Ch 9 2012

# Ch 9 2012 - 1 Chapter 9 Interest Rate Risk II 2 Overview...

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Chapter 9 Interest Rate Risk II 1

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Overview This chapter discusses a market value-based model for assessing and managing interest rate risk: Duration Computation of duration Economic interpretation Immunization using duration Repricing model (discussed in the previous chapter) is used by small banks, whereas the duration model is used by large banks and is a much better valuation model that takes market value risk into account. 2
Macaulay Duration Duration is the weighted average time to maturity using the relative present values of the cash flows as weights. Duration is a more accurate measure than maturity since it takes into account the time of arrival of all cash flows as well as maturity. Takes into account all the coupon payments as well as the repayment of principal at maturity. The units of duration are years. 3

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Some Properties of Macaulay Duration As we will also show the duration is equal to the elasticity of bond price with respect to the interest rate. Also equal to the times takes to recover the initial investment on a bond. We will show below that you can calculate duration on a entire portfolio as well. 4
Duration The duration of any fixed-income security that pays interest annually (assuming no credit risk or prepayment risk) is given by: D = Σ n t=1 [CF t • t/(1+R) t ] / Σ n t=1 [CF t /(1+R) t ] => D = Σ n t=1 [PV t • t] / Σ n t=1 [PV t ] D = duration measured in years t = number of periods in the future CF t = cash flow received at the end of period t n = last period in which cash-flow is received (equals maturity) R = is the annual yield or current level of interest rates in the market PV t = present value of the cash flow from period t 5

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Duration The duration of any fixed-income security that pays interest semi-annually is given by: D = Σ n t=1/2 [CF t • t/(1+R/2) 2t ] / Σ n t=1/2 [CF t /(1+R/2) 2t ] => D = Σ n t=1/2 [PV t • t] / Σ n t=1/2 [PV t ], D = duration measured in years t = number of periods in the future CF t = cash flow received at the end of period t n = last period in which cash-flow is received R = is the annual yield or current level of interest rates in the market PV = present value of the cash flow from period t 6
Since in an efficient market the price of a bond must equal the present value of all its cash flows, we can state the annual duration formula as follows: D =[Σ n t=1 (t × Present Value of CF t )]/ Price The numerator is equal to the PV of each cash flow multiplied or weighted by the length of time required to receive the cash flow. The denominator is the sum of the present value of all payments which should equal Price in an efficient market. 7

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## This note was uploaded on 02/17/2012 for the course FINA 465 taught by Professor Berger during the Spring '11 term at South Carolina.

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Ch 9 2012 - 1 Chapter 9 Interest Rate Risk II 2 Overview...

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