Problem Set 2 Derivatives

Problem 1 C(S,X,t) + B(X,t) = S + P(S,X,t) $12 + $89$95 + $2.50 $101 $97.50 Profit = $3.50

Problem 2 C(S,X,t) + B(X,t) = S + P(S,X,t) $11 + $42.70$50 + $3 $53.70 $53 Build a Box! $2 + $47.44$50 + $5 $49.44 $55

So, what comes from building the box? Problem 2 Initially: $55–$ –$53 + $ = $6. 26 At expiration you will pay $5 (option portion) and receive $5 (bond portion) so net zero S $45–$50 = –$5 Profit: $6. 26

Problem 3 C(S,X,t) + B(X,t) = S + P(S,X,t) $ $ $ $3. 75 $ Use a box to borrow $ $ $ $ $

So, what comes from building the box? Problem 3 S Initially: $ – $ $ – $3. 75 = $4. 75 $85–$90 = –$5 At expiration you will pay $5 no matter what Borrow at T-bill rate

Problems 4, 5, 6, 7

C(S,X,t) = S - B(X,t) + P(S,X,t) Keys for using OPT as an analytical tool C(S,X,t) = S - B(X,t) + P(S,X,t) Stock Call B(X,t) Stock Call B(X,t) S C X C t C C  R C P P P P P

Problem 8 New York $10 buys a put to sell £120 in exchange for $200 (exchange at the forward rate) London £5.58 buys a call to buy $200 in exchange for £120 (exchange at the forward rate) Answer: $10 *.62 = £6.20, so buy the calls in London & sell puts in New York $1 = £0.62 spot $1 = £0.60 forward

Problem 9 New York Find equilibrium price for a call to buy €100 in exchange for $135 (exchange at the forward rate) Answer: €5 * 1.32 = $6.60 Frankfurt €5 buys a put to sell $135 in exchange for €100 (exchange at the forward rate) € 1 = $1.32 spot € 1 = $1.35 forward

Problems for Discussion 10.Will the premium for a currency option be higher when there is greater uncertainty about the inflation differential in the two countries? 11.Explain the factors that determine the value of currency options such as the ones in problems 8 and Suppose a corporate treasurer complains that currency options are too expensive? Explain the advantages of currency options compared with forward contracts. Why do options command a premium?

PENs SCPERS BT Counterpary PEFCO $5 mm $5mm + Appreciation 1% Coupon Fixed Undisclosed Flow Appreciation

Equity Call Swap Investor Underwriter Illustration of an Equity Call Swap Equity Index Price Appreciation* * No depreciation—settlement at maturity Libor ± Spread

Problem 13  E(R) CML 3% 8% 5% 8% 10% Need to know beta Phillips is below the market line

Problem 14  E(R) CML 3% 8% 5% 8% 12% This is an arbitrage opportunity! ARCO is above the market line

Problem 15  E(R) SML 5% 15% 1.0 Stock B is undervalued % % 11% 0.5

Problem 16  E(R) SML 5% % 13% 0.8 It is in equilibrium This stock is on the market line

Problem 21 Value of new package (per Value Additivity Principle) $100,000,000 for Megalithic Iron Works $50,000,000 for Newton Brickyards $150,000,000 Total Less cash paid to Newton Stockholders: $100,000,000 Remaining value of Megalithic stock: $50,000,000

Problem 1 NYLONFRA $1=£0.60 $1 = € 0.80 £1 = €1.60 $1,000,000 £ 600,000 € 960,000 $1,200,000 Profit = $200,000

Problem 5 Moving from 6% coupon to 8% coupon Adds extra income of $2 per year Adds $9 to price ($76 compared with $69) Moving from 8% coupon to 10% coupon Also adds extra income of $2 per year But, adds $12 to price ($88 compared with $76) Therefore, the 10% bond is over-priced (compared with the 8% bond)

Problem 5 Buy $2 per year for 10 years Buy an 8% bond and sell a 6% bond ($67 - $76) Net outflow is $9 Sell $2 per year for 10 years Buy an 8% bond and sell a 10% bond ($88 - $76) $12 net inflow Profit $3

Problem 5 Buy two of the 8% coupon bonds $152 outflow Sell one 6% and one 10% bond $67 inflow $88 inflow $155 total inflow Result $3 current inflow Zero net future cash flows

Problem 5 Yield Convexity 12.10% 11.68% 12.22%

Problem 6 Moving from 6% coupon to 8% coupon Adds extra income of $2 per year Adds $12 to price ($79 compared with $67) Moving from 8% coupon to 10% coupon Also adds extra income of $2 per year But, adds $9 to price ($88 compared with $79) Therefore, the 8% bond is over-priced

Problem 6 Buy $2 per year for 10 years Buy a 10% bond and sell an 8% bond ($79 - $88) Net outflow is $9 Sell $2 per year for 10 years Buy a 6% bond and sell an 8% bond ($79 - $67) $12 net inflow Profit $3

Problem 6 Sell two of the 8% coupon bonds $158 inflow Buy one 6% and one 10% bond $67 outflow $88 outflow $155 total outflow Result $3 current inflow Zero net future cash flows

Problem 6 Yield Convexity 12.10% 11.68% 11.60%

Problem 7 Moving from 0% coupon to 6% coupon Adds extra income of $6 per year Adds $38.28 to price ($75.08 minus $36.80) Moving from 6% coupon to 8% coupon Adds extra income of $2 per year Adds $3.92 to price ($79 compared with $75.08) Therefore an extra $6 per year should cost three times as much, $11.76 The 0% bond is a bargain

Problem 7 Sell $6 per year for 10 years Sell a 6% bond and buy a 0% bond ($ $36.80) $38.28 net inflow Buy $6 per year for 10 years Buy three 8% bonds and sell three 6% bonds ($ $237) $11.76 net outflow Profit $26.52

Problem 7 Buy three 8% coupon bonds and one 0% bond $237 outflow (3*79) $36.80 outflow $ total outflow Sell four 6% coupon bonds $ inflow (4*75.08) Result $26.52 current inflow Zero net future cash flows

Problem 7 Yield Convexity 11.60% 10.25% 10.00%

Problem 8 Sell $1,000,000 of Texaco stock Buy $950,000 of market portfolio Buy $50,000 of T-bills Result Zero net investment Zero beta Positive expected inflow when Texaco takes hit

Problem 9 Sell $1,000,000 of GM stock Sell $50,000 of T-bills Buy $1,050,000 of market portfolio Result Zero net investment Zero beta Positive expected inflow when GM takes hit

Warm-up: Problem 2 NYLONZUR $1=£0.40 $1=CHF 1.30 £1=CHF 2.60 $1,000,000 £ 500,000 CHF 1,300,000 $1,250,000 Profit = $250,000

Problem 6 (Basis too big) $1,050, ,000 bu $1,150, ,000 bu Profit = $84, Money today Wheat today $2. 00 per bushel $2. 30 per bushel Wheat later Storage 10¢ $1,065, Money later 3% %

Problem 7 (Basis too small) $1,000, ,000 bu $1,010, ,000 bu Profit = $4, Money today Wheat today $2. 00 per bushel $2. 02 per bushel Wheat later Storage 10¢ $1,014, Money later 3% %

Problem 9 Net for RRNB: extra 1% each year This is includes a Floating/Floating Swap RRNB T-Bill + 1% CitiCorp LIBOR + 1% Counterparty T-Bill LIBOR BW Homes T + 2% Midland Bank LIBOR + 1% $10,000 per year profit!

Problem 10 Breakup Value $750,000,000 from Shug’s Restaurants $600,000,000 from Betty’s Boutiques $200,000,000 from airline liquidation $1,550,000,000 Total Market Value of Package: $1,000,000,000 Value of airline as going concern: $550,000,000

Problem 12 C(S,X,t) + B(X,t) = S + P(S,X,t) $10 + $89$95 + $1.75 $99 $96.75 Build a Box! $12 + $84.06$95 + $1.25 $96.06 $96.25

So, what comes from building the box? Problem 12 S Initially: $10 – $1.75 – $12 + $1.25= – $2.50 $90 – $85 = $5 At expiration you will receive $5 no matter what Double your money!