Question
Consider a default-free coupon bond with market price A. The bond matures in T years time, has face value P, a constant coupon rate i
Consider a default-free coupon bond with market price A. The bond matures in T
years time, has face value P, a constant coupon rate i > 0, and yield to maturity
t > 0. Coupons are paid annually, and all rates are expressed assuming annual
compounding.
i. Show if a bond sells at a discount to face value, then i < t .
ii. The current yield of a coupon bond is defined as the annual coupon
payment expressed as a fraction of the bond price. Show that the following
relationship holds for all discount bonds and provide an intuitive explanation:
yield to maturity > current yield > coupon rate.
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