Question

A five-year bond that pays a coupon once per year, can be replicated by A. A portfolio of four zero coupon bonds B. A portfolio of two zero coupon bonds C. A portfolio of three zero coupon bonds D. A portfolio of five zero coupon bonds

Answer 1

A five year bond that pays annual coupon will have the following cash flows:

Year 1 through 4: C

Year 5: F+C

Where C= annual coupon payment and F= Redemption value

This bond can be replicated by a portfolio of 5 Zero Coupon bonds as follows:

One Zero coupon bond of 1 year maturity with Face Value= C

One Zero coupon bond of 2 years maturity with Face Value= C

One Zero coupon bond of 3 years maturity with Face Value= C

One Zero coupon bond of 4 years maturity with Face Value= C

One Zero coupon bond of 5 year maturity with Face Value= F+ C

Therefore, the answer is option D