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Duration and Interest Rate Risk

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Duration and Interest Rate Risk

- 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

What is Duration?

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)

- Everything else equal,
- 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

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

- %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

- 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.