ACTSC 231 ch09-Actsc231

# ACTSC 231 ch09-Actsc231 - Chapter 9 Interest Rate...

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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 zero-coupon bonds now. Assume you have the following three bonds for choices: (1) 3-year zero-coupon \$1,000 bond priced at an annual yield rate of 5%. (2) 5-year zero-coupon \$1,000 bond priced at an annual yield rate of 3%. (3) 7-year zero-coupon \$1,000 bond priced at an annual yield rate of 5%. • Observations: XBox 5-year bond is not as attractively priced as the other two. XBox If you purchase the 3-year 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 7-year 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 3-year bonds and 7-year 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 3-year zero-coupon bond with \$22,675.74 redemption amount and a 7-year zero-coupon 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 two-year zero-coupon 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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ACTSC 231 ch09-Actsc231 - Chapter 9 Interest Rate...

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