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Unformatted text preview: Chapter 9. Interest Rate Sensitivity ACTSC231 — Mathematics of Finance Department of Statistics and Actuarial Science University of Waterloo Fall 2010 Instructor: Chengguo Weng C. Weng ([email protected]) – p. 1/1 7 Motivating Example • Image that you are obligated to pay $50,000 five years from now. To cover this liability, you decide to buy zerocoupon bonds now. Assume you have the following three bonds for choices: (1) 3year zerocoupon $1,000 bond priced at an annual yield rate of 5%. (2) 5year zerocoupon $1,000 bond priced at an annual yield rate of 3%. (3) 7year zerocoupon $1,000 bond priced at an annual yield rate of 5%. • Observations: XBox 5year bond is not as attractively priced as the other two. XBox If you purchase the 3year bond, you will be exposed to reinvestment risk . The interest rate in the 4th and 5th years might be very low. XBox If you purchase the 7year bond, you have to sell the bond at time 5. If the interest rate has risen, you may have a problem meeting your obligation. • Question: can we split our investment b/t the 3year bonds and 7year bonds so as to gain the high return rate while avoid the risk from the fluctuation of the interest rate? = ⇒ Employ immobilization strategies. C. Weng ([email protected]) – p. 2/1 7 Immunization Example • Example 9.1: To finance an obligation of $50,000 in five years, we purchase a 3year zerocoupon bond with $22,675.74 redemption amount and a 7year zerocoupon bond with $27,562.51 redemption amount. Suppose at the end of three years, no matter what the yield rate i may be, we sell the remaining bond at a purchase price to yield i , combine the proceeds with the $22,675.74 from the redeemed bond, and use the total to buy a twoyear zerocoupon bond. Illustrate that this immunizes against interest rate risk by showing that it produces the needed $50,000 five years after your initial bond purchases if i = 20% , i = 5% or i = 1% ....
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 Fall '09
 Chisholm
 Bond duration, C. Weng, [email protected])

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