1. Http:\\www.tfii.org 1 Zvi Wiener Fixed Income

2. Http:\\www.tfii.org 2 Plan Pricing of Bonds Measuring yield Bond Price Volatility Factors Affecting Yields and the Term Structure of IR Treasury and Agency Securities Markets Corporate Debt Instruments Municipals

3. Http:\\www.tfii.org 3 Plan Non-US Bonds Mortgage Loans Mortgage Pass-Through Securities CMO and Stripped MBS ABS Bonds with Embedded Options Analysis of MBS Analysis of Convertible Bonds

4. Http:\\www.tfii.org 4 Plan Active Bond Portfolio Management Indexing Liability Funding Strategies Bond Performance Measurement Interest Rate Futures Interest Rate Options Interest Rate Swaps, Caps, Floors

5. Http:\\www.tfii.org 5 Characteristics of a Bond Issuer Time to maturity Coupon rate, type and frequency Linkage Embedded options Indentures Guarantees or collateral

6. Http:\\www.tfii.org 6 Sources Fabozzi, “Bond Markets, Analysis and Strategies”, Prentice Hall. P. Wilmott, Derivatives, Wiley. Hull, White, Manuscript.

7. Http:\\www.tfii.org 7 Sectors Treasury sector: bills, notes, bonds Agency sector: debentures (no collateral) Municipal sector: tax exempt Corporate sector: US and Yankee issues – bonds, notes, structured notes, CP – investment grade and noninvestment grade Asset-backed securities sector MBS sector

8. Http:\\www.tfii.org 8 Basic terms Principal Coupon, discount and premium bonds Zero coupon bonds Floating rate bonds Inverse floaters Deferred coupon bonds Amortization schedule Convertible bonds

9. Http:\\www.tfii.org 9 Basic Terms The Money Market Account LIBOR = London Interbank Offer Rate, see BBA Internet site FRA = Forward Rate Agreement Repos, reverse repos Strips = Separate Trading of Registeres Interest and Principal of Securities

10. Http:\\www.tfii.org 10 Basic Terms gilts (bonds issued by the UK government) JGB = Japanese Government Bonds Yen denominated issued by non-Japanese institutions are called Samurai bonds

11. Http:\\www.tfii.org 11 Major risks Interest rate risk Default risk Reinvestment risk Currency risk Liquidity risk

12. Http:\\www.tfii.org 12 Time Value of Money present value PV = CF t /(1+r) t Future value FV = CF t (1+r) t Net present value NPV = sum of all PV -PV5555105

13. Http:\\www.tfii.org 13 Term structure of interest rates Yield = IRR How do we know that there is a solution?

14. Http:\\www.tfii.org 14 Price-Yield Relationship Price and yield (of a straight bond) move in opposite directions. yield price

15. Http:\\www.tfii.org 15 General pricing formula

16. Http:\\www.tfii.org 16 Accrued Interest Accrued interest = interest due in full period* (number of days since last coupon)/ (number of days in period between coupon payments)

17. Http:\\www.tfii.org 17 Day Count Convention Actual/Actual - true number of days 30/360 - assume that there are 30 days in each month and 360 days in a year. Actual/360

18. Http:\\www.tfii.org 18 Floater The coupon rate of a floater is equal to a reference rate plus a spread. For example LIBOR + 50 bp. Sometimes it has a cap or a floor.

19. Http:\\www.tfii.org 19 Inverse Floater Is usually created from a fixed rate security. Floater coupon = LIBOR + 1% Inverse Floater coupon = 10% - LIBOR Note that the sum is a fixed rate security. If LIBOR>10% there is typically a floor.

20. Http:\\www.tfii.org 20 Price Quotes and Accrued Interest Assume that the par value of a bond is $1,000. Price quote is in % of par + accrued interest the accrued interest must compensate the seller for the next coupon.

21. Http:\\www.tfii.org 21 Annualizing Yield Effective annual yield = (1+periodic rate) m -1 examples Effective annual yield = 1.04 2 -1=8.16% Effective annual yield = 1.02 4 -1=8.24%

22. Http:\\www.tfii.org 22 Bond selling atRelationship ParCoupon rate=current yield=YTM DiscountCoupon rate<current yield<YTM PremiumCoupon rate>current yield>YTM Yield to call uses the first call as cashflow. Yield of a portfolio is calculated with the total cashflow.

23. Http:\\www.tfii.org 23 YTM and Reinvestment Risk YTM assumes that all coupon (and amortizing) payments will be invested at the same yield.

24. Http:\\www.tfii.org 24 YTM and Reinvestment Risk An investor has a 5 years horizon BondCouponMaturityYTM A5%39.0% B6%208.6% C11%159.2% D8%58.0% What is the best choice?

25. Http:\\www.tfii.org 25 Bond Price Volatility Consider only IR as a risk factor Longer TTM means higher volatility Lower coupons means higher volatility Floaters have a very low price volatility Price is also affected by coupon payments Price value of a Basis Point = price change resulting from a change of 0.01% in the yield.

26. Http:\\www.tfii.org 26 Duration and IR sensitivity

27. Http:\\www.tfii.org 27 Duration

28. Http:\\www.tfii.org 28 Duration

29. Http:\\www.tfii.org 29 Duration Bonddurationprice impact of +1% YTM A3 yr B1 yr C10 yr D20 yr -3% -1% -10% -20%

30. Http:\\www.tfii.org 30 Measuring Price Change

31. Http:\\www.tfii.org 31 The Yield to Maturity The yield to maturity of a fixed coupon bond y is given by

32. Http:\\www.tfii.org 32 Macaulay Duration Definition of duration, assuming t=0.

33. Http:\\www.tfii.org 33 Macaulay Duration What is the duration of a zero coupon bond? A weighted sum of times to maturities of each coupon.

34. Http:\\www.tfii.org 34 Meaning of Duration r $

35. Http:\\www.tfii.org 35 Convexity r $

36. Http:\\www.tfii.org 36 FRA Forward Rate Agreement A contract entered at t=0, where the parties (a lender and a borrower) agree to let a certain interest rate R*, act on a prespecified principal, K, over some future time period [S,T]. Assuming continuous compounding we have at time S:-K at time T: Ke R*(T-S) Calculate the FRA rate R* which makes PV=0 hint: it is equal to forward rate

37. Http:\\www.tfii.org 37 ALM Duration Does NOT work! Wrong units of measurement Division by a small number

38. Http:\\www.tfii.org 38 ALM Duration A similar problem with measuring yield

39. Http:\\www.tfii.org 39 Do not think of duration as a measure of time!

40. Http:\\www.tfii.org 40 Key rate duration Principal component duration Partial duration

41. Http:\\www.tfii.org 41 Factors affecting Bond yields and TS Base interest rate - benchmark interest rate Risk Premium - spread Expected liquidity Market forces - Demand and supply

42. Http:\\www.tfii.org 42 Taxability of interest qualified municipal bonds are exempts from federal taxes. After tax yield = pretax yield (1- marginal tax rate)

43. Http:\\www.tfii.org 43 Do not use yield curve to price bonds PeriodAB 1-9$6$1 10$106$101 They can not be priced by discounting cashflow with the same yield because of different structure of CF. Use spot rates (yield on zero-coupon Treasuries) instead!

44. Http:\\www.tfii.org 44 On-the-run Treasury issues Off-the-run Treasury issues Special securities Lending Repos and reverse repos

45. Http:\\www.tfii.org 45 Forward Rates Buy a two years bond Buy a one year bond and then use the money to buy another bond (the price can be fixed today). (1+r 2 )=(1+r 1 )(1+f 12 )

46. Http:\\www.tfii.org 46 Forward Rates (1+r 3 )=(1+r 1 )(1+f 13 )= (1+r 1 )(1+f 12 )(1+f 13 ) Term structure of instantaneous forward rates.

47. Http:\\www.tfii.org 47 Determinants of the Term Structure Expectation theory Market segmentation theory Liquidity theory Mathematical models: Ho-Lee, Vasichek, Hull-White, HJM, etc.

48. Http:\\www.tfii.org 48 What is the duration of a floater? What is the duration of an inverse floater? How coupon payments affect duration? Why modified duration is better than Macaulay duration? How duration can be used for hedging? Home Assignment