1. Problem Set 3 Understanding the Yield Curve

2. Disney Case ¥ 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 Tokyo Disney Disney IBJ Borrow in Japan, invest in Europe French Utility

3. Currency Swap German rate x €1,000,000 € 1,000,000 2 2 U.S. rate x $1,500,000 German rate x €1,000,000 U.S. rate x $1,500,000 1 1 € 1,000,000 $1,500,000 € 1,000,000 3 3 $1,500,000 € 1,000,000 $1,500,000 Illustration of a straight currency swap Step 1 is notional Steps 2 & 3 are net Borrow in US, invest in Europe Borrow in Europe, invest in US

4. Problem 40 Two-year bond R = 6.5% P/YR = 1 N = 2 Let’s say PV = $10,000 Then FV = $11,342. 25 Rollover Strategy Start with $10,000 1st year add 6% $10,600 2nd year add 7.5% $11,395 2-year average return is 6.75% Expected return is higher with rollover strategy What risks are involved?

5. Problem 41 Two-year bond R = 7% P/YR = 1 N = 2 Let’s say PV = $10,000 Then FV = $11,449. 00 Rollover Strategy Start with $10,000 1st year add 6% $10,600 2nd year add 7.5% $11,395 2-year average return is 6.75% Expected return is higher with two-year bond What pressures would result? Given the expectations, equilibrium 2-year rate would be 6.75% (Problem 42)

6. Problem 43 Start with $1000 1st year add 5% $1050 2nd year add 6% $1113 3rd year add 7% $1190. 91 Average return: PV is –1000 FV is 1190. 91 P/YR is 1 N is 3 Calculate interest Result is 6. 00 %

7. Problem 44 Start with $1,000,000 1st year add 6% $1,060,000 2nd year add 6.5% $1,128,900 3rd year add 7% $1,207,923 4th year add 8% $1,304,556. 84 Average return: PV is –1,000,000 FV is 1,304,556. 84 P/YR is 1 N is 4 Calculate interest Result is 6. 8724 %

8. Expectations Theory We’ve just had some practice building up the yield curve according to the expectations theory Now, let’s do some arbitrage!

9. Problem 45 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!

10. Problem 45 0 121920 Sell $300. 32 $12 $412$12 Buy $12$237. 00 $12$312$12 NPV is clearly positive Net $26. 52 0000 Buy 0$36. 80 0$1000

11. Problem 45 Yield Risk (Convexity) 11.60% 10.24% 10.00%

12. Coupon Stripping 6% coupon (2 pmts/yr) 10 years to maturity Price: $76. 71 8% coupon (2 pmts/yr) 10 years to maturity Price: $89. 72 Let’s combine these components into a zero- coupon bond Buy four of the 6% Sell three of the 8% Net: $100 in 10 years Pay $306. 84 Receive $269. 16 Net Payment: $37. 68 Implied interest is 10% APR (2 P/YR)

13. Coupon Stripping Buy Sell 0 12 $306. 84 $12 $412 $269. 16 $12 1920 $312 $12 Implied interest is 10% APR (2 P/YR) Net $37. 68 00$1000

14. Coupon Stripping Stripped zeroes of different maturities can be used to construct the yield curve Better than using duration

15. Problem 46 Moving from 6% coupon to 8% coupon Adds extra income of $2 per year Adds $9 to price ($76 compared with $67) 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)

16. Problem 46 0 121920 Buy $152. 00 $8 $208$8 Sell $3$67. 00 $3$103$3 NPV is clearly positive Net $3. 00 0000 Sell $5$88. 00 $5$105$5

17. Problem 46 Yield 12.10% 11.68% 12.22% Risk (Convexity)

18. Problem 47 Yield 8% 8.5% Risk (Convexity)

19. Problem 47 NPV is always positive 0 11416 121113 15 Buy $174. 00 $6 $206 $6 Sell $90. 61 $3 $103 Sell $88. 35 $3 $103 Net $4. 96 0 0$100 $3 $203 $3 $103

20. Problem 48 Yield 8.50% 8.38% 8.00% Risk (Convexity)

21. Problem 48 NPV is always positive 0 11416 121113 15 Sell $178. 88 $6 $206 $6 Buy $88. 44 $3 $103 Buy $86. 35 $3 $103 Net $4. 09 0 0$100 $3 $203 $3 $103

22. Problem 49 Yield 8% 8.5% Risk (Convexity)

23. Problem 49 NPV is always positive 0 11416 121113 15 Sell $178. 88 $6 $206 $6 Buy $90. 61 $3 $103 Buy $85. 70 $3 $103 Net $2. 57 0 0$100 $3 $203 $3 $103

24. Problem 50 Yield 8% 7.75% 7% Risk (Convexity)

25. Problem 50 NPV is always positive 0 11416 121113 15 Buy $181. 36 $6 $206 $6 Sell $90. 61 $3 $103 Sell $93. 95 $3 $103 Net $3. 20 0 0$100 $3 $203 $3 $103

26. Problem 51 $170. 96 £84.63 $200 Profit = £0. 77 NY today $1. 00 = £ 0. 495 $1. 00 = £ 0. 50 LON today LON later $200 NY later What is not balanced? Price £83.86 Face £100 Price $85.48 Future $100 £100 £83.86

27. Problem 52 €8,885 $12,439. 00 €10,000 Profit = $899. 20 FRA today €1. 00 = $1. 40 €1. 00 = $1. 35 NY today NY later €10,000 FRA later What is not balanced? Price $85.48 Face $100 Price €88.85 Future €100 $13,500 $11,539. 80

28. JunkCo Arbitrage Fixed If net is positive, underwriter pays party. If net is negative, party pays underwriter. Illustration of a Floating/Fixed Swap Party Underwriter Counterparty Variable Fixed Variable

29. JunkCo Arbitrage 11% Fixed Net for AAA Corp: During 1st year, borrows at T-Note rate During remaining time, net flow is zero This is better than AAA could do by itself JunkCo Underwriter AAA Corp T-Bill 11% Fixed T-Bill Lender T + 3% Lender 11% Fixed T-Bill Sinking Fund After 1st year Net for JunkCo: Net is 14% fixed This is better than JunkCo could do by itself Net for Underwriter: Net flows are zero Gains fees, future opportunities, & goodwill

30. JunkCo Arbitrage How is this possible? Answer: Quality gap is inconsistent Maturity Rate Yield Curves AAA Junk Quality Gap

31. Myron Labs Arbitrage 8% Fixed, £ Principal 1 1 BT, £ Principal 8% Fixed, $ Principal BT, $ Principal 1st yr £ Principal after 1st yr After 1st year £1,000,000 $2,000,000 Variation on a currency swap Myron Labs Intermediary Advanced Devices Lender 8% Fixed BT-Bill Sinking Fund, £ After 1st year Lender BT + 2% Dynamic Hedge Volatility $2,000,000 £1,000,000 End of last year

32. BF Goodrich Rabobank 11% Fixed Net for Rabobank: During initial time, borrows at LIBOR – x During remaining time, net flow is x This is better than Rabo could do by itself BFG Morgan Rabobank LIBOR – x 11% Fixed LIBOR – x Lender LIBOR +.50% Lender 11% Fixed LIBOR Sinking Fund At refinancing Net for Goodrich: Net is fixed 11.5% + x This is better than BFG could do by itself Net for Underwriter: Net flows are zero Gains fees, future opportunities, & goodwill

34. IRRM Products Listed Products –Futures –Options Custom Products –Swaps –Caps –Floors –Collars

35. Caps Premium Client Underwriter Today *Payments are made periodically (say, monthly or quarterly) over the life of the contract, with rates appropriately adjusted for the number of periods per year Illustration of a 7% Interest Rate Cap on LIBOR Max[(LIBOR – 7%), 0] Underwriter Later* Client

36. Floors Premium Client Underwriter Today *Payments are made periodically (say, monthly or quarterly) over the life of the contract, with rates appropriately adjusted for the number of periods per year Illustration of a 3% Interest Rate Floor on LIBOR Max[(3% – LIBOR), 0] Underwriter Later* Client

37. Collars Premium Client Underwriter Today *Payments are made periodically (say, monthly or quarterly) over the life of the contract, with rates appropriately adjusted for the number of periods per year Illustration of a 3,7 Collar on LIBOR Max[(LIBOR – 7%), 0] + Max[(3% – LIBOR), 0] Underwriter Later* Client

39. Another Approach to Yield Curve Bond A No coupon 6 months to maturity Price: $98. 52 Yield: 3% Bond B 3% coupon (2 pmts/yr) 1 year to maturity Price: $99. 52 Let’s use this information to find pure one-year rate implied in the second bond 1st payment is $1. 50 6-month rate is 3% PV is $1. 48 Final payment: $101. 50 Cost is $99. 52 – $1. 48 = $98. 04 Implied one-year rate is 3.5% APR (2 P/YR)

40. Finding the Yield Curve Simplified: 0 12 Start: $99. 52 $1. 50 $101. 50 Net: $98. 04 0101. 50 Implied one-year rate is 3.5% APR (2 P/YR) $1. 48 $1. 50

41. Another Approach to Yield Curve Background data: 6-month rate: 3% 1-year rate: 3.5% Bond C: 3% coupon 18 months to maturity Price: $99. 10 Let’s use this information to find pure 18-month rate implied in the second bond 1st pmt has PV $1. 48 2nd pmt has PV $1. 45 Final payment: $101. 50 Cost is $99. 10 – $1. 48 – $1. 45 = $96. 17 Implied 18-month rate is 3. 63 % APR (2 P/YR)

42. Finding the Yield Curve Simplified: Implied 18-month rate is 3. 63 % APR (2 P/YR) $1. 48 $1. 50 0 123 Start: $99. 10 $1. 50 $101. 50 $1. 50 Net: $96. 17 0101. 50 0 $1. 45 $1. 50

43. Another Approach to Yield Curve Background data: 6-month rate: 3% 1-year rate: 3.5% 18-month rate: 3.63% Bond D: 3% coupon 2 years to maturity Price: $98. 67 Let’s use this information to find pure two-year rate implied in the second bond 1st pmt has PV $1. 48 2nd pmt has PV $1. 45 3rd pmt has PV $1. 42 Final payment: $101. 50 Cost is $98. 67 – $1. 48 – $1. 45 – $1. 42 = $94. 32 Implied 2-year rate is 3. 70 % APR (2 P/YR)

44. Finding the Yield Curve Simplified: Implied 2-year rate is 3. 70 % APR (2 P/YR) $1. 48 $1. 50 0 123 $1. 45 $1. 50 4 Start: $98. 67 $1. 50 $101. 50 $1. 50 Net: $94. 32 0101. 50 00 $1. 42 $1. 50

45. Deriving Implied Forward Rates Bond A No coupon 6 months to maturity Price: $98. 52 Yield: 3% Bond B 3% coupon 1 year to maturity Price: $99. 52 Yield: 3.49%

46. Deriving Implied Forward Rates NY today $101. 01 $101. 50 $99. 52 $1. 50 Implied forward rate is 4% APR (2 P/YR) 3.00% NY 6 mos 4.00% 3.49% NY 1 year Net receipt $99. 51 Sell a one-year bond Invest $99. 52 for 6 months at 3%

47. Lock in a future loan Bond A: 3% coupon 1 year to maturity Price: $99. 52 Bond B: 3% coupon 18 months to maturity Price: $99. 10 Buy a one-year bond and sell an 18-month bond Net payment $99. 52 - $99. 10 = $0. 42 In 6 months: Receive: $1. 50 Pay: $1. 50 Net zero In 1 year: Receive: $101. 50 Pay: $1. 50 Net $100 Paid $0. 42 to contract a $100 loan in 1 year at 3% APR In 18 months: Pay: $101. 50

48. Lock in a future loan Buy $99. 52 $1. 50 $101. 50 0 123 Net $0. 42 0$100$101. 50 Sell $1. 50 $99. 10 $ 1. 50 $ 101. 50 Paid $0. 42 to contract a $100 loan in 1 year at 3% APR

50. Nikkei Put Warrants

51. PENs SCPERS BT Counterparty PEFCO $5 mm $5mm + Appreciation 1% Coupon Fixed Undisclosed Flow Appreciation What happens to Tokyo Index?

52. Nikkei Put Warrants (Bringing innovation to retail) Goldman Sachs Option Premium At Beginning Counterparty Flow Dep Depriciation At Maturity Kingdom of Denmark Public Market Flow Dep

53. Alternative Plan SCPERS BT PEFCO $5 mm $5mm + App 1% Fixed App Flow App Goldman Sachs Price Flow Dep Kingdom of Denmark Public Market Dynamic Hedge Volatility

55. CitiCorp

56. MARKETING Capital Adequacy Will It Meet Competitive Requirements in a Virtual Space with Tomorrow’s Financial Services Dominators? INNOVATION HUMAN CAPITAL Credit Quality Liquidity ENTERPRISE RISK MANAGEMENT Bank of the Future Foundations & Structure VISION (PLANNING & STRATEGY) COST TRACKING & PRICING Relationships & Capabilities

57. Capital Adequacy Basel Accord

58. Exhibit 9

59. Market Timing for Bonds The basic idea of market timing is to get into the market before it rises and get out before it falls –Translation: Long duration in advance of falling interest rates Short duration in advance of rising interest rates Extreme market timing –Very long duration in advance of falling interest rates –Very long negative duration in advance of rising interest rates

60. Basic Bond Market Timing So, if you hold a portfolio of bonds worth $1,000,000 (duration 15 years) and you think you can predict ups and downs of interest rates, do the following: –When you think the rate is about to fall, hold the portfolio without any position in the bond futures, so duration is 15 years –When you think the rate is about to rise, continue to hold the portfolio while selling $1,000,000 worth of the bond futures, so duration is near 0

61. Immunization Immunization might be appropriate for a bank with the following – Asset portfolio has average duration of 10 years –Liability portfolio has average duration of 1 year Immunization would use the same techniques as market timing strategies in order to –Shorten the duration of the asset portfolio –Adjust the duration of the liability portfolio so they are both nearly the same

63. Connecticut Municipal Swap

64. Yield Curve

67. Advantage of Deductibility

68. Yield Curve

69. Exhibit 3

70. Exhibit 4

71. Exhibit 5

72. Exhibit 6

74. Problem 6 Yield 8% 7.75% Risk (Convexity)

75. Problem 6 NPV is always positive 0 11416 121113 15 Sell $181. 36 $6 $206 $6 Buy $90. 61 $3 $103 Buy $88. 35 $3 $103 Net $2. 40 0 0$100 $3 $203 $3 $103

76. Problem 12 Suppose you know GM will announce bad news –Beta is 1.05 –Describe a no-money-in, hedged position designed to benefit from the information

77. Problem 13 S $ 0 X Prime Primes get dividends plus appreciation up to defined point S $ 0 X Score Scores get remaining appreciation What if Prime + Score > Stock?

78. Equities as commodities (Problem 11) $ 1,000,000 CHF 1,564,500 $ 1,050,000 Profit = CHF 19,457. 04 CHF 1. 50 = $ 1 CHF 1. 49 = $ 1 NY today NY later Spot 1000 Future 1040 Dividend 1% CHF 1,545,042. 96 ZUR today ZUR later R = 6% What is not balanced? CHF 1,500,000

79. Bonds as commodities (Problem 1) 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

80. Bonds as commodities (Problem 2) 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 7.50% 7.25% NY 270 days

81. Bonds as commodities (Problem 3) 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