1. Lecture 8

2.  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. Interest rate, percent Bond Price, percent

4. Maturity (years)YTM 13.0% 53.5% 103.8% 154.1% 204.3% 304.5% Usually the yield on treasuries (but can be any category of bond) The Living Yield Curve http://www.smartmoney.com/onebond/index.cfm?story=y ieldcurve http://www.smartmoney.com/onebond/index.cfm?story=y ieldcurve

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

6. Feb 2004 Nov 2014

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) Year 1981 1987 & present 1976 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. Macauley Duration Formula C t (t) ( 1 + R ) t P o D =  t = 1 n

10. Debt & Risk Example (Bond 1) Calculate the duration of a 5 year 10.5% coupon bond @ 8.5% YTM YearCFPV@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 YearCFPV@YTM% of Total PV% x Year 1105 2105 3105 4105 5 1105

12. Debt & Risk Example (Bond 1) Calculate the duration of a 5 year 10.5% coupon bond @ 8.5% YTM YearCFPV@YTM% of Total PV% x Year 110596.77 210589.19 310582.21 410575.77 5 1105734.88 1078.82

13. Debt & Risk Example (Bond 1) Calculate the duration of a 5 year 10.5% coupon bond @ 8.5% YTM YearCFPV@YTM% of Total PV% x Year 110596.77.090 210589.19.083 310582.21.076 410575.77.070 5 1105734.88.681 1078.821.00

14. Debt & Risk Example (Bond 1) Calculate the duration of a 5 year 10.5% coupon bond @ 8.5% YTM YearCFPV@YTM% of Total PV% x Year 110596.77.0900.090 210589.19.0830.164 310582.21.0760.227 410575.77.0700.279 5 1105734.88.6813.406 1078.821.004.166 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? YearCFPV@YTM% of Total PV% x Year 1 9082.95.0810.081 2 9076.45.0750.150 3 9070.46.0690.207 4 9064.94.0640.256 5 1090724.90.7113.555 1019.701.004.249 Duration

16. Modification of the Macauley formula may produce  Po  R Po (1 + R ) --------- = - D ----------- or  Po Po --------- = - MD (  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?  Po.0020 995.60 (1 +.0605) --------- = - 2.316 -----------  Po = - $ 4.35 Price drops