Duration Lecture

# Duration Lecture - Debt Instruments and Markets Professor...

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Debt Instruments and Markets Professor Carpenter Duration 1 Duration Outline and Reading Outline Interest Rate Sensitivity Dollar Duration Duration Buzzwords Parallel shift Basis points Modified duration Macaulay duration Reading Veronesi, Chapter 3 Tuckman, Chapters 5 and 6

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Debt Instruments and Markets Professor Carpenter Duration 2 Duration The duration of a bond is a linear approximation of minus the percent change in its price given a 100 basis point change in interest rates. (100 basis points = 1% = 0.01) For example, a bond with a duration of 7 will gain about 7% in value if interest rates fall 100 bp. For zeroes, duration is easy to define and compute with a formula. For securities or portfolios with multiple fixed cash flows, we must make assumptions about how rates shift together. We will assume all zero rates move by the same amount. To compute duration for other instruments requires further assumptions and numerical estimation. Other Duration Concepts Concept 1: Percent change in the bond's price given 100 bp change in rates Concept 2: Average maturity of the bond's cash flows, weighted by present value. Concept 3: Holding period over which the return from investing in the bond is riskless, or immunized from immediate parallel shifts in interest rates. Math fact: For a security with fixed cash flows, these turn out to be the same. For securities with random cash flows, such as options and callable bonds, concept 2 doesn't apply. We'll focus on concept 1.
Debt Instruments and Markets Professor Carpenter Duration 3 Start with the notion of dollar duration: Concept: Application: change in value -dollar duration x change in rates in decimal Class Problem : Suppose a bond portfolio has a dollar duration of 10,000,000. Approximately how much will value change if rates rise 20 basis points? Dollar Duration dollar duration - change in dollar value change in interest rates (in decimal) Dollar Duration - Δ p/ Δ r = - Slope of Price Rate Function Price Interest Rate (in decimal) Δ price Δ rate Example: Security with Fixed Cash Flows

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Debt Instruments and Markets Professor Carpenter Duration 4 In practice people use DV01 = DVBP = Dollar Value of a Basis Point How much will a bond value change if rates change 1 bp? Approx. change in value = -\$dur x change in rates DV01 = \$dur x 0.0001 Change in value - DV01 x change in rate in basis points Example: Bond with \$dur = 10,000,000 has DV01 = 1000. 20 bp rate rise causes -1000 x 20 = - \$20,000 price change. Dollar Duration vs. DV01, DVBP, BPV Duration Duration approximates the percent change in price for a 100 basis point change in rates: Duration Percent change in price per 100 bp changes in rates = Dollar change in price per 100bp price × 100 = Dollar duration × 0.01 price × 100 = Dollar duration price
Debt Instruments and Markets Professor Carpenter Duration 5 Example: Security with Duration 7, Price 100, Dollar Duration 700 0.03 0.04 Price in \$ Interest Rate in decimal 100 107 93 0.02 Duration = 7 = -% Δ price per 100 bp \$Dur = 700 = - Δ p/ Δ r = -(107-100)/(0.02-0.03) \$Dur = 700 = Duration

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