Question

for the following questions, use a 10 year coupon bond with a face value $1500 coupon payments of 200 anually and an interest and an interest rate of 9% for each of the following questions show the equation in general form and then your answer

• a. calculate the duration of the bond (using the formula)
• b. Calculate the modified duration of the bond
• c. Calculate the dollar change in price when interest rates increase by 2% using duration
• d. Calculate the dollar change in price when interest rates increase by 2% using modified duration
• e. calculate the % change in price when interest rates increase by 2% using duration
• f. Calculate the % change in price when interest rates increase by 2% using modified duration
• g.calculate the convexity of the bond

Answer 1

1.

Price=Present value of cash flows=Present value of coupons+Present value of face value=(200/1.09+200/1.09^2+200/1.09^3+200/1.09^4+5*200/1.09^5+200/1.09^6+200/1.09^7+200/1.09^8+200/1.09^9+200/1.09^10+1500/1.09^10)=2437.09286

=(1*200/1.09+2*200/1.09^2+3*200/1.09^3+4*200/1.09^4+5*200/1.09^5+6*200/1.09^6+7*200/1.09^7+8*200/1.09^8+9*200/1.09^9+10*200/1.09^10+10*1500/1.09^10)/2437.09286

=5.12670

2.

Modified Duration=Macaulay Duration/(1+rate)

=5.12670/1.09

=4.703394495

3.

=-Price*change in rates*duration

=-2437.09286*2%*5.12670

=-249.8848793

4.

=-Price*change in rates*modified duration

=-2437.09286*2%*4.703394495

=-229.2521828

5.

=-change in rates*duration

=-2%*5.12670

=-10.2534%

6.

=-change in rates*modified duration

=-2%*4.703394495

=-9.4068%