The current coupon rate, yield to maturity, and market price for the 10-year US Treasury bond are 2.625%, 3.33% and 94-02 respectively. Note, the price is expressed as a percentage of par (like other bonds) but the number after the dash represents 32nds of a percent. In other words, this bond is selling for 94 plus 2/32nds of a percent of par. If par is $1000, then this bond is selling for $940.625.
a. Assume that this bond will mature in precisely 10 years, pay coupons semi-annually, and has a par value of $1000. Compute the present value of this series of payments to confirm that the yield to maturity is correct to within 0.01%.
b. Compute the duration of this bond and use it to estimate the new value of the bond if rates were to suddenly decline by 0.80%.
c. Calculate the bond's value directly (using the present value approach) assuming that rates declined 0.80% from the yield to maturity reported in Bloomberg.
d. Compare your answers to b. and c. Explain the source of any difference. Which is more correct?
The problem set deals with estimating the price, duration and yield to maturity for bonds.