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Duration and Interest Rate Risk

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?

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Duration and Interest Rate Risk

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  1. Duration and Interest Rate Risk

  2. 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

  3. 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

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

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

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

  7. 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.

  8. 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.

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

  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 =

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

  12. 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.

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