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Duration and Interest Rate RiskPowerPoint Presentation

Duration and Interest Rate Risk

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Presentation Transcript

Why Study Duration

- Duration: measures the sensitivity of bond price change on interest rate change
- Objective: to see how much price change in bond value due to interest rate changes – a way to gauge interest rate risk

A measurement of the life of the bond on a present value basis

Formula for Duration

How to Calculation Duration

- find bond price

- find discounted cash flow in each period

- go through the worksheet

Calculate Duration on a $1000 Ten-year 10% Coupon Bond When its interest rate is 10% (Table 4)

Calculate Duration on a $1000 Ten-year 10% Coupon Bond When its interest rate is 20% (Table 5)

Calculating Duration, its interest rate is 20% (Table 5)i = 20% 10-yr 10% Coupon Bond

- Everything else equal, its interest rate is 20% (Table 5)
- 1. When the maturity of a bond lengthens, the duration rises as well.
- 2. When interest rates rise, the duration of a coupon bond falls.

- 3. The higher is the coupon rate on the bond, the shorter is the duration of the bond.
- 4. Duration is additive: the duration of a portfolio of securities is the weighted-average of the durations of the individual securities, with the weights equaling the proportion of the portfolio invested in each.

Exercise the duration of the bond.

Calculating duration for an 11-year 20% coupon bond when current interest rate is 10%

Duration and Interest-Rate Risk the duration of the bond.

- %ΔP - DUR x Δi/(1+i)
- i 10% to 11%:
- For a coupon bond with coupon rate of 10%, DUR = 6.76 Yrs
- %ΔP =
- ΔP =

For a 10 year, 20% coupon bond, DUR = 5.72 Yrs, if interest rate increases from 10% to 11%

%ΔP =

ΔP =

Duration and Interest-Rate Risk rate increases from 10% to 11%

- The greater is the duration of a security, the greater is the percentage change in the market value of the security for a given change in interest rates. Therefore, the greater is the duration of a security, the greater is its interest-rate risk.

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