1 / 45

Factors Affecting Bond Yields and the Term Structure of Interest Rates

Factors Affecting Bond Yields and the Term Structure of Interest Rates. Zvi Wiener Based on Chapter 5 in Fabozzi Bond Markets, Analysis and Strategies. Base Interest Rate. Treasury Libor Prime. r zero. Time to maturity. 0 3m 6m 1yr 3yr 5yr 10yr 30yr. Term Structure of Interest Rates.

abram
Download Presentation

Factors Affecting Bond Yields and the Term Structure of Interest Rates

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Factors Affecting Bond Yields and the Term Structure of Interest Rates Zvi Wiener Based on Chapter 5 in Fabozzi Bond Markets, Analysis and Strategies http://pluto.mscc.huji.ac.il/~mswiener/zvi.html

  2. Base Interest Rate • Treasury • Libor • Prime Fabozzi Ch 5

  3. rzero Time to maturity 0 3m 6m 1yr 3yr 5yr 10yr 30yr Term Structure of Interest Rates Yield curve Fabozzi Ch 5

  4. http://bond.yahoo.com/rates.html • http://www.ratecurve.com/yc2.html Fabozzi Ch 5

  5. Normal Inverted Yield Curve = Term Structure of IR Flat r maturity Fabozzi Ch 5

  6. Fabozzi Ch 5

  7. Types of Issuers • Governments • Agencies • Corporate • Municipals • Others … Fabozzi Ch 5

  8. Factors affecting Bond yields and TS • Base interest rate - benchmark interest rate • Risk Premium - spread • Expected liquidity • Market forces - Demand and supply Fabozzi Ch 5

  9. Taxability of interest • qualified municipal bonds are exempts from federal taxes. • After tax yield = pretax yield (1- marginal tax rate) Fabozzi Ch 5

  10. Do not use yield curve to price bonds • Period A B • 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! Fabozzi Ch 5

  11. On-the-run Treasury issues • Off-the-run Treasury issues • Special securities • Lending • Repos and reverse repos Fabozzi Ch 5

  12. 30 yr US Treasuries Fabozzi Ch 5

  13. 10 yr US Treasuries Fabozzi Ch 5

  14. Duration and Term Structure of IR Fabozzi Ch 5

  15. Partial Duration Key rate duration Fabozzi Ch 5

  16. 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. Fabozzi Ch 5

  17. 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. Fabozzi Ch 5

  18. Term Structure of IR • If we knew the future IR: • 0(Today) 8% • 1 10% • 2 11% • 3 11% Fabozzi Ch 5

  19. Term Structure of IR • If we knew the future IR: • 0(Today) 8% • 1 10% • 2 11% • 3 11% Fabozzi Ch 5

  20. Spot rate is the yield to maturity on zero-coupon bonds. r1 = 8% r1 = 10% r3 = 11% r4 = 11% Fabozzi Ch 5

  21. Future versus Spot Rates r1 = 8% r1 = 10% r3 = 11% r4 = 11% y1= 8% y2= 8.995% y3= 9.66% y4= 9.993% Fabozzi Ch 5

  22. Forward Rates • Suppose you will need a loan in two years from now for one year. • How one can create such a loan today? • Go short a three-year zero coupon bond. • Go long a two-year zero coupon bond. Fabozzi Ch 5

  23. Suppose you will need a loan in two years from now for one year. • How one can create such a loan today? • Go short a three-year zero coupon bond. • Go long a two-year zero coupon bond. • +1 0 0 -1.3187 • -1 0 +1.188 0 0 1 2 3 Fabozzi Ch 5

  24. Forward Rates • (1 + yn)n = (1 + yn-1)n-1(1 + fn) • (1 + yn)n • (1 + yn-1)n-1 • +1 -1.3187 • -1 +1.188 0 1 2 3 Fabozzi Ch 5

  25. Forward Rates • (1 + yn)n = (1 + yn-1)n-1(1 + fn) • (1 + yn)n • (1 + yn-1)n-1 • +1 -1.3187 • -1 +1.188 0 1 2 3 fn Fabozzi Ch 5

  26. Forward Rates • In other words we can lock now interest rate for a loan which will be taken in future. • To specify a forward interest rate one should provide information about • today’s date • beginning date of the loan • end date of the loan Fabozzi Ch 5

  27. 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+r2)=(1+r1)(1+f12) Fabozzi Ch 5

  28. Forward Rates • (1+r3)=(1+r1)(1+f13)= (1+r1)(1+f12)(1+f13) • Term structure of instantaneous forward rates. Fabozzi Ch 5

  29. Forward Rates - Advanced • Let P(t,s) be the price at time t of a pure discount bond maturing at time s > t. Then the yield to maturity R(t,T) is the internal rate of return at time t on a bond maturing at t+T. • P(t, t+T) = Exp[-R(t,T)*T] • Then • R(t,T) = - Log[P(t, t+T)]/T Fabozzi Ch 5

  30. Forward Rates - Advanced • The integral of the forward rates gives the yield to maturity: Fabozzi Ch 5

  31. Forward Rates - Advanced • The integral of the forward rates gives the yield to maturity: • or alternatively Fabozzi Ch 5

  32. Fabozzi Ch 5

  33. 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: KeR*(T-S) • Calculate the FRA rate R* which makes PV=0 • hint: it is equal to forward rate Fabozzi Ch 5

  34. The Expectations Hypothesis • Suggested by Lutz. • Forward interest rates is the expected future spot rate. • Cox-Ingersoll-Ross have investigated this hypothesis and find that it is not consistent with an economic equilibrium. • However it gives often a right direction for expectations. Fabozzi Ch 5

  35. Liquidity Preference • Hicks (1939) suggested that lenders demand a premium for locking up their money for long period of time. • This implies that the term structure will be always upward sloping. • The theory ignores the borrowing side of the market. Fabozzi Ch 5

  36. Market Segmentation and Preferred Habitat Theories • Modigliani and Sutch • The market is segmented, investors absolutely prefer one maturity over another. • This means that there is no connection between interest rates for different maturities. Fabozzi Ch 5

  37. Modern Theories • Equilibrium Theories: CIR, BP • Non-equilibrium Theories: Dothan, Vasicek, • Ho-Lee, Hull-White, HJM • Most of them are based on a Brownian Motion as a source of market uncertainty. Fabozzi Ch 5

  38. Brownian Motion B Time Fabozzi Ch 5

  39. Brownian Motion • Starts at the origin • Is continuous • Is normally distributed at each time • Increments are independent • Markovian property • Technical conditions Fabozzi Ch 5

  40. Home AssignmentChapter 5 • Ch. 5: Questions 2, 3, 10, 13. Fabozzi Ch 5

  41. Measuring the Term Structure • There are too many data plus some noise. • The easiest way to measure the TS is with liquid zero coupon bonds. • We obtain a series of points. Fabozzi Ch 5

  42. Measuring the Term Structure rzero Time to maturity 0 3m 6m 1yr 3yr 5yr 10yr 30yr Fabozzi Ch 5

  43. rzero Time to maturity 0 3m 6m 1yr 3yr 5yr 10yr 30yr First Order Spline Fabozzi Ch 5

  44. Second Order Spline rzero Time to maturity 0 3m 6m 1yr 3yr 5yr 10yr 30yr Fabozzi Ch 5

  45. Measuring the Term Structure • There are too many data plus some noise. • The easiest way to measure the TS is with liquid zero coupon bonds. • We obtain a series of points. • One can connect them with a spline. • First order is good for pricing simple bonds. • For swaps one need a very high precision. Fabozzi Ch 5

More Related