago and Santa Claus lives at the North Pole.
  2. Suppose Santa wants to lock in the June 1 price of $2,000 by using a long futures hedge. Describe the transactions, in both the cash and futures markets, that will be required to complete this hedge. Assume the cash price on December 25 is $1,800 and the December futures price is $1,900. Calculate the net cost, after hedging, on a per metric ton basis. Comment on whether this hedge was successful or not.
  3. In your answer to (b), did the basis widen or narrow? Did Santa benefit or lose from this change in basis? What is your general conclusion regarding how changes in the basis affect the effectiveness of hedging for long hedgers?
  4. Assume instead that the basis is positive, that is, the cash price on June 1 at the North Pole is $2,400 when the December futures is $2,200. If the cash price again falls by $200 and the futures by $300, explain how your conclusion in c does or does not change.

Risk Management with Options. Newmont Mining is the largest gold-mining company in the US. While other companies mine a wide portfolio of metals, Newmont is nearly a “pure play” in the gold sector. As such, they have a considerable exposure to fluctuation in the price of gold, so have a real interest in managing the effect of changes in gold prices on their earnings. Suppose Newmont is considering a range of options strategies to help manage their risk. It is currently June 1, and the December futures contract is trading for $1,200 per ounce. Each option contract controls 100 ounces of gold (one futures contract). Use this information to answer the following questions.

  1. Suppose Newmont would like to use a put hedge on the December futures contract. They decide to use an at-the-money option (strike price = $1,200) and pay a $20 premium for doing so. Describe what the payoff diagram for this strategy would look like by explaining what happens to the net value of their position if the futures contract either falls to $1,100 per ounce, or rises to $1,300 per ounce.
  2. Is the put hedge strategy in part a better or worse than a straight futures hedge? Explain your reasoning.
  3. Instead of a put hedge, Newmont is also considering a covered call strategy as they do not think the $1,200 price is sufficient to make their profit goals. If a call on the December contract (strike = $1,200) is trading for $30, explain how they can manage the risk of their cash position using this strategy. Show again by calculating the net value of their position if the futures price falls to $1,100 per ounce, and rises to $1,300 per ounce.