Question

:  A bond has a 7.5% annual coupon rate with 4 years to maturity and pays annual coupon

1.       What is the price of the bond if the yield to maturity is 5%

1.2       What is price of the bond if the yield to maturity increases by 0.2%?

3.       What is the % change in the price of the bond when yield increases by 0.2%?

                              

1.4       What is the bond duration?

4.       What is the modified duration?

5.       Using the modified duration, what is the percentage change in the price if the yield                                                  

      increases by 0.2%

1.6       What can you conclude regarding the error-estimate based on the modified duration?

            

Answer 1

Clipboard Font Number Styles Cells Editing Alignment C 7.50% D E F G H I J K L M Coupon rate period Yield Par value (assumed) Price 5% 1000 1088.65 7 8 1.2 Revised yield Price 5.20% 1081.18 9 10 11 12 1.4 13 14 15 16 17 Cash flow PV @ 5% 75 71.43 71.43 75 68.03 136.05 75 64.79194.36 1075 884.41 3537.62 1088.65 3939.47 Duration Modified duration - Duration/(1+ yield/ % change in price if ytm increase by .2% 3.62 3.57 -0.71% 1.6 Convexity adjustment is required to correct the estimate error as modified duration do not consider convexity

Clipboard Font To Number Styles Cells Editing Alignment B C D E F 1 0.075 Coupon rate period Yield Par value (assumed) Price 0.05 1000 =PV(C3,C2,-C4*C1,-C4) 5 6 7 8 9 1.2 Revised yield Price =C3+0.2% =PV(C8,C2,-C4*C1,-C4) 11 12 13 1.4 Year HNM Cash flow =1000*7.5% =1000*7.5% =1000*7.5% = 1000*7.5%+1000 PV @ 5% =C13/(1+5%)^B13 =D13*B13 =C14/(1+5%)^B14 =D14*B14 =C15/(1+5%)^B15 =D15*B15 =C16/(1+5%)^B16 =D16*B16 =SUM(D13:D16) SUM(E13:E16) 20 21 Duration Modified duration - Duration/(1+ yield/maturity) % change in price if ytm increase by .2% =E17/D17 =C19/(1+5%/4) --C20*0.2% 22 23 1.6 Convexity adjustment is required to correct the estimate error as modified duration do not consider convexity 24 25.