Question

A coupon bond issued by a European firm has a remaining maturity of 5 years. The bond has a 2% coupon paid annually. The current yield to maturity (YTM) of the bond is 0.5% (annual compounding). What are the MacAuley's Duration and Modified Duration measures of the bond? Modified Duration = MacAuley's Duration / (1+ YTM). (Modified duration provides a useful measure of interest rate risk of the bond.)

Answer 1

Macaulay Duration=Sum(t*PV of Cash flows)/Sum(PV of Cash flows)=(1*2%*1000/1.005+2*2%*1000/1.005^2+3*2%*1000/1.005^3+4*2%*1000/1.005^4+5*2%*1000/1.005^5+5*1000/1.005^5)/(2%*1000/1.005+2%*1000/1.005^2+2%*1000/1.005^3+2%*1000/1.005^4+2%*1000/1.005^5+1000/1.005^5)=4.815607063

Modified Duration=4.815607063/(1+0.5%)=4.791648819