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CHAPTER 25
DERIVATIVES AND HEDGING RISK
Answers to Concepts Review and Critical Thinking Questions
1. Since the firm is selling futures, it wants to be able to deliver the lumber; therefore, it is a supplier.
Since a decline in lumber prices would reduce the income of a lumber supplier, it has hedged its
2. Buying call options gives the firm the right to purchase pork bellies; therefore, it must be a consumer
of pork bellies. While a rise in pork belly prices is bad for the consumer, this risk is offset by the gain
3. Forward contracts are usually designed by the parties involved for their specific needs and are rarely
sold in the secondary market, so forwards are somewhat customized financial contracts. All gains
and losses on the forward position are settled at the maturity date. Futures contracts are standardized
4. The firm is hurt by declining oil prices, so it should sell oil futures contracts. The firm may not be
able to create a perfect hedge because the quantity of oil it needs to hedge doesn’t match the standard
5. The firm is directly exposed to fluctuations in the price of natural gas since it is a natural gas user. In
6. Buying the call options is a form of insurance policy for the firm. If cotton prices rise, the firm is
protected by the call, while if prices actually decline, they can just allow the call to expire worthless.
7. A put option on a bond gives the owner the right to sell the bond at the option’s strike price. If bond
prices decline, the owner of a put option profits. However, since bond prices and interest rates move
8. The company would like to lock in the current low rates, or at least be protected from a rise in rates,
allowing for the possibility of benefit if rates actually fall. The former hedge could be implemented
9. A swap contract is an agreement between parties to exchange assets over several time intervals in the
future. A swap contract is usually an exchange of cash flows, but not necessarily so. Since a forward
contract is also an agreement between parties to exchange assets in the future, but at a single point in
10. The firm will borrow at a fixed rate of interest, receive fixed rate payments from the dealer as part of
11. Transaction exposure is the short-term exposure due to uncertain prices in the near future. Economic
exposure is the long-term exposure due to changes in overall economic conditions. There are a
12. The risk is that the dollar will strengthen relative to the yen, since the fixed yen payments in the
future will be worth fewer dollars. Since this implies a decline in the $/¥ exchange rate, the firm
13. a. Buy oil and natural gas futures contracts, since these are probably your primary resource costs.
If it is a coal-fired plant, a cross-hedge might be implemented by selling natural gas futures,
c. Sell corn futures, since a record harvest implies low corn prices.
d. Buy silver and platinum futures, since these are primary commodity inputs required in the
e. Sell natural gas futures, since excess supply in the market implies low prices.
g. Sell stock index futures, using an index most closely associated with the stocks in your fund,
h. Buy Swiss franc futures, since the risk is that the dollar will weaken relative to the franc over
i. Sell euro futures, since the risk is that the dollar will strengthen relative to the Euro over the
14. Sysco must have felt that the combination of fixed rate bonds plus a swap would result in an overall
15. He is a little naïve about the capabilities of hedging. While hedging can significantly reduce the risk
of changes in foreign exchange markets, it cannot completely eliminate it. Basis risk is the primary
16. Kevin will be hurt if the yen loses value relative to the dollar over the next eight months.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Basic
1. The initial price is $2,912 per metric ton and each contract is for 10 metric tons, so the initial
contract value is:
And the final contract value is:
2. The price quote is $16.544 per ounce and each contract is for 5,000 ounces, so the initial contract
value is:
At a final price of $16.61 per ounce, the value of the position is:
Final contract value = ($16.61 per oz.)(5,000 oz. per contract)
Final contract value = $83,050
Since this is a short position, there is a loss on each contract of:
At a final price of $16.43 per ounce, the value of the position is:
Final contract value = ($16.43 per oz.)(5,000 oz. per contract)
Final contract value = $82,150
Since this is a short position, there is a gain per contract of:
With a short position, you make a profit when the price falls, and incur a loss when the price rises.
3. The call options give the manager the right to purchase oil futures contracts at a futures price of $65
per barrel. The manager will exercise the option if the price rises above $65. Selling put options
obligates the manager to buy oil futures contracts at a futures price of $65 per barrel. The put holder
will exercise the option if the price falls below $65. The payoffs per barrel are:
The payoff profile is identical to that of a forward contract with a $65 strike price.
4. When you purchase the contracts, the initial value is:
So, your cash flow is:
So, your cash flow is:
Day 2 cash flow = $1,213,000 – 1,217,000
Day 2 cash flow = –$4,000
The Day 3 account value is:
The Day 4 account value is:
Day 4 account value = 10(100)($1,212)
Day 4 account value = $1,212,000
So, your cash flow is:
5. When you purchase the contracts, your cash outflow is:
Cash outflow = 25(42,000)($1.36)
Cash outflow = $1,428,000
At the end of the first day, the value of your account is:
The Day 2 account value is:
Day 2 account value = 25(42,000)($1.37)
Day 2 account value = $1,438,500
So, your cash flow is:
So, your cash flow is:
Day 3 cash flow = $1,438,500 – 1,459,500
Day 3 cash flow = –$21,000
The Day 4 account value is:
6. The duration of a bond is the average time to payment of the bond’s cash flows, weighted by the
ratio of the present value of each payment to the price of the bond. Since the bond is selling at par,
the market interest rate must equal 6.1 percent, the annual coupon rate on the bond. The price of a
bond selling at par is equal to its face value. Therefore, the price of this bond is $1,000. The relative
value of each payment is the present value of the payment divided by the price of the bond. The
contribution of each payment to the duration of the bond is the relative value of the payment
multiplied by the amount of time (in years) until the payment occurs. So, the duration of the bond is:
Year PV of payment Relative value Payment weight
1 $57.49 .05749 .05749
