Chapter 7

# Chapter 7 - Chapter 7 Introduction to the Measurement of...

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1 Chapter 7 Introduction to the Measurement of Interest Rate Risk

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2 Introduction In Chapter 2 , we first discuss the interest rate risk in bond investment. We know that: Bond price and interest rate move in opposite directions In particular, a rise in the interest rates will lead to a decline in the bond value. This is known as the interest rate risk to bond investors The key in measuring the interest rate risk is the accuracy in estimating the value of the bond portfolio after an adverse interest rate move We can do so using either the full valuation approach or the duration/convexity approach
3 Full valuation approach This approach revalues a bond or bond portfolio for a given interest rate change scenario . It is also known as scenario analysis (as in ADMS3530 ) On the following two slides, we illustrate this approach using a portfolio of two bonds, bond A and bond B We consider two scenarios: In Scenario 1 , there is a parallel increase in the yields on both bonds by 50 basis points In Scenario 2 , there is a parallel decrease in the yields on both bonds by 100 basis points We can also do a similar analysis for a nonparallel shift in yields (see Exhibit 3 on p.159 )

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4 Full valuation approach Both bonds A and B are option free Bond A is 8% coupon payable semiannually, 5 years, \$100 par, yields at 6%, and sells at \$108.53 (N = 10; PMT = 4; FV = 100; I/Y = 3; CPT PV = -\$108.53) Bond B is 5% coupon payable semiannually, 15 years, \$100 par, yields at 7%, and sells at \$81.61 (N = 30; PMT = 2.5; FV = 100; I/Y = 3.5; CPT PV = -\$81.61) The value of the bonds and the value of the portfolio consisting of bonds A and B in each scenario are summarized in the table on the next slide …
5 Full valuation approach Scenario Yield change Bond A Bond B Porfolio Portfolio value change Current None \$108.53 \$81.61 \$190.14 None 1 50 basis points ( ) \$106.32 \$77.71 \$184.03 3.21% ( ) 2 100 basis points ( ) \$113.13 \$90.20 \$203.33 6.94% ( ) In Scenario 1 (i.e., interest rates rise ), bond A declines by 2.04% [= (\$106.32 - \$108.53) / \$108.53] in price, and bond B drops by 4.78% in price In Scenario 2 (i.e., interest rates drops ), bond A increases by 4.24% in price, and bond B rises by 10.53% in price

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6 Full valuation approach Bond B is a longer maturity bond and has a lower coupon rate : both of which mean higher interest rate risk The changes in bond B price are 4.78% and 10.53%, both higher than the corresponding changes in bond A price (2.04% and 4.24%, respectively) Recall from Chapter 2 : Higher (lower) coupon rate means lower (higher) interest rate risk Longer (shorter) maturity means higher (lower) interest rate risk Higher (lower) yield means lower (higher) interest rate risk
7 In-class exercise 1 A portfolio manager wants to take advantage of the expected decline in yields over the next several months. Which of the following combinations of maturity and coupon rate would most likely result in the biggest increase in portfolio value?

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