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 price risk by selling lumber futures. Losses in the spot market due to a fall in lumber prices are offset by gains on the short position in lumber futures.
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 on the call options; if pork belly prices actually decline, the consumer enjoys lower costs, while the call option expires worthless.
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 facilitate liquidity and to allow them to be traded on organized futures exchanges. Gains and losses on futures are marked-to-market daily. Default risk is greatly reduced with futures since the exchange acts as an intermediary between the two parties, guaranteeing performance. Default risk is also reduced because the daily settlement procedure keeps large loss positions from accumulating.
You might prefer to use forwards instead of futures if your hedging needs were different from the standard contract size and maturity dates offered by the futures contract.
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 contract size on crude oil futures, or perhaps the exact settlement date the company requires isn’t available on these futures. Also, the firm may produce a different grade of crude oil than that specified for delivery in the futures contract.
5. The firm is directly exposed to fluctuations in the price of natural gas since it is a natural gas user. In addition, the firm is indirectly exposed to fluctuations in the price of oil. If oil becomes less expensive relative to natural gas, its competitors will enjoy a cost advantage relative to the firm.
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.
However, options hedges are costly because of the initial premium that must be paid. The futures contract can be entered into at no initial cost, with the disadvantage that the firm is locking in one price for cotton; it can’t profit from cotton price declines.
7. The put option on the bond gives the owner the right to sell the bond at the option’s strike price. If bond prices decline, the owner of the put option profits. However, since bond prices and interest rates move in opposite directions, if the put owner profits from a decline in bond prices, he would also profit from a rise in interest rates. Hence, a call option on interest rates is conceptually the same thing as a put option on bond prices.
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 by selling bond futures; the latter could be implemented by buying put options on bond prices or buying call options on interest rates.
9. A swap contract is an agreement between parties to exchange assets over several time intervals in the future. The 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 time, a swap can be viewed as a series of forward contracts with different settlement dates.
The firm participating in the swap agreement is exposed to the default risk of the dealer, in that the dealer may not make the cash flow payments called for in the contract. The dealer faces the same risk from the contracting party, but can more easily hedge its default risk by entering into an offsetting swap agreement with another party.
10. The firm will borrow at a fixed rate of interest, receive fixed rate payments from the dealer as part of the swap agreement, and make floating rate payments back to the dealer; the net position of the firm is that it has effectively borrowed at floating rates.
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 of instruments available to hedge transaction exposure, but very few long-term hedging instruments exist. It is much more difficult to hedge against economic exposure, since fundamental changes in the business generally must be made to offset long-run changes in the economic environment.
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 should sell yen futures. The way the interest rate is quoted will affect the calculation of which currency is strengthening.
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, since coal and natural gas prices are somewhat negatively related in the market; coal and natural gas are somewhat substitutable.
b. Buy sugar and cocoa futures, since these are probably your primary commodity inputs.
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 manufacture of photographic film.
e. Sell natural gas futures, since excess supply in the market implies low prices.
f. Assuming the bank doesn’t resell its mortgage portfolio in the secondary market, buy bond futures.
g. Sell stock index futures, using an index most closely associated with the stocks in your fund, such as the S&P 100 or the Major Market Index for large blue-chip stocks.
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h. Buy Swiss franc futures, since the risk is that the dollar will weaken relative to the franc over the next six months, which implies a rise in the $/SFr exchange rate.
i. Sell euro futures, since the risk is that the dollar will strengthen relative to the Euro over the next three months, which implies a decline in the $/€ exchange rate.
14. Sysco must have felt that the combination of fixed plus swap would result in an overall better rate. In other words, the variable rate available via a swap may have been more attractive than the rate available from issuing a floating-rate bond.
15. He is a little nạve about the capabilities of hedging. While hedging can significantly reduce the risk of changes in foreign exchange markets, it cannot completely eliminate it. Basis risk is the primary reason that hedging cannot reduce 100% of any firm’s exposure to price fluctuations. Basis risk arises when the price movements of the hedging instrument do not perfectly match the price movements of the asset being hedged.
16. Kevin will be hurt if the yen loses value relative to the dollar over the next eight months.
Depreciation in the yen relative to the dollar results in a decrease in the ¥/$ 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.
Basic
1. The initial price is $2,414 per metric ton and each contract is for 10 metric tons, so the initial contract value is:
Initial contract value = ($2,414 per ton)(10 tons per contract) = $24,140 And the final contract value is:
Final contract value = ($2,431 per ton)(10 tons per contract) = $24,310 You will have a gain on this futures position of:
Gain on futures contract = $24,310 – 24,140 = $170
2. The price quote is $31.187 per ounce and each contract is for 5,000 ounces, so the initial contract value is:
Initial contract value = ($31.187 per oz.)(5,000 oz. per contract) = $155,935 At a final price of $31.39 per ounce, the value of the position is:
Final contract value = ($31.39 per oz.)(5,000 oz. per contract) = $156,950 Since this is a short position, there is a net loss of:
5,000($31.39 – 31.187) = $1,015 per contract Since you sold five contracts, the net loss is:
Net loss = 5($1,015) = $5,075
At a final price of $30.86 per ounce, the value of the position is:
Final contract value = ($30.86 per oz.)(5,000 oz. per contract) = $154,300 Since this is a short position, there is a net gain of:
5,000($31.187 – 30.86) = $1,635 per contract Since you sold five contracts, the net gain is:
Net gain = 5($1,635) = $8,175
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 $95 per barrel. The manager will exercise the option if the price rises above $95. Selling put options obligates the manager to buy oil futures contracts at a futures price of $95 per barrel. The put holder will exercise the option if the price falls below $95. The payoffs per barrel are:
Oil futures price: $90 $92 $95 $98 $100
Value of call option position: 0 0 0 3 5
Value of put option position: –5 –3 0 0 0
Total value: –$5 –$3 $0 $3 $5
The payoff profile is identical to that of a forward contract with a $95 strike price.
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4. When you purchase the contracts, the initial value is:
Initial value = 10(100)($1,580) Initial value = $1,580,000
At the end of the first day, the value of your account is:
Day 1 account value = 10(100)($1,587) Day 1 account value = $1,587,000 So, your cash flow is:
Day 1 cash flow = $1,587,000 – 1,580,000 Day 1 cash flow = $7,000
The day 2 account value is:
Day 2 account value = 10(100)($1,582) Day 2 account value = $1,582,000 So, your cash flow is:
Day 2 cash flow = $1,582,000 – 1,587,000 Day 2 cash flow = –$5,000
The day 3 account value is:
Day 3 account value = 10(100)($1,573) Day 3 account value = $1,573,000 So, your cash flow is:
Day 3 cash flow = $1,573,000 – 1,582,000 Day 3 cash flow = –$9,000
The day 4 account value is:
Day 4 account value = 10(100)($1,584) Day 4 account value = $1,584,000 So, your cash flow is:
Day 4 cash flow = $1,584,000 – 1,573,000 Day 4 cash flow = $11,000
You total profit for the transaction is:
Profit = $1,584,000 – 1,580,000 Profit = $4,000
5. When you purchase the contracts, your cash outflow is:
Cash outflow = 25(42,000)($2.46) Cash outflow = $2,583,000
At the end of the first day, the value of your account is:
Day 1 account value = 25(42,000)($2.42) Day 1 account value = $2,541,000
Remember, on a short position you gain when the price declines, and lose when the price increases.
So, your cash flow is:
Day 1 cash flow = $2,583,000 – 2,541,000 Day 1 cash flow = $42,000
The day 2 account value is:
Day 2 account value = 25(42,000)($2.47) Day 2 account value = $2,593,500 So, your cash flow is:
Day 2 cash flow = $2,541,000 – 2,593,500 Day 2 cash flow = –$52,500
The day 3 account value is:
Day 3 account value = 25(42,000)($2.50) Day 3 account value = $2,625,000 So, your cash flow is:
Day 3 cash flow = $2,593,500 – 2,625,000 Day 3 cash flow = –$31,500
The day 4 account value is:
Day 4 account value = 25(42,000)($2.56) Day 4 account value = $2,688,000 So, your cash flow is:
Day 4 cash flow = $2,625,000 – 2,688,000 Day 4 cash flow = –$63,000
You total profit for the transaction is:
Profit = $2,583,000 – 2,688,000 Profit = –$105,000
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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 7 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 $65.42 .06542 .06542
2 61.14 .06114 .12228
3 873.44 .87344 2.62032
Price of bond $1,000 Duration = 2.80802
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 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 $74.07 .07407 .07407
2 68.59 .06859 .13717
3 63.51 .06351 .19052
4 793.83 .79383 3.17533
Price of bond $1,000 Duration = 3.57710
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 = $31 + 590 + 340 + 98 + 485 Market value of assets = $1,544
So, the market value weight of each asset is:
Federal funds deposits = $31 / $1,544 = .020 Accounts receivable = $590 / $1,544 = .382 Short-term loans = $340 / $1,544 = .220 Long-term loans = $98 / $1,544 = .063 Mortgages = $485 / $1,544 = .314
Since the duration of a group of assets is the weighted average of the durations of each individual asset in the group, the duration of assets is:
Duration of assets = .020(0) + .382(.20) + .220(.65) + .063(5.25) + .314(12.85) Duration of assets = 4.59 years
b. The total market value of liabilities in millions is:
Market value of liabilities = $645 + 410 + 336 Market value of liabilities = $1,391
Note that equity is not included in this calculation since it is not a liability. So, the market value weight of each asset is:
Checking and savings deposits = $645 / $1,391 = .464 Certificates of deposit = $410 / $1,391 = .295
Long-term financing = $336 / $1,391 = .242
Since the duration of a group of liabilities is the weighted average of the durations of each individual asset in the group, the duration of liabilities is:
Duration of liabilities = .464(0) + .295(1.60) + .242(9.80) Duration of liabilities = 2.84 years
c. Since the duration of assets does not equal the duration of its liabilities, the bank is not immune from interest rate risk.
Intermediate
9. a. You’re concerned about a rise in corn prices, so you would buy March contracts. Since each contract is for 5,000 bushels, the number of contracts you would need to buy is:
Number of contracts to buy = 140,000/5,000 = 28
By doing so, you’re effectively locking in the settle price in March, 2012 of $6.05 per bushel of corn, or:
Total price for 140,000 bushels = 28($6.05)(5,000) = $847,000
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b. If the price of corn at expiration is $6.13 per bushel, the value of you futures position is:
Value of futures position = ($6.13 per bu.)(5,000 bu. per contract)(28 contracts) = $858,200 Ignoring any transaction costs, your gain on the futures position will be:
Gain = $858,200 – 847,000 = $11,200
While the price of the corn your firm needs has become $11,200 more expensive since November, your profit from the futures position has netted out this higher cost.
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 the spread between ABC and XYZ’s fixed rate costs is only 1%, while their differential is 2%
in floating rate markets, there is an opportunity for a 3% total gain by entering into a fixed for floating rate swap agreement.
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 ẵ% for ABC and ẵ% for XYZ:
ABC ABC ABC ABC ABC
Dealer LIBOR +1%
10.5%
XYZ LIBOR +2.5%
Debt Market LIBOR +1%
Debt Market 10%
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 $30,000 at the beginning of each year for four years, we can find the present value of each payment using the PV equation:
PV = FV / (1 + R)t
So, the PV each year of college is:
Year 10 PV = $30,000 / (1.09)10 = $12,672.32 Year 11 PV = $30,000 / (1.09)11 = $11,625.99 Year 12 PV = $30,000 / (1.09)12 = $10,666.04 Year 13 PV = $30,000 / (1.09)13 = $9,785.36
So, the total PV of the college cost is:
PV of college = $12,672.32 + 11,625.99 + 10,666.04 + 9,785.36 PV of college = $44,749.71
Now, we can set up the following table to calculate the liability’s duration. The relative value of each payment is the present value of the payment divided by the present value of the entire liability. The contribution of each payment to the duration of the entire liability is the relative value of the payment multiplied by the amount of time (in years) until the payment occurs.
Year PV of payment Relative value Payment weight
10 $12,672.32 .28318 2.83182
11 11,625.99 .25980 2.85780
12 10,666.04 .23835 2.86019
13 9,785.36 .21867 2.84269
PV of college $44,749.71 Duration = 11.39250
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 Relative value Payment weight
.5 $34.15 .03291 .01645
1.0 33.31 .03211 .03211
1.5 32.50 .03132 .04698
2.0 937.66 .90366 1.80733
Price of bond $1,037.62 Duration = 1.90287
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 +S0 –S0(1 + R)
Total cash flow 0 –S0(1 + R)
Cash flows from Strategy 2:
Today 1 Year
Purchase silver 0 –F
Total cash flow 0 –F