1. Fall-01 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html FIBI Zvi Wiener 02-588-3049 mswiener@mscc.huji.ac.il Fixed Income Instruments 2

2. Zvi WienerFIFIBI - 2 slide 2 Plan FI-2 Example of Duration and Convexity Treasuries Agencies Corporate Municipals The Treasury Securities Markets: Overview and Recent Developments, by D. Dupont and B. Sack, Federal Reserve Bulletin, Dec-99.

3. Zvi WienerFIFIBI - 2 slide 3 Example Portfolio consists of $1M of a bond with duration of 1 year and $1M worth of a bond with duration of 20 years. What is the duration of the portfolio?

4. Zvi WienerFIFIBI - 2 slide 4 Rough calculation Duration of the first bond is 1 year, of the second bond is 20 years. This means that when IR go 1% up we will lose 1% of the first bond and 20% of the second. All together we will lose 10.5% of the portfolio. The duration is (roughly) 10.5 years.

5. Zvi WienerFIFIBI - 2 slide 5 Value Parallel shift value

6. Zvi WienerFIFIBI - 2 slide 6 Duration

7. Zvi WienerFIFIBI - 2 slide 7 Convexity For a simple bond portfolio it does not help much! It is much more important to consider 2 risk factors!

8. Zvi WienerFIFIBI - 2 slide 8 Portfolio 2 value Money +1-2+2 Term Structure 5%6%7% Time 0 1 520 Assets duration = 7.19 Liabilities duration = 4.7169

9. Zvi WienerFIFIBI - 2 slide 9 8% Coupon Bond Zero Coupon Bond

10. Zvi WienerFIFIBI - 2 slide 10 Macaulay Duration

11. Zvi WienerFIFIBI - 2 slide 11 Understanding of Duration/Convexity What happens with duration when a coupon is paid? How does convexity of a callable bond depend on interest rate? How does convexity of a puttable bond depend on interest rate?

12. Zvi WienerFIFIBI - 2 slide 12 Callable bond The buyer of a callable bond has written an option to the issuer to call the bond back. Rationally this should be done when … Interest rate fall and the debt issuer can refinance at a lower rate.

13. Zvi WienerFIFIBI - 2 slide 13 Puttable bond The buyer of a such a bond can request the loan to be returned. The rational strategy is to exercise this option when interest rates are high enough to provide an interesting alternative.

14. Zvi WienerFIFIBI - 2 slide 14 Embedded Call Option r regular bond callable bond strike

15. Zvi WienerFIFIBI - 2 slide 15 Embedded Put Option r regular bond putable bond

16. Zvi WienerFIFIBI - 2 slide 16 Convertible Bond Payoff Stock Convertible Bond Straight Bond

17. Zvi WienerFIFIBI - 2 slide 17 Timing of exercise European American Bermudian Lock up time

18. Zvi WienerFIFIBI - 2 slide 18 Passive Bond Management Passive management takes bond prices as fairly set and seeks to control only the risk of the fixed-income portfolio. Indexing strategy – attempts to replicate a bond index Immunization – used to tailor the risk to specific needs (insurance companies, pension funds)

19. Zvi WienerFIFIBI - 2 slide 19 Bond-Index Funds Similar to stock indexing. Major indices: Lehman Brothers, Merill Lynch, Salomon Brothers. Include: government, corporate, mortgage- backed, Yankee bonds (dollar denominated, SEC registered bonds of foreign issuers, sold in the US).

20. Zvi WienerFIFIBI - 2 slide 20 Bond-Index Funds Properties: many issues not all are liquid replacement of maturing issues Tracking error is a good measurement of performance. According to Salomon Bros. With $100M one can track the index within 4bp. tracking error per month.

21. Zvi WienerFIFIBI - 2 slide 21 Cellular approach

22. Zvi WienerFIFIBI - 2 slide 22 Immunization Immunization techniques refer to strategies used by investors to shield their overall financial status from exposure to interest rate fluctuations.

23. Zvi WienerFIFIBI - 2 slide 23 Net Worth Immunization Banks and thrifts have a natural mismatch between assets and liabilities. Liabilities are primarily short-term deposits (low duration), assets are typically loans or mortgages (higher duration). When will banks lose money, when IR increase or decline?

24. Zvi WienerFIFIBI - 2 slide 24 Gap Management ARM are used to reduce duration of bank portfolios. Other derivative securities can be used. Capital requirement on duration (exposure). Basic idea: to match duration of assets and liabilities.

25. Zvi WienerFIFIBI - 2 slide 25 Target Date Immunization Important for pension funds and insurances. Price risk and reinvestment risk. What is the correlation between them?

26. Zvi WienerFIFIBI - 2 slide 26 Target Date Immunization Accumulated value 0 t* t Original plan

27. Zvi WienerFIFIBI - 2 slide 27 Target Date Immunization Accumulated value 0 t* t IR increased at t*

28. Zvi WienerFIFIBI - 2 slide 28 Target Date Immunization Accumulated value 0 t*Dt

29. Zvi WienerFIFIBI - 2 slide 29 Target Date Immunization Accumulated value 0 t*Dt Continuous rebalancing can keep the terminal value unchanged

30. Zvi WienerFIFIBI - 2 slide 30 Good Versus Bad Immunization value 0 8% r Single payment obligation $10,000

31. Zvi WienerFIFIBI - 2 slide 31 Good Versus Bad Immunization value 0 8% r Single payment obligation Good immunizing strategy $10,000

32. Zvi WienerFIFIBI - 2 slide 32 Good Versus Bad Immunization value 0 8% r Single payment obligation Good immunizing strategy $10,000

33. Zvi WienerFIFIBI - 2 slide 33 Good Versus Bad Immunization value 0 8% r Single payment obligation Good immunizing strategy $10,000 Bad immunizing strategy

34. Zvi WienerFIFIBI - 2 slide 34 Standard Immunization Is very useful but is based on the assumption of the flat term structure. Often a higher order immunization is used (convexity, etc.). Another reason for goal oriented mutual funds (retirement, education, housing, medical expenses).

35. Zvi WienerFIFIBI - 2 slide 35 Cash Flow Matching and Dedication Is a very reasonable strategy, but not always realizable. Uncertainty of payments. Lack of perfect match Saving on transaction fees.

36. Zvi WienerFIFIBI - 2 slide 36 Active Bond Management Mainly speculative approach based on ability to predict IR or credit enhancement or market imperfections (identifying mispriced loans).

37. Zvi WienerFIFIBI - 2 slide 37 Substitution Swap Exchange of one bond for a very similar bond. Motivation: belief that one of them is mispriced. Example: 20-yr, 9% coupon Ford Motor bond callable after 5 years at $1,050 versus a 9% coupon Chrysler bond with 20 yr to maturity.

38. Zvi WienerFIFIBI - 2 slide 38 Contingent Immunization 0 5 yrt value $10,000 $12,000

39. Zvi WienerFIFIBI - 2 slide 39 Contingent Immunization 0 5 yrt value $10,000 $12,000 Stop boundary

40. Zvi WienerFIFIBI - 2 slide 40 Contingent Immunization 0 5 yrt value $10,000 $12,000 Stop boundary

41. Zvi WienerFIFIBI - 2 slide 41 Contingent Immunization 0 5 yrt value $10,000 $12,000 Stop boundary

42. Zvi WienerFIFIBI - 2 slide 42 Interest Rate Swap One of the major fixed-income tools. Example: 6m LIBOR versus 7% fixed. Exchange of net cash flows. Risk involved: IR risk, default risk (small). Why the default risk on IR swaps is small?

43. Zvi WienerFIFIBI - 2 slide 43 Interest Rate Swap Company A Company B Swap dealer 6.95% 7.05% LIBOR No need in an actual loan. Can be used as a speculative tool or for hedging.

44. Zvi WienerFIFIBI - 2 slide 44 Currency Swap A similar exchange of two loans in different currencies. Subject to a higher default risk, because of the principal. Is useful for international companies to hedge currency risk.

45. Zvi WienerFIFIBI - 2 slide 45 The Treasuries Securities Market US Treasury debt $3.6Trillion daily transactions: $190B yields are viewed as benchmarks 1776, first US issue (Revolutionary War) Increase during the Civil war, WW1, tripled during the great depression exploded during WW2.

46. Zvi WienerFIFIBI - 2 slide 46 Types of Treasuries securities $3.2T - marketable – Bills - up to one year – Notes 1-10 years when issued – Bonds longer then 10 years 57% are notes, 20% bills and 20% bonds. Some are callable (by the Treasury) 97% are nominal

47. Zvi WienerFIFIBI - 2 slide 47 Nonmarketable securities Government account series (83%) State and Local Government Series (7%) saving bonds (7%) held by off-budget government programs, like social security, local governments, etc. yield is at least 5bp below marketable Treasuries.

48. Zvi WienerFIFIBI - 2 slide 48 Issuance of Treasuries regularly scheduled auctions = primary market. 2,000 brokers and dealers are registered Prime dealers are selected by NY Fed - counterparites for open market operations.

49. Zvi WienerFIFIBI - 2 slide 49 Auctions The process begins several days before. “when issued market” after the announcement but before it takes place. On the day of the auctions bids may be submitted to FED. Competitive bids - quantity and yield Noncompetitive bids - small orders

50. Zvi WienerFIFIBI - 2 slide 50 Auctions Uniform price method for 2, 5 year notes, TIPS Other issues have multiple price auction Bidders get securities at their bid price. Non-competitive get at the average price of competitive bids.

51. Zvi WienerFIFIBI - 2 slide 51 Auctions $6.5B of 13-week bills and $7.5B of 26 week bills - weekly $10B of 52 week bills - every four weeks $15B of 2-year notes, every 4 weeks $12B of ten -year notes and $10B of 30 years bonds - semiannually. Sometimes an old issue may be reopen.

52. Zvi WienerFIFIBI - 2 slide 52 Cancellations 198620 year bond 1990 4 year note 1993 7 year note 1998 3 year note

53. Zvi WienerFIFIBI - 2 slide 53 Market Primarily OTC (over the counter) market. Officially registered at NYSE, but volume is negligible. Market makers in Treasuries - bid-offer spread. Six primary dealers - 50% of trades (22 hr/day). 94% - NY, 4% - London, 2% Tokyo.

54. Zvi WienerFIFIBI - 2 slide 54 Quoting conventions Coupon securities are quoted in terms of price expressed in dollars. Clean price excludes accrued interest. Accrued interest = next coupon*fraction of time that passed. Bills are quoted in terms of discount rate as % of face value. Assuming 360 days in a year, i.e. multiplied by 360 and divided by the actual number of days remaining to maturity.

55. Zvi WienerFIFIBI - 2 slide 55 Price quotes for T-Bills Bank discount basis Y d - annualized yield on a bank discount basis D - dollar discount = face - price F - face value t - number of actual days to maturity

56. Zvi WienerFIFIBI - 2 slide 56 Price quotes for T-Bills

57. Zvi WienerFIFIBI - 2 slide 57 Price quotes for T-Bills 100 days to maturity price = $97,569 will be quoted at 8.75%

58. Zvi WienerFIFIBI - 2 slide 58 Price quotes for T-Bills The quoted yield is based on the face value and not on the actual amount invested. The yield is annualized on 360 days basis. Bond equivalent yield = CD equivalent yield

59. Zvi WienerFIFIBI - 2 slide 59 Price quotes for Notes and Bonds Actual/actual day count convention. Example: 50 days have passed, 183 days in the period and yearly coupon per $100 is $8, then AI = $8/2 *50/183 = $1.0929

60. Zvi WienerFIFIBI - 2 slide 60 Recordkeeping National Book-Entry System (NBES) maintains records for depository institutions. Most trades are delivery versus payment. Federal Reserve grants finality and provides an intraday credit to financially healthy depository institutions.

61. Zvi WienerFIFIBI - 2 slide 61 Ownership FED 12% Depository institutions7% Institutional investors27% State and local governm.7% Foreign and international33% Others14%

62. Zvi WienerFIFIBI - 2 slide 62 STRIPS Separate Trading of Registered Interest and Principal of Securities. Stripping and reconstitution. About 33% of all outstanding T-bonds are stripped. Creates zero-coupon securities. US company must pay tax on accrued interest is taxed every year, so strips create a negative CF.

63. Zvi WienerFIFIBI - 2 slide 63 Determinants of the Yield Curve Federal Reserve sets a target level for the fed funds rate - the rate at which depository institutions make uncollaterized overnight loans to one another. Long-term rates reflect expectations of future rates and can be influenced by the outlook for monetary policy.

64. Zvi WienerFIFIBI - 2 slide 64 Liquidity Bid-offer spread 1-2 cents per $100 face Corporate bonds for example 13 cents High yield bonds 19 cents on-the-run - recently issued in a particular maturity class. With time became off-the-run. Flight to Quality (fall 98) bid-ask 16-25 cents.

65. Zvi WienerFIFIBI - 2 slide 65 Repurchase Agreements Borrowing and lending using Treasuries and other debt as collateral. Repo (loan). You sell a security to counterparty and agree to repurchase the same security at a specified price at a later date (often next day). Reverse Repo - you agree to purchase a security and sell it back at a specified price later.

66. Zvi WienerFIFIBI - 2 slide 66 Repurchase Agreements Most repos are general-collateral repo rate. Some securities are special (for example on- the-run). Specialness peaks around next auction, then declines sharply. NY FED operates a securities lending for primary dealers using FED’s portfolio while posting other Treasury security as collateral.

67. Zvi WienerFIFIBI - 2 slide 67 Treasury Based Derivatives Futures and options for 2, 5, 10 year notes and bonds are listed by CBOT and CFFE. CNE offers futures and options on bills and other short term interest rate products. End of October 99 open interest for CBOT long-bond futures was 635,000 (each one based on $100,000 face value). Daily volume 300,000 contracts.

68. Zvi WienerFIFIBI - 2 slide 68 Treasury Based Derivatives CBOT also offers options on Treasury futures - contract that allows the holder to buy/sell a future contract at a specified price. Cheapest-to-deliver option and conversion factor (compare to commodities).

69. Zvi WienerFIFIBI - 2 slide 69 TIIS = TIPS Treasury Inflation Indexed (Protected) Securities. Since 97, $92B were issued, based on the non- seasonally adjusted CPI lagged 2.5 months. The quoted price do not reflect the accumulated inflation compensation. Real price = quoted*index ratio + accrued interest I-bonds saving bonds that are also CPI indexed.

70. Zvi WienerFIFIBI - 2 slide 70 TIIS = TIPS 5, 10, 30 years notes and bonds. Less liquid: 2-6 cents per $100 face. CBOT offers options and futures on TIPS Canada, France, England, Israel have similar types of debt.

71. Zvi WienerFIFIBI - 2 slide 71 T-bills markets Issuance of T-bills was cut sharply. Between Dec-96 and Sep-99 the total outstanding amount of coupon securities declined 7% while bills declined 16%. Treasury Debt buybacks. Reverse auctions trying to remove small issues.