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Understanding Duration and Its Impact on Interest Rate Risk in Bonds

This guide explains the concept of duration as a measure of a bond's sensitivity to interest rate changes. Duration indicates how bond prices will adjust with fluctuating interest rates, serving as a metric for interest rate risk. We cover the calculation of duration for bonds, including examples with different coupon rates and market interest rates. Key factors such as the impact of bond maturity, coupon rates, and portfolio duration are discussed to give a comprehensive understanding of how they influence bond valuation and risk management.

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Understanding Duration and Its Impact on Interest Rate Risk in Bonds

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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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