Question

12. The current price of a 1-year zero-coupon Treasury bond is $975 (with $1,000 par value). If the annual forward rate between year 1 and 2 implied by the zero yield curve is equal to 4.5%, what is the current price of a 2-year zero-coupon Treasury bond (with $1,000 par value)? (a) $950.63 (b) $933.01 (c) $924.56 (d) $1,000.00

Answer 1

Current Price of 1 Year Zero Coupon Bond (ZCB) = $ 975 and Par Value = $ 1000

Let the one year ZCB rate be R1

Therefore, 975 = 1000 / (1+R1)

R1 = 0.0256 or 2.56 %

Annual Implied Forward Rate between Year 1 and Year 2 (one-year rate one-year from now) = f = 4.5 %

Let the two-year ZCB rate be R2. Then, according to the pure expectations theory, we get:

(1+R1) x (1+f) = (1+R2)^(2)

(1.0256) x (1.045) = (1+R2)^(2)

R2 = 0.03525 or 3.525 %

Therefore, 2 year ZCB price = 1000 / (1.03525)^(2) = $ 933.0599 ~ $ 933.01

Hence, the correct option is (b).