Consider four different bonds all having the same yield-to-maturity. Bond A is a consol that pays $50 every period forever and is currently priced at $764.29. Bond B, C and D have the same par value of $1, 000. However, they differ in their maturity and coupon rate. While bond B and C have a maturity of 5 years, bond D has a maturity of 8 years. Also, bond B and D have a coupon rate of 5% whereas bond C has a coupon rate of 7.5%.
(a) Calculate the prices for bond B, C and D.
(b) Calculate the duration for all bonds.
(c) Calculate the duration adjusted for convexity for all bonds.
(d) Suppose the yield-to-maturity increases by 1%. Calculate the price changes on the individual bonds based on the two duration measure and based directly on the pricing formula. Compare your answers. (e) Suppose the yield-to-maturity decreases by 1%. Calculate the price changes on the individual bonds based on the two duration measure and based directly on the pricing formula. Compare your answers.
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