Simple YTM calculation

Question

I'm working the following problem, but getting the wrong answer. Any feedback appreciated.

Suppose you bought a five-year zero-coupon Treasury bond for $800 per $1000 face value. Assume the yield to maturity on comparable bonds increases to 7% after you purchase the bond and remains there. Calculate your holding period return (annual return) if you sell the bond after one year.

First, I calculated the value in 1 year at the time of sale. Since it is a five year bond right now, next year it will be a 4 year bond, and at that point, rates will be 7%. Thus, the price will be $1000/(1.07)^4=762.90. Since it was purchased for $800, the return for the year = 762.9/800 - 1 = -0.046, or -4.6%. Is my analysis correct? Any advice appreciated, thank you very much in advance.

Answer 1

from a comment on the question:

Don't Treasury bonds pay interest semiannually? If so, you may need to consider compounding in your answer (which you don't seem to be doing). – Karl Commented May 17 at 21:46

Karl's correct. The yields on Treasury's are usually expressed as an annual percentage rate or APR. APRs measure only simple interest, i.e., no compounding. Convention in Treasury markets is that interest compounds semi-annually to coincide with coupon payments on T-notes and T-bonds. T-bills actually have their own yield convention called bank discount basis.

The question says "five-year zero coupon Treasury bond," which I'm guessing would be a STRIP. In this case, the value of the bond can be calculated as follows.

price(1) = 1,000/(1+0.07/2)^(8) = $759.41

The holding period return over the year is therefore.

ret(0,1) = 759.41/800 - 1 = -0.0507375