An insurance company must make a payment of $19,487 in seven years. The current yield curve in the market is flat at 10% per annum for all maturities. The company’s portfolio manager wishes to fully fund this obligation using a two-bond portfolio that is composed of two bonds: (1) a three-year zero-coupon bond and (2) a perpetuity paying annual coupons. (b) To immunize the company’s obligation, what should be the total market value of the three-year zero-coupon bond in the two-bond portfolio now? What is the total face value of the three-year zero-coupon bonds in the two-bond portfolio? (c) Carefully explain why bond duration is lower for a bond with high coupons than for a bond with low coupons, assuming that all other characteristics of the bonds are the same. (d) If the yield to maturity of a 10-year zero-coupon bond is up by 50 basis points from 4% to 4.5% immediately after the purchase of this bond, what is the percent change in the value of this bond?
An insurance company must make a payment of $19,487 in seven years. The current yield curve in the market is flat at 10% per annum for all maturities. The company’s
(b) To immunize the company’s obligation, what should be the total market value of the three-year zero-coupon bond in the two-bond portfolio now? What is the total face value of the three-year zero-coupon bonds in the two-bond portfolio?
(c) Carefully explain why bond duration is lower for a bond with high coupons than for a bond with low coupons, assuming that all other characteristics of the bonds are the same.
(d) If the yield to maturity of a 10-year zero-coupon bond is up by 50 basis points from 4% to 4.5% immediately after the purchase of this bond, what is the percent change in the
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