Question

John Q. Investor purchased a semi-annual coupon-bearing Treasury at par. The duration was 17 years. Yield then rose 1% to 5.77%. Therefore, the price of the Treasury after the rate change is _____ %. (Express the price as a percentage of the face value. Round your answer to three places after the decimal. Just write the number and do NOT include the “%” sign ) Related formula:

Answer 1

Since investor purchased Treasury at par, hence price of bond =1000
Since Bond is sold at par ,hence initial price =1000
Original YTM =5.77%-1% =4.77%
Duration =17
Change in YTM =1%
Change in Price =-Duration/(1+YTM/2)*Change in YTM*Price =-17/(1+4.77%/2)*1%*1000 =-16.603995%
New Price =1000-1000*16.603995%=833.96

Price as percentage of face value =833.96/1000 =83.396%