Question

Consider a 3-year 11% coupon bond with a face value of $100. Suppose that the yield on the bond is 12% per annum with continuous compounding. The bond pays coupon every 6 months. Use the modified duration to calculate the effect on the bond’s price for a 0.1% increase in its yield.

A $90.12

B $96.42

C $94.73

D $98.32

Answer 1

Rate compounded semi annually=(e^(0.12/2)-1)*2=12.3673%

Modified Duration=1/2*(1*5.5/(1+6.91%/2)+2*5.5/(1+12.3673%/2)^2+3*5.5/(1+12.3673%/2)^3+4*5.5/(1+12.3673%^2)^4+5*5.5/(1+12.3673%/2)^5+6*(100+5.5)/(1+12.3673%/2)^6)/(5.5/(12.3673%/2)*(1-1/(1+12.3673%/2)^6)+100/(1+12.3673%/2)^6)*1/(1+12.3673%/2)
=2.492143846

Price=5.5/(12.3673%/2)*(1-1/(1+12.3673%/2)^6)+100/(1+12.3673%/2)^6=96.65758162

New price=96.65758162*(1-0.1%*2.492143846)=96.41669702