CHAPTER 24 –
1
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.
2. Buying call options gives the firm the right to purchase pork bellies; therefore, it must be a consumer
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 to
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,
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
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 variety
12. The risk is that the dollar will strengthen relative to the yen, since the fixed yen payments in the future
13. a. Buy oil and natural gas futures contracts, since these are probably its primary resource costs. If
it is a coal-fired plant, a cross-hedge might be implemented by selling natural gas futures, since
coal and natural gas prices are somewhat negatively related in the market; coal and natural gas
are somewhat substitutable.
14. The company must have felt that the combination of fixed rate bonds plus a swap would result in an
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. Depreciation
in the yen relative to the dollar results in a decrease in the ¥/$ exchange rate. Since Kevin is hurt by a
decrease in the exchange rate, he should take on a short position in yen-per-dollar futures contracts to
hedge his risk.
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.
1. The initial price is $2,554 per metric ton and each contract is for 10 metric tons, so the initial contract
value is:
Initial contract value = ($2,554 per ton)(10 tons per contract)
2. The price quote is $16.541 per ounce and each contract is for 5,000 ounces, so the initial contract value
is:
Initial contract value = ($16.541 per oz.)(5,000 oz. per contract)
Initial contract value = $82,705
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)
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
4. When you purchase the contracts, the initial value is:
Initial value = 10(100)($1,310)
Initial value = $1,310,000
At the end of the first day, the value of your account is:
Day 1 account value = 10(100)($1,317)
The Day 3 account value is:
Day 3 account value = 10(100)($1,306)
Day 3 account value = $1,306,000
So, your cash flow is:
Day 3 cash flow = $1,306,000 – 1,313,000
5. When you purchase the contracts, your cash outflow is:
Cash outflow = 25(42,000)($2.01)
Cash outflow = $2,110,500
At the end of the first day, the value of your account is:
Day 1 account value = 25(42,000)($2.03)
Day 2 cash flow = $52,500
The Day 3 account value is:
Day 3 account value = 25(42,000)($2.02)
Day 3 account value = $2,121,000
So, your cash flow 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
Payment weight
1
$57.49
.05749
2
.10837
3
888.32
7. 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 8.6 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
Year
PV of payment
Payment weight
1
$79.19
.07919
2
72.92
.14584
3
67.14
.20143
4
$1,000
8. The duration of a portfolio of assets or liabilities is the weighted average of the duration of the
portfolio’s individual items, weighted by their relative market values.
a. The total market value of assets in millions is:
Market value of assets = $43 + 555 + 340 + 103 + 498
Market value of assets = $1,539
CHAPTER 24 –
8
So, the market value weight of each asset is:
b. The total market value of liabilities in millions is:
Market value of liabilities = $605 + 395 + 285
Market value of liabilities = $1,285
Note that equity is not included in this calculation since it is not a liability. So, the market value
9. a. You’re concerned about a rise in corn prices, so you would buy July contracts. Since each contract
is for 5,000 bushels, the number of contracts you would need to buy is:
Number of contracts to buy = 160,000/5,000
Number of contracts to buy = 32
10. a. XYZ has a comparative advantage relative to ABC in borrowing at fixed interest rates, while
ABC has a comparative advantage relative to XYZ in borrowing at floating interest rates. Since
b. If the swap dealer must capture 2% of the available gain, there is 1% left for ABC and XYZ. Any
division of that gain is feasible; in an actual swap deal, the divisions would probably be negotiated
by the dealer. One possible combination is .5% for ABC and .5% for XYZ:
ABC
ABC
ABC
ABC
ABC
Dealer
LIBOR +1%
LIBOR +2.5%
10.5%
XYZ
10.0%
11. The duration of a liability is the average time to payment of the cash flows required to retire the
liability, weighted by the ratio of the present value of each payment to the present value of all payments
related to the liability. In order to determine the duration of a liability, first calculate the present value
of all the payments required to retire it. Since the cost is $45,000 at the beginning of each year for four
years, we can find the present value of each payment using the PV equation:
12. 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. We need to find the present value of the
bond’s payments at the market rate. 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. Since this bond has semiannual coupons, the years will include half-years. So, the duration of
the bond is:
Year
PV of payment
Payment weight
.5
$20.50
.01039
1.0
20.01
.02027
1.5
19.53
.02969
2.0
926.78
13. Let R equal the interest rate change between the initiation of the contract and the delivery of the asset.
Cash flows from Strategy 1:
Today
1 Year
Purchase silver
–S0
0
Borrow
Total cash flow
0
Purchase silver
0
Total cash flow
.23029
14. a. The forward price of an asset with no carrying costs or convenience value is:
Forward price = S0(1 + R)
Since you will receive the bond’s face value of $1,000 in 11 years and the 11 year spot interest
rate is currently 7 percent, the current price of the bond is:
b. If both the 1-year and 11-year spot interest rates unexpectedly shift downward by 2 percent, the
appropriate interest rate to use when pricing the bond is 5 percent, and the appropriate interest
rate to use in the forward pricing equation is 3 percent. Given these changes, the new price of the
bond will be:
15. a. The forward price of an asset with no carrying costs or convenience value is:
Forward price = S0(1 + R)
Since you will receive the bond’s face value of $1,000 in 18 months, we can find the price of
the bond today, which will be:
CHAPTER 24 –
12
b. It is important to remember that 100 basis points equals 1 percent and one basis point equals
.01%. Therefore, if all rates increase by 30 basis points, each rate increases by .003. So, the new
price of the bond today will be:
16. The financial engineer can replicate the payoffs of owning a put option by selling a forward contract
and buying a call. For example, suppose the forward contract has a settle price of $50 and the exercise
price of the call is also $50. The payoffs below show that the position is the same as owning a put with
an exercise price of $50: