1. Extra Practice 2

2. Problem 1 ¥102,440 $1,000 ¥105,513. 20 $1,005 Profit = 0 $1 = ¥102.44 $1 = ¥104.99 ¥1 = $0.0095 NY today NY later ¥105,513. 20 TOK today TOK later R = 3% R = 0.5%

3. Problem 2 (Reference: Set 1, #4&5, 10-18 ) Real rate –Switzerland: (0.25% – 0%)/1.00 = 0.25% –England: (?% – 2%)/1.02 = 0.25% Equilibrium nominal rate in England would be 2.2550%

4. Problem 3 (Reference: Set 1, #7) $1310 CHF 1152.80 $1320 CHF 1135.20 Equilibrium NY today $1 = CHF 0. 88 $1 = CHF 0. 8600 CHF 1 = $ 1.1628 ZUR today ZUR later Spot CHF 1152.80 Future CHF 1135.20 $1320 NY later Spot $1310 Future $1320

5. Real return after tax R (1 – t) – i 1+i r = 3% (1 –.35) – 2% 1.02 r = r = –0.0490% Problem 4 (Reference: Set 1, #16-18)

6. Problem 5 (Reference: Set 1, #1 & 2) TokyoFRANYC €1= ¥ 141.40 ¥1 = $0. 0101 $1 = ¥98. 98 €0.70 = $1 ¥141.40 €1 $1.4286 ¥141.40 Equilibrium

7. Problem 6 (Reference: Set 1, #12 & 13; see #2) Direct Approach N = 5 I/YR = 5.06% P/YR = 1 FV = 1000 PMT = 0 Compute PV Result: $781.29 2-Step Approach N = 5 I/YR = 2% FV = 1000 Compute PV Result: $905.7308 Input this as FV I/YR = 3% Compute PV Result: $781.29

8. Problem 7 (Reference: Set 2, #8) New York Find price of a put to sell £61 in exchange for $100 (exchange at the forward rate) Answer: * = £2.50/0.59 = $4. 24 London £2. 50 buys a call to exchange $100 for £61 (exchange at the forward rate) $1 = £0.59 spot

9. Problem 8 (Reference: Set 1, #21-24) NY today $1,000,411. 04 $1,003,705. 40 $1,000,000 $1,000,411. 04 Profit = 0 0.5% NY 30 day 2% 1.5% NY 90 day

10. Problem 9 (Reference: Set 3, #45 & 46) Generic Interest Rate Arbitrage: Different Coupons C (Example: 5%) C–x (Example: 4%) C+x (Example: 6%) Requires three equally-spaced coupons Price should be average of the two “bookends” Price is $70 Price is $85 Price is $77.50

11. Problem 10 (Reference: Set 2, #8 & 9) With currency options, a New York call on the Euro is the same as a Frankfurt put on the dollar The premia should match when compared at the spot exchange rate –When rendered on the same scale Choice C is correct

12. Problem 11 $9360. 34 £5429 $10,000 Profit = 0 NY today $1. 00 = £ 0. 58 $1. 00 = £ 0. 61 LON today LON later $10,000 NY later Price £89 Face £100 Price $93.60 Future $100 £6100 £5429

13. Problem 12 (Reference: Set 3, #45) Coupon Stripping Moving from the 7% coupon to the 6% coupon reduces income by $1 per year, and reduces the price by $5 Moving from the 6% coupon to the 5% coupon reduces income by $1 per year, and reduces the price by $5 Moving from the 5% coupon to the 4% coupon reduces income by $1 per year, and reduces the price by $5 So, reducing the income by $1 per year should reduce the price by $5 Thus, the price of a zero-coupon bond would be $80 –$20= $60 (so YTM is 7.43%)

14. Problem 13 FRA today $1,000,000 €720,000 $1,002,468. 78 €723,559. 41 Profit = 0 NY today $1 = € 0.72 € 1=$1.3855 $1 = €0.7218 FRA later 1% NY later 0.5% $1,002,468. 78

15. Problem 14 (Reference: Set 1, #7) $1340 £ 804 $1370 £ 794.60 Equilibrium NY today $1 = £0.60 $1 = £ 0. 5800 £ 1 = $ 1.7241 LON today LON later Spot £804 Future £794.60 $1370 NY later Spot $1340 Future $1370

16. Problem 15 (Reference: Set 1, #8) CHF 880,000 $ 1,000,000 CHF881,085. 60 $ 1,015,347. 59 Profit = 0 $1 = CHF0.88 $ 1=CHF0.8678 CHF1 = $1.1524 NY today NY later Spot 1870 Future 1880 Dividend 1% CHF881,085. 60 ZUR today ZUR later R = 0.25%

17. Problem 16 $10,800,000 ¥756,000,000 ¥734,400,000 Net ¥21,600,000 (or $308,571. 43 ) $10,000,000 $ 8,700,000 Net $1,300,000 (or ¥88,400,000) $1= ¥ 70. 00 $1 = ¥ 68. 00 ¥ 680,000,000 100,000 bbl US today TOK today TOK later US later Oil $ 108. 00 Oil $ 87. 00 Oil ¥ 7,344 Oil ¥ 6,800 100,000 bbl

18. Problem 17 (Reference: Set 1, #12 & 13; see #2) Direct Approach N = 5 I/YR = 1.4706% P/YR = 1 PV = –1000 PMT = 0 Compute FV Result: $1075.7241 2-Step Approach N = 5 I/YR = 3.5% PV = –1000 Compute FV Result: $1187.6863 I/YR = 2% Compute PV Result: $1075.7241

19. Problem 18 (Reference: Set 1, #21-24) NY today $1,000,328. 82 $1,001,480. 54 $1,000,000 $1,000,328. 82 Profit = 0 0.4% NY 30 days 0.7000% 0.6% NY 90 days

20. Problem 19 (Reference: Set 1, #12 & 13) Direct Approach N = 12 I/YR = 8.15% P/YR = 1 FV = 1000 PMT = 0 Compute PV Result: $390.5546 2-Step Approach N = 12 I/YR = 5% FV = 1000 PV = 556.8374 Input this as FV I/YR = 3% Compute PV Result: $390.5546

21. Problem 20 (Reference: Set 3, #51& 52) $74. 6667 €56.00 Profit = 0 NY today $1. 00 = € 0. 75 $1. 00 = € 0. 70 FRA today FRA later NY later Price €80 Face €100 Price ? Future $100 $100 €70 €56.00

22. Problem 21 (Reference: Set 1, #7) €81,000 $108,000 €78,000 $111,428. 5714 Profit =0; U.S. Future = $111. 43 $1. 00 = €0. 75 $1. 00 = €0. 70 NY today NY later Spot $108. 00 Future ? €78,000 RTD today Spot €81. 00 Future €78. 00 RTD later

23. Problem 22 (Reference: Set 1, #7) CNY658,800 $108,000 CNY656,038. 40 $107,000 Profit = 0; U.S. Future = $107. 00 Beijing today $1. 00 = CNY 6. 10 $1. 00 = CNY 6. 1312 NY today NY later Spot $108 Future ? CNY656,038. 40 Beijing later Spot CNY658. 80 Future CNY656. 0384

24. Problem 23 (Reference: Set 1, #9) CHF 917,500 $ 1,000,000 CHF 927,508. 14 $ 1,030,000 Profit = 0 $1 = CHF 0.9175 $1 = CHF 0.9005 CHF 1 = $1.1105 NY today NY later Spot 1780 Future 1815.60 Dividend 1% CHF 927,508. 14 ZUR today ZUR later R = 2.2%

25. Problem 24 (Reference: Set 3, #51& 52) $77. 2325 £48 Profit = 0 NY today $1. 00 = £ 0. 6215 $1. 00 = £ 0. 60 LON today LON later NY later Price £80 Face £100 Price ? Future $100 $100 £60 £48

26. Problem 25 (Reference: Set 1, #3) FRA today $1,000,000 €745,000 $1,050,143. 60 €756,103. 39 Profit = $0 NY today $1 = €0. 7450 $1 = €0. 72 FRA later 3.00% NY later 9.9226% $1,050,143. 60

27. Problem 26 (Reference: Set 1, #7) £744,000 $1,200,000 £ 727,200 $1,212,000 Profit = 0 LON today $1. 00 = £0. 62 $1. 00 = £0. 6000 £1. 00 = $1. 6667 NY today NY later Spot $1200 Future $1212 £ 727,200 LON later Spot £744 Future £727.20

28. Problem 27 (Reference: Set 1, #3) IND today $1,000 IDR 11,700,000 $1,001. 23 IDR 11,845,134. 43 Profit = $0 NY today $1 = IDR 11,700 $1 = IDR 11,830. 54 IDR 1 = $0. 0000845 IND later 2.5% NY later 0.25% $1,001. 23

29. Problem 28 € 8,200,000 ¥1,107,000,000 ¥1,100,000,000 Net ¥7,000,000 (or €51,851. 85 ) € 8,030,303. 03 € 8,000,000 Net € 30,303. 03 (or ¥4,000,000) €1= ¥ 135. 00 €1 = ¥ 132. 00 ¥ 1,060,000,000 100,000 bbl ROT today TOK today TOK later ROT later Oil € 82. 00 Oil € 80. 00 Oil ¥ 11,000 Oil ¥ 10,600 100,000 bbl

31. Problem 25 ¥ 925,000,000 CYN 68,181,820 CYN 70,075,757. 58 Net CYN 1,893,937. 58 (¥ 25 million) ¥ 921,736,250 ¥ 920,000,000 Net ¥ 1,736,250 (CYN 131,037.74) CYN1=¥13. 20 CYN1 = ¥13. 25 100,000 bbl Tokyo today Beijing today Beijing later Tokyo later Oil CYN 681.8182 Oil CYN 695.65 Oil ¥9250 Oil ¥9,200 100,000 bbl

32. Problem 25 (prices in £) £7,100,000 £6,302,079.69 Net £797,920.31 £8,391,608. 39 £7,500,000. 00 Net £891,608. 39 £1= Rp14,281 £1 = Rp14,300 £8,391,608.39 100,000 bbl Rot today Tokyo today Tokyo later Rot later Oil 71 Oil £75 Oil £83.9161 Oil £63.0208 100,000 bbl

33. Question 13 ¥ Debt Support 2 2 € Debt Support ¥ Debt Support € Debt Support 1 1 ¥ Principal € Principal ¥ Principal Variation on a currency swap Step 1 is notional Step 2 is net Borrow in Europe against income from Japan U.S. Company Intermediary Borrow in Japan, invest in Europe French Company

34. Fisher Effect: R = r + i + ri Prob: r = 3% i = 2% R = 5.06% (Reference: Set 1, #10-15)

35. 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