Question

Suppose you have a bond that currently has 10 years left until maturity. The coupon rate (CR) is 7.5% and the YTM is also 7.5%. The bond has a face value of $1,000 and is compounded semiannually. According to Duration, what is the expected change in the price of the bond if the YTM increases to 7.8%

Answer 1

Par Value =1000
Coupon =7.5%*1000 =75
YTM =7.5%
Since YTM is same as coupon rate price equal to par value
Price =1000
Macaulay Duration =(1*75/(1+7.5%)+2*75/(1+7.5%)^2+3*75/(1+7.5%)^3+4*75/(1+7.5%)^4+5*75/(1+7.5%)^5+6*75/(1+7.5%)^6+7*75/(1+7.5%)^7+8*75/(1+7.5%)^8+9*75/(1+7.5%)^9+10*1075/(1+7.5%)^10)/1000 =7.3789
Modified duration =7.3789/(1+7.5%)=6.8641
Change in Price =-Modified Duration*Change in YTM*Price =-6.8641*(7.8%-7.5%)*1000 =-20.59
Expected change in price =-20.59