Question

You observe that the current three-year discount factor for default-risk free cash flows is 0.68. Remember, the t-year discount factor is the present value of $1 paid at time t, i.e. ???? = (1 + ????)−??, where ???? is the t-year spot interest rate (annual compounding). Assume all bonds have a face value of $100 and that all securities are default-risk free. All cash flows occur at the end of the year to which they relate.

a) What is the price of a zero-coupon bond maturing in exactly 3 years?

b) Your friend makes the following observation about the above bond: “Since there is no risk of default and there are no coupons to re-invest, buying the 3-year zero coupon bond today is a risk-free investment; that is, you are guaranteed to earn an annual return of 13.72% (i.e. 3-year spot rate)”. Explain why your friend is not entirely correct and how you would modify the statement to make it correct.

Answer 1

a). Price of a 3-year zero coupon bond = par value*discount factor = 100*0.68 = 68

b). A zero coupon bond will be default free only if it is a Treasury zero. Otherwise, with municipal or corporate zero bonds, default risk is there. Additionally, zero coupon bonds are subject to interest rate risk if sold before maturity. If interest rates increase then bond price will decrease. So, for the given 3 year zero coupon bond, there is no guarantee that it will earn 13.72% return p.a.