# Duration and Interest Rate Risk - PowerPoint PPT Presentation

1 / 12

Duration and Interest Rate Risk. 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. What is Duration?

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Duration and Interest Rate Risk

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

#### Presentation Transcript

Duration and Interest Rate Risk

### 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

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)

### Calculating Duration, i = 20% 10-yr 10% Coupon Bond

• 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%

### Duration and Interest-Rate Risk

• %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.