CorporateFinance公司理财机械工业出版社

1、Corporate Finance公司理财机械工业出版社Chapter 25: Derivatives and Hedging Risk25.1 a. A forward contract is an arrangement calling for the future delivery of an asset at an agreed-uponprice.b. A futures contract obliges traders to purchase or sell an asset at an agreed-upon price on a specifiedfuture date. Th

2、e long position is held by the trader who commits to purchase. The short position isheld by the trader who commits to sell. Futures differ from forward contracts in their standardization,exchange trading, margin requirements, and daily settling (marking to market.25.2 1. Futures contracts are standa

3、rdized and traded on exchanges, while forward contracts are tailor-made tosuit the specific needs of two counterparties. The standardization of contracts increases the liquidity offutures markets in comparison to forward markets and also allows traders to enter into their positionswith a certain deg

4、ree of anonymity.2.The holder of a futures contract is insulated from default risk due to clearing corporations and marginrequirements. The owner of a forward contract has no guarantee that his counterparty will not default,and therefore forward holders must carefully evaluate each others credit ris

5、k before entering into acontract.3.Since futures positions are marked-to-market at the close of trading, gains and losses on futurespositions are realized daily, while gains or losses on a forward contract are not realized until thedelivery of the asset.25.3 a. i. Since the futures price of wheat is

6、 $5.10 per bushel at the end of trading on March 18, thedelivery price on that date is $5.10 per bushel.per barrel in order to receive the wheat. The difference between the price that you pay atdelivery and the price at which you entered into the contract is reconciled by daily marked-to-market gain

7、s and losses.iii. On March 15, you entered into a long futures position in wheat at a price of $5.00 per bushel.Since the closing futures price is $5.03 per bushel, your account receives a cash inflow of $0.03 atthe end of the day. Your position in wheat futures increases to $5.03 per bushel (= $5.0

8、0 + $0.03.On March 16, your opening long position in wheat futures is $5.03 per bushel. Since the closingfutures price is $5.08 per bushel, your account receives a cash inflow of $0.05 at the end of theday. Your position in wheat futures increases to $5.08 per bushel (= $5.00 + $0.03 + $0.05.On Marc

9、h 17, your opening long position in wheat futures is $5.08 per bushel. Since the closingfutures price is $5.12 per bushel, your account receives a cash inflow of $0.04 at the end of theday. Your position in wheat futures increases to $5.12 per bushel (= $5.00 + $0.03 + $0.05 +$0.04.On March 18, your

10、 opening long position in wheat futures is $5.12 per bushel. Since the closingfutures price is $5.10 per bushel, your account experiences a cash outflow of $0.02 at the end ofthe day. Your position in wheat futures decreases to $5.10 per bushel (= $5.00 + $0.03 + $0.05 +$0.04 - $0.02. Since you rece

11、ive a notice of delivery on this date, you will pay the $5.10 futures price and receive 1 bushel of wheat.Therefore, the net amount that you pay for one bushel of wheat is $5.00 per bushel.b. i. Since the futures price wheat is $4.98 per bushel at the end of trading on March 18, the delivery price o

12、n that date is $4.98 per bushel .ii. On the delivery date, the long and short positions in a futures contract transact with the clearingcorporation at the current futures price. Therefore, you will pay the current futures price of $4.98 per barrel in order to receive the wheat. The difference betwee

13、n the price that you pay at delivery and the price at which you entered into the contract is reconciled by daily marked-to-market gains and losses.iii. On March 15, you entered into a long futures position in wheat at a price of $5.00 per bushel.Since the closing futures price is $5.03 per bushel, y

14、our account receives a cash inflow of $0.03 at the end of the day. Your position in wheat futures increases to $5.03 per bushel (= $5.00 + $0.03.On March 16, your opening long position in wheat futures is $5.03 per bushel. Since the closingfutures price is $5.08 per bushel, your account receives a c

15、ash inflow of $0.05 at the end of the day. Your position in wheat futures increases to $5.08 per bushel (= $5.00 + $0.03 + $0.05.On March 17, your opening long position in wheat futures is $5.08 per bushel. Since the closing futures price is $5.12 per bushel, your account receives a cash inflow of $

16、0.04 at the end of the day. Your position in wheat futures increases to $5.12 per bushel (= $5.00 + $0.03 + $0.05 + $0.04.On March 18, your opening long position in wheat futures is $5.12 per bushel. Since the closing futures price is $5.10 per bushel, your account experiences a cash outflow of $0.0

17、2 at the end of the day. Your position in wheat futures decreases to $5.10 per bushel (= $5.00 + $0.03 + $0.05 + $0.04 - $0.02.On March 19, your opening long position in wheat futures was $5.10 per bushel. Since the closing futures price is $4.98 per bushel, you will experience a cash outflow of $0.

18、12 at the end of the day. Your position in wheat futures decreases to $4.98 per bushel (= $5.00 + $0.03 + $0.05 + $0.04 - $0.02 - $0.12. Since you will receive a notice of delivery on this date, you will pay the $4.98 futures price and receive 1 bushel of wheat. Notice that even though you only paid

19、 $4.98 for the delivery of wheat, the net amount that you paid for it out of your pocket is $5.00 per bushel, the futures price at which you originally entered into the position.18Pay Futures Price of $5.10 at Delivery -$5.10Total Net Cash FlowEventTherefore, the net amount that you pay for one bush

20、el of wheat is $5.00 per bushel.25.4 a. The forward price of an asset with no carrying costs or convenience value is:Forward Price = S 0(1+ r where S 0 = the current price of the underlying assetr = the interest rate between the initiation of the forward contract and the delivery dateSinc e you will

21、 receive the bonds face value of $1,000 in 11 years and the 11-year spot interest rate is currently 8% per annum, the current price of the bond is $428.88 = $1,000 / (1.0811 .Since the forward contract defers delivery of the bond for one year, the appropriate interest rate to use in the forward pric

22、ing equation is the one-year spot interest rate of 3%:Forward Price = $428.88(1.03 = $441.75 Therefore, the forward price of your contract is $441.75.b. If both the 1-year and 11-year spot interest rates unexpectedly shift downward by 2%, the appropriateinterest rates to use when pricing the bond is

23、 6% per annum (EAY, and the appropriate interest rate to use in the forward pricing equation is 1% per annum (EAY. Given these changes, the current price of the bond increases to $526.79 = $1,000 / (1.0611. The new forward price of the contract is: Forward Price = $526.79(1.01 = $532.06 Therefore, t

24、he forward price of an otherwise identical contract will increase to $532.06 given theunexpected change in the 1-year and 11-year spot interest rates.25.5 a. You would create a short position by selling futures contracts.b. A short position reduces your overall risk if you are hurt by decreases in t

25、he price of the underlyingasset. For example, if you are selling oil in one year at the spot price, you will make less money if the price of oil falls over the next year. In order to hedge this risk, you should sell oil futures contracts that expire in approximately one year.c. You would create a lo

26、ng position by purchasing futures contracts.Cash Flow March 15Enter into Long Futures Positon at $5.00 per bushel None March 15Futures Price Increases to $5.03 per bushel $0.03March 16Futures Price Increases to $5.08 per bushel $0.05March 17Futures Price Increases to $5.12 per bushel $0.04March 18Fu

27、tures Price Decreases to $5.10 per bushel -$0.02March 19Futures Price Decreases to $4.98 per bushel -$0.12March 19Pay Futures Price of $4.98 at Delivery -$4.98Total Net Cash FlowEventd. A long position reduces your overall risk if you are hurt by increases in the price of the underlyingasset. For ex

28、ample, if you are planning to purchase oil in one year at the spot price, you will have topay more for the oil if the spot price increases over the next year. In order to hedge this risk, youshould buy oil futures contracts that expire in approximately one year.25.6 If Mark Fisher believes that the

29、futures price of silver will fall over the next month, he should take on ashort position in silver futures contracts with approximately one month until expiration. By selling futures contracts now, he will be locking in a sales price that is higher than what he believes he will be able topurchase si

30、lver futures for in one months time.25.7 William Santiago is a little naïve about the capabilities of hedging. While hedging can significantly reducethe risk of changes in foreign exchange markets, it cannot completely eliminate it. Basis risk is the primary reason that hedging cannot reduce 10

31、0% of any firms exposure to price fluctuations. Basis risk arises when the price movements of the hedging instrument do not perfectly match the price movements of the assetbeing hedged.25.8 a. The forward price of an asset with no carrying costs or convenience value is:Forward Price = S0(1+ rwhere S

32、0= the current price of the underlying assetr = the interest rate between the initiation of the forward contract and the delivery date Since you will receive the bonds face value of $1,000 in 18 months and the 18-month spot interestrate is currently 10.67% (EAY, the current price of the bond is $858

33、.92 = $1,000 / (1.10673/2.Since the forward contract defers delivery of the bond for six months, the appropriate interest rate touse in the forward pricing equation is the six-month spot interest rate of 9.83% (EAY.Therefore, the forward price of your contract is $900.15.b. It is important to rememb

34、er that 100 basis points equals 1% and one basis point equals 0.01%.Therefore, if all rates increase by 30 basis points, each rate increases by 0.003. The new 18-month spotrate (EAY is 0.1097 (= 0.1067 + 0.003, and the new 6-month spot rate (EAY is 0.1013 (= 0.0983 +0.003.Since the owner of a forwar

35、d contract will receive the bonds face value of $1,000 in 18 months andthe 18-month spot interest rate is currently 10.97% (EAY the current price of the bond is $855.44 =$1,000 / (1.10973/2.Since the forward contract defers delivery of the bond for six months, the appropriate interest rate touse in

36、the forward pricing equation is the six-month spot interest rate of 10.13% (EAY.Therefore, the forward price of an otherwise identical contract is $897.72 given the 30 basis pointincrease in all semiannual rates.25.9 Let r equal the interest rate between the initiation of the contract and the delive

37、ry of the asset.Cash Flows From Strategy 1Today 1 YearPurchase Silver-S0-Borrow+S0-S0(1+rTotal Cash Flow0-S0(1+rCash Flows from Strategy 2Today 1 YearPurchase Silver Forward-fTotal Cash Flow0-fNotice that each strategy results in the ownership of silver in one year for no cash outflow today.Since th

38、e payoffs from both the strategies are identical, the two strategies must cost the same in orderto preclude arbitrage.The forward price (f of a contract on an asset with no carrying costs or convenience value equals thecurrent spot price of the asset (S0 multiplied by 1 plus the appropriate interest

39、 rate between theinitiation of the contract and the delivery date of the asset.Therefore, f must equal S0(1+r.25.10 Kevin will be hurt if the yen loses value relative to the dollar over the next eight months. Depreciationin the yen relative to the dollar results in a decrease in the yen / dollar exc

40、hange rate. Since Kevin ishurt by a decrease in the exchange rate, he should take on a short position in yen per dollar futurescontracts in order to hedge his risk.25.11 a. Your former roommates annual mortgage payments form a 20-year annuity, discounted at thelong-term interest rate of 10%. Solve f

41、or the payment amount so that the present value of theannuity equals $300,000, the amount of principal that your former roommate plans to borrow.C = $35,238Therefore, your former roommates annual mortgage payment will be $35,238.b.The most significant risk that you face is interest rate risk. If the

42、 current market rate of interestrises between today and the date that you meet with the president of MAX, the fair value of themortgage will decrease, and the president will only be willing to purchase the mortgage from youfor a price less than $300,000. If this is the case, you will not be able to

43、loan your formerroommate the full $300,000 that you promised her.c.Treasury bond prices have an inverse relationship with interest rates. As interest rates rise,Treasury bonds become less valuable; as interest rates fall, Treasury bonds become more valuable.Since you are hurt when interest rates ris

44、e, you are also hurt when Treasury bonds decrease invalue. In order to protect yourself from decreases in the price of Treasury bonds, you should takea short position in Treasury bond futures to hedge his interest rate risk. Since three-monthTreasury bond futures contracts are available and each con

45、tract is for $100,000 of T-bonds, youwould take a short position in three 3-month Treasury bond futures contracts in order to hedgeyour $300,000 exposure to changes in the market interest rate over the next three monthsd.i. If the market interest rate is 12% on the date that you meet with the presid

46、ent ofMAX, the fair value of the mortgage equals an annuity that makes annual payments of$35,238 for 20 years, discounted at 12%.= $263,208Therefore, MAXs president will be willing to pay you $263,208 for the mortgage if themarket interest rate is 12% on the date of your meeting.ii. An increase in t

47、he interest rate will cause the value of the T-bond futures contracts to decrease.iii. You will make money on your short position in the T-bond futures contracts if interest rates rise.e.i. If the market interest rate is 9% on the date that you meet with the president ofMAX, the fair value of the mo

48、rtgage equals an annuity that makes annual payments of$35,238 for 20 years, discounted at 9%.= $321,672Therefore, MAXs president will be willing to pay you $321,672 for the mortgage if themarket interest rate is 9% on the date of your meeting.ii. A decrease in the interest rate will cause the value

49、of the T-bond futures contracts to increase.iii. You will lose money on your short position in the T-bond futures contracts if interest rates fall.25.12 a. The price of a bond equals the present value of its cash flows.b. If the market rate of interest increases to 14% per annum, the price of each b

50、ond will be:c.The percentage change in the price of each bond is calculated as follows:Percentage Change in Bond Price = (New Price / Old Price 1Percentage Change in Bond A = ($877.19 / $900.90 1= -2.63%Percentage Change in Bond B = ($519.37 / $593.45 1= -12.48%Percentage Change in Bond C = ($269.74

51、 / $352.18 1= -23.41%Therefore, Bond C experienced the greatest percentage change in price.25.13 a. The price of a bond equals the present value of its cash flows.Since Bond A pays an annual coupon of 7%, the bonds owner will receive $70 (= 0.07 * $1,000at the end of each year in addition to the bon

52、ds $1,000 face value when the bond matures at theend of year 4.The price of Bond A is $904.90.Since Bond B pays an annual coupon of 11%, the bonds owner will receive $110 (= 0.11 *$1,000 at the end of each year in addition to the bonds $1,000 face value when the bond maturesat the end of year 4.The

53、price of Bond B is $1,031.70.The duration of a bond is the average time to payment of the bonds cash flows, weighted by theratio of the present value of each payment to the price of the bond.The relative value of each payment is the present value of the payment divided by the price of thebond. The c

54、ontribution of each payment to the duration of the bond is the relative value of thepayment multiplied by the amount of time (in years until the payment occurs.Bond APayment PV of Payment Relative Value Time to Payment (in yearsDurationThe duration of Bond A is 3.6031 years.Bond BPayment PV of Payme

55、nt Relative Value Time to Payment (in yearsDurationThe duration of Bond B is 3.4529 years.b. If the market interest rate decreases to 7% per annum:= $1,000c.Bond A should experience a greater percentage change in its price. Bond A has a higher durationthan Bond B since a larger proportion of its pay

56、ments occur in later years. Bonds with higherdurations will experience greater percentage changes in price for a given movement in the interestrate.d. The percentage change in the price of each bond is:Percentage Change in Bond Price = (New Price / Old Price 1Percentage Change in Bond A = ($1,000 /

57、$904.90 1= 10.51%Percentage Change in Bond B = ($1,135.49 / $1,031.70 1= 10.06%25.14 The duration of a bond is the average time to payment of the bonds cash flows, weighted by the ratioof the present value of each payment to the price of the bond.Since the bond is selling at par, the market interest

58、 rate must equal 9%, the annual coupon rate on thebond. 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 pay