Lecture 8.  Longer term bonds prices are more sensitive to interest rate changes  If a bond is more sensitive to interest rate changes, it is riskier.

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Presentation transcript:

Lecture 8

 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

Interest rate, percent Bond Price, percent

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 ieldcurve ieldcurve

Interest Rates Maturity (years)

Feb 2004 Nov 2014

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 & present

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.

Macauley Duration Formula C t (t) ( 1 + R ) t P o D =  t = 1 n

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

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

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

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

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

Debt & Risk Example (Bond 2) Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is this bond’s duration? of Total PV% x Year Duration

Modification of the Macauley formula may produce  Po  R Po (1 + R ) = - D or  Po Po = - MD (  R ) D (1 + R ) MD =

Duration & Bond Price Volatility Example The duration of a bond is The price of the bond is If the YTM increases from 6.05% to 6.25%, what is the change in the bond price?  Po ( ) =  Po = - $ 4.35 Price drops

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