This question is from GARP Practice Exam 2, 2006 (Question 61)

How do they find the Duration input of the 6% coupon bond?, in the following question:

What is the best estimate of the market value of a portfolio of USD 100 Million invested in recently issued 6% 10 year bonds and USD 100 million of long 10 year zero coupon bond if intrest rates decline by 0.50%?

a) USD 219 million

b) USD 195 million

c) USD 209 million

d) USD 206 million

The solution says:

ANSWER C

To calculate the best estimate of the market value of the portfolio if interest rates decline 0.5%, one needs to calculate the change in the market value of each bond using duration. The duration of the 10 yr zero coupon bond is 10.Thus, the change in the value of this bond equals 10x0.005x100,000,000 which equals 5 million.

The duration of the newly issued 6% bond is 7.802 assuming that the price of the bond is par. Given a duration of 7.802 assuming that the price of the bond is par.

Given a duration of 7.802 the change in the value of the bond equals 7.802x0.005x100000000=3.91million.

I understand there rational of assuming that the bond is at par because it is recently issued. However, I STILL DONT SEE HOW THEY SOLVE THE DURATION TO BE 7.802 FROM THAT ONE ASSUMPTION!!

*I have looked at all the duration formulas and I can not make the connection!

Secondly, not as important- but why cant one solve for portfolio duration and then work out the Market value estimate?

David Please help I am sure I am not the only one who would like to know the answer for this.

Thanks!

DavidM