1. Problem Set 1 Parity Relationships & Arbitrage

2. Problem 1 NYLONFRA $1=£0.60 $1 = € 0.75 £1 = € 1.50 $1,000,000 £ 600,000 € 900,000 $1,200,000 Profit = $200,000

3. Problem 2 NYLONZUR $1=£0.46 $1=CHF 0.92 £1=CHF 1.60 $1,000,000 £ 575,000 CHF 920,000 $1,250,000 Profit = $250,000

4. Problem 3 FRA today $1,000,000 €769,230. 77 $1,027,766. 31 €784,554. 44 Profit = $22,822. 69 NY today $1.30 = € 1 $1.31 = € 1 FRA later 4% NY later 1% $1,004,943. 62 What is not balanced?

5. Problem 4 Real rate in Switzerland: (6% – 1%) / 1.01 = 4.95% Real rate in United States: (2% – 0.5%) / 1.005 = 1.49% Money will flow to the higher real rate, flowing from the U.S. into Switzerland Pressures will be on The U.S. nominal rate to rise The Swiss nominal rate to decline

6. Problem 5 Real rate in Japan: (5% – 1%) / 1.01 = 3.96% Real rate in UK: (10% – 7%) / 1.07 = 2.80% Money will flow to the higher real rate, flowing from the UK into Japan Pressures will be on The UK nominal rate to rise The Japanese nominal rate to decline

7. Problem 6 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% HSBC Bank LIBOR + 1% $10,000 per year profit!

8. Problem 7: Gold $1,215,306. 29 1000 oz. $1,294,937. 14 1000 oz. Profit = $73,622. 84 NY today $1. 00 = £ 0. 6089 $1. 00 = £ 0. 5886 LON today LON later Spot £740 Future £762.20 $1,221,314. 30 NY later 1% What is not balanced?

9. Problem 7: Silver $1,212,021. 68 60,000 oz. $1,291,539. 25 60,000 oz. Profit = $73,525. 79 NY today $1. 00 = £ 0. 6089 $1. 00 = £ 0. 5886 LON today LON later Spot £12.30 Future £12.67 $1,218,013. 45 NY later 1% What is not balanced?

10. Problem 7: Tin $1,221,875. 51 120,000 lbs $1,301,936. 80 120,000 lbs Profit = $74,020. 80 NY today $1. 00 = £ 0. 6089 $1. 00 = £ 0. 5886 LON today LON later Spot £6.20 Future £6.386 $1,227,916. 00 NY later 1% What is not balanced?

11. Problem 8 € 769,230. 77 $ 1,000,000 € 808,736. 22 $ 1,059,444. 44 Profit = € 20,303. 67 $1.30 = € 1 $1.31 = € 1 NY today NY later Spot 1350 Future 1410 Dividend 1.5% € 788,432. 55 FRA today FRA later R = 5% What is not balanced?

12. Problem 9 CHF 920,000 $ 1,000,000 CHF 1,012,511. 06 $ 1,059,444. 44 Profit = CHF 69,545. 73 $1 = CHF 0.9200 $1 = CHF 0.9557 NY today NY later Spot 1350 Future 1410 Dividend 1.5% CHF 942,965. 33 ZUR today ZUR later R = 5% What is not balanced?

13. Fisher Effect: R = r + i + ri Prob 10: r = 3% i = 4% R = 7.12% Prob 11: r = 3% i = 5% R = 8.15% Prob 12: r = 3% i = 5% R = 8.15% FV = $1000, PV = $456. 81 Prob 13: r = 4% i = 3% R = 7.12% FV = $1000, PV = $933. 53 Prob 14: r = 4% i = 3% R = 7.12% Prob 15: r = 4% i = 3% R = 7.12% FV=$1000, PV = $502. 68

14. Illustration of Real Return after tax Year zero: Invest $100 R is 9% i is 5% Marginal tax rate is 28% One year later: Collect $109 Pay tax of $2.52 –Tax is 28% of $9 –$106.48 left over Reinvest $105 –Keeps real principal intact Spend $1.48 Expected real profit is $1.48/1.05 = $1.41 Expected real return after tax is 1.41% R (1 – t) – i 1 + i r =

15. Real return after tax R (1 – t) – i 1+i r = 9% (1 –.28) – 5% 1.05 r = r = 1.41% Problem 16

16. Real return after tax R (1 – t) – i 1+i r = 4% (1 –.28) – 3% 1.03 r = r = – 0.12% Problem 17

17. Real return after tax R (1 – t) – i 1+i r = 21.5% (1 –.7) – 15% 1.15 r = r = – 7.43% Real World Example: January 1981

18. Real return after tax R (1 – t) – i 1+i r = 10% (1 –.28) – 9% 1.09 For CD, r = r = – 1.65% Problem 18 12% (1 –.28) – 9% 1.09 For loan, r = r = – 0.33% Conclusion: Saving is a drag! Borrow the money and buy now

19. Basis too big, Problem 19 $1,050,000 500,000 bu. $1,150,000 500,000 bu. Profit = $46,928. 59 Money today Wheat today $2. 00 = 1 bushel $2. 30 = 1 bushel Wheat later Storage $0. 10 $1,103,071. 41 Money later 10% Return is 18.45%

20. Basis too small, Problem 20 $1,000,000 500,000 bu. $1,015,000 500,000 bu. Profit = $35,544. 20 Money today Wheat today $2. 00 = 1 bushel $2. 03 = 1 bushel Wheat later Storage $0. 10 $1,050,544. 20 Money later 10% Borrow at 3.02%

21. Bonds as commodities (Problem 21) NY today $1,024,960. 58 $1,051,580. 58 $1,000,000 $1,025,592. 43 Profit = $631. 85 10.00% NY 90 days 10.15% 10.20% NY 180 days

22. Bonds as commodities (Problem 22) NY today $1,017,408. 41 $1,035,732. 50 $1,000,000 $1,017,634. 17 Profit = $225. 76 7.00% NY 90 days 7.15% 7.12% NY 180 days

23. Bonds as commodities (Problem 23) NY today $1,035,630. 37 $1,055,088. 67 $1,000,000 $1,035,758. 04 Profit = $127. 67 7.10% NY 180 days 7.5% 7.25% NY 270 days

24. Bonds as commodities (Problem 24) NY today $1,017,408. 41 $1,055,088. 67 $1,000,000 $1,055,739. 13 Profit = $650. 46 7.00% NY 90 days 7.50% 7.25% NY 270 days

25. Problem 25 Suppose the futures price of Plantonium (a mineral which your firm uses heavily) is $55 per unit for delivery in six months. At the same time the spot price is $60. Assuming that the futures market is reasonably efficient, which of the following is the best choice? a. The market expects a significant increase in available supplies of plantonium between now and the delivery date.

26. Problem 26 After the Chernobyl nuclear disaster in Russia, the prices of agricultural commodities were quickly bid much higher in active trading on the U.S. spot and futures markets. b.Automatically, without government intervention, this put in place incentives to reduce consumption and increase production of basic foodstuffs; in turn leading to an increase in potential future supplies c.This action was motivated by the desire for profits d.Both b and c