chap025 - Chapter 25: Derivatives and Hedging Risk 25.1 on...

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Unformatted text preview: Chapter 25: Derivatives and Hedging Risk 25.1 on the b. at a to buy a are forwards 25.2 1. 2. 3. 25.3 a. b. a. A forward contract is an agreement to either purchase or sell a specific amount of a specific good on a specific date at a specific price. It represents an obligation both parties--the party agreeing to buy in the future at a specified price and party agreeing to sell in the future at a specified price. A futures contract is identical to a forward contract in that it is an agreement to either purchase or sell a specific amount of a specific good on a specific date specific price. It represents an obligation on both parties--the party agreeing in the future at a specified price and the party agreeing to sell in the future at specified price. The difference between futures and forwards is that futures standardized contracts trading on exchanges with daily resettlement while are agreements tailored to the needs of the counterparties. Futures contracts have standard features and are traded on exchanges, while forward contracts are less standard and are not traded on exchanges. Risk positions in futures are generally reversed prior to delivery, while forward contracts usually involve delivery. The futures market is largely insulated from default risk by features such as markto-market and margin call provisions. i) ii) iii) i) ii) iii) $5.10 $5.00 $0.03 + $0.05 + $0.04 - $0.02 - $5.10 = -$5.00 $4.98 $5.00 $0.03 + $0.05 + $0.04 - $0.02 - $0.12 - $4.98 = -$5.00 25.4 PForw.Cont = Face value (1 + r1 ) / (1 + r11 )11 Both r1 and r11 decreased, but r11 has 11th power. Thus, (1 + r11 )11 has more effect of downward shift. Therefore, the price of the forward contract will increase. Sell a futures contract. A short hedge is a wise strategy if you must hold inventory, the price of which may change before you can sell it. Buy a futures contract. A long hedge is a wise strategy if you are locked into a future selling price for a good. 25.5 a. b. c. d. 25.6 Mary Johnson is investing on wheat futures not on commodity wheat. Since she believes that wheat futures price will fall in the future, she will take a short position on the wheat futures contract. 25.7 Your friend is a little naive about the capabilities of hedging. Hedging will reduce risk, but it cannot eliminate it. There can be a difference in basis between the prices in two different locales. The random nature of the basis adds risk to hedging. A party to a futures contract is also subject to mark-to-mark risk. Finally, very few contracts ever make delivery. Without assured delivery, the basis risk may be magnified. For example, a farmers contracts for wheat on the Chicago exchange, but is unable to deliver to Chicago. He must sell his wheat on the local market. The local prices may be very different from the Chicago prices. The text discusses these differences more fully. Answers to End-of-Chapter Problems B-209 25.8 a. b. ii P = 50 (1.048) / (1.050) 2 + 50 (1.048) / (1.052) 3 + 50 (1.048) / (1.055) 4 + 1050 (1.048) / (1.057) 5 = $968.84 i). The value of the forward contract should fall. ii) P = 50 (1.048) / (1.053) 2 + 50 (1.048) / (1.055) 3 + 50 (1.048) / (1.058) 4 iii + 1050 (1.048) / (1.060) 5 iv = $918.32 Today's cash flow -S0 0 -F / (1 + rf) Cash flow at maturity S1 S1 - F F 25.9 Strategy 1. Buy silver 2. Long on futures Lend $F / (1 + rf) Payoff for the two strategies are the same in one month at the maturity of the futures contract. Therefore, S0 = F / (1 + rf) or F = S0 (1 + rf) 25.10 Since she needs US dollars one year later, she should buy US dollar futures to hedge against exchange rate risk. 25.11 a. b. c. 25.12 a. $300,000 = C 0.10 = 8.51356 C C = $35,237.89 Interest rate changes. Hedge by writing a futures contract on Treasury bonds. 20 i) ii) iii) 20 $35,237.89 0.12 = $263,207.43 b. i) ii) iii) A: B: C: A: B: C: A: B: C: Year 1 Interest rate T bond and Short position in T bond Mortgage The loss on the mortgage is entirely offset by the gain in the futures market. The net gain or loss is zero. 20 $35,237.89 0.09 = $321,670.69 The opposite to ii) in a. The net gain or loss is zero. $1,000 / 1.11 = $900.90 $1,000 / 1.115 = $593.45 $1,000 / 1.1110 = $352.18 $1,000 / 1.14 = $877.19 $1,000 / 1.145 = $519.37 $1,000 / 1.1410 = $269.74 -($900.90 - $877.19) / $900.90 = -0.0263 = -2.63% -($593.45 - $519.37) / $593.45 = -0.1248 = -12.48% -($352.18 - $269.74) / $352.18 = -0.2341 = -23.41% Payment $100 Present value $100 / (1 + r) Relative value {$100/(1+r)}/($100/r) = r/(1+r) 25.13 a. b. c. 25.14 B-210 Answers to End-of-Chapter Problems 2 3 4 . . . $100 $100 $100 . . . $100 / (1 + r)2 $100 / (1 + r)3 $100 / (1 + r)4 . . . 100 / r {$100/(1+r)2}/($100/r) = r/(1+r)2 {$100/(1+r)3}/($100/r) = r/(1+r)3 {$100/(1+r)4}/($100/r) = r/(1+r)4 . . . 1.0 = 1 r / (1 + r) + 2 r / (1 + r)2 + 3 r / (1 + r)3 + 4 r / (1 + r)4 + ... = r [1 / (1 + r) + 2 / (1 + r)2 + 3 / (1 + r)3 + 4 / (1 + r)4 + ...] Duration / (1 + r) = r [1 / (1 + r)2 + 2 / (1 + r)3 + 3 / (1 + r)4 + ...] Duration - Duration / (1 + r) = {1 - 1 / (1 +r)} Duration = r [1 / (1 + r) + 1 / (1 + r)2 + 1 / (1 + r)3 + 1 / (1 + r)4 + ...] = r (1 / r) =1 Therefore, {r / (1 + r)} Duration = 1 or Duration = (1 + r) / r Duration r = 12% Duration = (1 + 0.12 )/ 0.12 = 9.333 years r = 10% Duration = (1 + 0.10 )/ 0.10 = 11.0 years 25.15 a. $70 / 1.1 +$70 / 1.12 + $70 / 1.13 + $1,070 / 1.14 = $904.90 B: $110 / 1.1 + $110 / 1.12 + $110 / 1.13 + $1,110 / 1.14 = $1,031.70 A: This bond is selling at par. Its price is $1,000. B: $110 / 1.07 + $110 / 1.072 + $110 / 1.073 + $1,110 / 1.074 = $1,135.49 A: ($1,000 - $904.90) / $904.90 = 0.1051 = 10.51% B: ($1,135.49 - $1,031.70) / $1,031.70 = 0.1006 = 10.06% The 7% bond has a higher duration since more of its total repayments occur in the later years. Bond with higher duration have greater percentage changes in their prices than do low duration bonds for a given percentage change in the interest rate. A: b. c. d. Answers to End-of-Chapter Problems B-211 25.16 Payment $90 90 1,090 Duration = 2.76 years 25.17 Payment $90 90 90 1,090 Duration = 3.53 years 25.18 Payment $50 50 50 1,050 Duration = 3.72 years 25.19 PV 0 0 $13,150.32 $11,435.06 $9,943.53 $8,646.55 $43,175.47 Duration = 1 0 + 2 0 + 3 0.30458 + 4 0.26485 + 5 0.23030 + 6 0.20027 = 4.33 years 25.20 a. Year 1 2 3 4 5 6 Payment 0 0 $20,000 $20,000 $20,000 $20,000 Relative value 0 0 0.30458 0.26485 0.23030 0.20027 1.0000 PV $47.6190 45.3515 43.1919 863.8376 Relative value 0.04762 0.04535 0.04319 0.86384 Maturity 1 2 3 4 Duration 0.04762 0.09070 0.12957 3.45536 3.72325 PV $82.5688 75.7512 69.4965 772.1835 Relative value 0.08257 0.07575 0.0695 0.7722 Maturity 1 2 3 4 Duration 0.08257 0.15150 0.2085 3.0888 3.5315 PV $82.5688 75.7512 841.6800 Relative value 0.08257 0.07575 0.84168 Maturity 1 2 3 Duration 0.08257 0.15150 2.52504 2.75911 b c. 25.21 a. Dollar amounts are in millions. 0 ($43 / $1,255) + 0.33333 ($615 / $1,255) + 0.75 ($345 / $1,255) + 5 ($55 / $1,255) + 15 ($197 / $1,255) = 2.943 years Dollar amounts are in millions. 0 ($490 / $1,110) + 1.5 ($370 / $1,110) + 10 ($250 / $1,110) = 2.752 years No. Besdall is not immune to interest rate risk since the product of market value times duration is different for assets than for liabilities. 2.943 $1,255 million = duration $1,110 million Liability duration = 2.943 ($1,255) / $1,110 = 3.327 Answers to End-of-Chapter Problems B-212 b. Duration $1,255 million = 2.752 $1,110 million Asset duration = 2.752 ($1,110) / $1,255 = 2.434 Duration of assets = 0 $100 / $1,800 + 1 $500 / $1,800 + 12 $1,200 / $1,800 = 8.278 years Duration of liabilities = 0 $300 / $1,200 + 1.1 $400 / $1,200 + 18.9 $500 / $1,200 = 8.242 years No, it is not immunized from interest rate risk. Duration of asset market value of asset = 8.278 $1,800 = $14,900.4 Duration of liability market value of liability = 8.242 $1,200 = $9,890.0 To be immunized from interest rate risk, either (1) increase the duration of liabilities without changing the duration of the assets or (2) decrease the duration of assets without changing the duration of liabilities. Yes, there is an opportunity for the Miller Company and the Edwards company to benefit from a swap. Miller has the comparative advantage in the Fixed-rate market while Edwards has the comparative advantage in the floating rate market. Miller Company Edwards Company Fixed Rate 10% 15% Floating Rate LIBOR +0.3% LIBOR +2.0% 25.22 a. b. 25.23 a. In the floating rate market, the lender usually has the opportunity to review the floating rates every 6 months. If the creditworthiness of Edwards Company declined, the lender has the option of increasing the spread over LIBOR that is charged. b. The Strategy: 1. Miller borrows at fixed rate loan of 10%. 2. Edwards borrows at floating rate loan of LIBOR +2.0% 3. Enter into a swap (with a notional principal) Miller: 3 sets of interest-rate cash flows. 1. It pays 10% per annum to outside lenders. 2. It receives 11.65% per annum from Miller. 3. It pays LIBOR +0.15% to Edwards. Edwards: 3 sets of interest-rate cash flows. 1. It pays LIBOR +2.0% per annum to outside lenders. 2. It receives LIBOR +0.15% from Miller. 3. It pays 11.65% to Miller. Answers to End-of-Chapter Problems B-213 Miller Borrowing at LIBOR +0.15% floating rate (cheaper by 0.15% than it would have to pay if it borrows directly from the floating rate market.) Edwards Borrowing at 11.65% Fixed (cheaper by 3.35% than it would pay if it borrows directly from the fixed rate market.) Both sides are better off by 1.50% per annum. B-214 Answers to End-of-Chapter Problems ...
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