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Derivatives

Derivatives. Lecture 8. Bond Price Sensitivity. Longer term bonds prices are more sensitive to interest rate changes If a bond is more sensitive to interest rate changes, it is riskier Maturity and “Duration” tell us “HOW SENSITIVE”. Bond Price. YTM. Duration & Bond Prices.

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Derivatives

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  1. Derivatives Lecture 8

  2. Bond Price Sensitivity • Longer term bonds prices are more sensitive to interest rate changes • If a bond is more sensitive to interest rate changes, it is riskier • Maturity and “Duration” tell us “HOW SENSITIVE” Bond Price YTM

  3. Duration & Bond Prices Bond Price, percent Interest rate, percent

  4. Term Structure of Interest Rates Maturity (years)YTM 1 3.0% 5 3.5% 10 3.8% 15 4.1% 20 4.3% 30 4.5% Usually the yield on treasuries (but can be any category of bond) The Living Yield Curve http://www.smartmoney.com/onebond/index.cfm?story=yieldcurve

  5. Yield Curve Interest Rates 8.04 6.00 4.84 2 3 10 Maturity (years)

  6. Term Structure (Feb 2004) Nov 2014 Feb 2004

  7. Term Structure & Yield Curve Spot Rate - The actual interest rate today (t=0) Forward Rate - The interest rate, fixed today, on a loan made in the future at a fixed time. Future Rate - The spot rate that is expected in the future Yield To Maturity (YTM) - The IRR on an interest bearing instrument YTM (r) 1981 1987 & present 1976 Year 1 5 10 20 30

  8. Debt & Risk Duration Duration is the average point in time at which a bond holder receives the cash flows from the bond, adjusted for the time value of money (i.e. present value). Used to measure the average life of debt, on a present value basis Is the tool that tells us the difference in risk between two different bonds.

  9. Debt and Risk Macauley Duration Formula n Ct(t) ( 1 + R ) t Po S t = 1 D =

  10. Debt & Risk Example (Bond 1) Calculate the duration of a 5 year 10.5% coupon bond @ 8.5% YTM Year CF PV@YTM % of Total PV % x Year

  11. Debt & Risk Example (Bond 1) Calculate the duration of a 5 year 10.5% coupon bond @ 8.5% YTM Year CF PV@YTM % of Total PV % x Year 1 105 2 105 3 105 4 105 5 1105

  12. Debt & Risk Example (Bond 1) Calculate the duration of a 5 year 10.5% coupon bond @ 8.5% YTM • Year CF PV@YTM % of Total PV % x Year • 1 105 96.77 • 2 105 89.19 • 3 105 82.21 • 4 105 75.77 • 5 1105 734.88 • 1078.82

  13. Debt & Risk Example (Bond 1) Calculate the duration of a 5 year 10.5% coupon bond @ 8.5% YTM • Year CF PV@YTM % of Total PV % x Year • 1 105 96.77 .090 • 2 105 89.19 .083 • 3 105 82.21 .076 • 4 105 75.77 .070 • 5 1105 734.88 .681 • 1078.82 1.00

  14. Debt & Risk Example (Bond 1) Calculate the duration of a 5 year 10.5% coupon bond @ 8.5% YTM • Year CF PV@YTM % of Total PV % x Year • 1 105 96.77 .090 0.090 • 2 105 89.19 .083 0.164 • 3 105 82.21 .076 0.227 • 4 105 75.77 .070 0.279 • 5 1105 734.88 .681 3.406 • 1078.82 1.00 4.166 Duration

  15. Debt & Risk Example (Bond 2) Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is this bond’s duration? • Year CF PV@YTM % of Total PV % x Year • 1 90 82.95 .081 0.081 • 2 90 76.45 .075 0.150 • 3 90 70.46 .069 0.207 • 4 90 64.94 .064 0.256 • 5 1090 724.90 .711 3.555 • 1019.70 1.00 4.249 Duration

  16. Duration & Bond Price Volatility Modification of the Macauley formula may produce D Po D R Po (1 + R ) --------- = - D ----------- or D Po Po --------- = - MD (D R ) D (1 + R ) MD = ---------

  17. Duration & Bond Price Volatility Example The duration of a bond is 2.316. The price of the bond is 99.56. If the YTM increases from 6.05% to 6.25%, what is the change in the bond price? D Po .0020 995.60 (1 + .0605) --------- = - 2.316 ----------- D Po = - $ 4.35 Price drops

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