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Fixed Income 2

Fixed Income 2. Zvi Wiener. 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. Example.

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Fixed Income 2

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  1. Fixed Income 2 Zvi Wiener

  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. FI-2

  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? FI-2

  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. FI-2

  5. Value value Parallel shift FI-2

  6. Duration FI-2

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

  8. Portfolio 2 Time 0 1 5 20 value Money +1 -2 +2 Term Structure 5% 6% 7% Assets duration = 7.19 Liabilities duration = 4.7169 FI-2

  9. Zero Coupon Bond 8% Coupon Bond FI-2

  10. Macaulay Duration FI-2

  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? FI-2

  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. FI-2

  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. FI-2

  14. regular bond strike callable bond Imbedded Call Option r FI-2

  15. putable bond Imbedded Put Option regular bond r FI-2

  16. Stock Convertible Bond Straight Bond Convertible Bond Payoff Stock FI-2

  17. Timing of exercise • European • American • Bermudian • Lock up time FI-2

  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) FI-2

  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). FI-2

  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. FI-2

  21. Cellular approach FI-2

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

  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? FI-2

  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. FI-2

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

  26. Target Date Immunization Accumulated value Original plan 0 t* t FI-2

  27. Target Date Immunization Accumulated value IR increased at t* 0 t* t FI-2

  28. Target Date Immunization Accumulated value 0 t* D t FI-2

  29. Target Date Immunization Accumulated value Continuous rebalancing can keep the terminal value unchanged 0 t* D t FI-2

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

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

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

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

  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). FI-2

  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. FI-2

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

  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. FI-2

  38. Contingent Immunization value $12,000 $10,000 0 5 yr t FI-2

  39. Contingent Immunization value $12,000 $10,000 Stop boundary 0 5 yr t FI-2

  40. value $12,000 $10,000 Stop boundary 0 5 yr t Contingent Immunization FI-2

  41. value $12,000 $10,000 Stop boundary 0 5 yr t Contingent Immunization FI-2

  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? FI-2

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

  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. FI-2

  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. FI-2

  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 FI-2

  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. FI-2

  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. FI-2

  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 FI-2

  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. FI-2

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