Problem: 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.
1) 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%.
2) 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%.
3) 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.
4) Compare your answers to b. and c. Explain the source of any difference. Which is more correct?