Portfolio Rebalancing based on the dollar duration. Bond Coupon Maturity Price/V
ID: 2793495 • Letter: P
Question
Portfolio Rebalancing based on the dollar duration.
Bond
Coupon
Maturity
Price/Value
YTM
Duration
Dollar Duration
Bond X
3.00%
2
$ 1,000,000
3.00%
1.93
Bond Y
4.00%
5
$ 1,000,000
4.00%
4.49
Bond Z
5.00%
10
$ 1,000,000
5.00%
7.79
$ 3,000,000
a) What is the bond portfolio’s duration?
b) A bond portfolio’s dollar duration is equal to the sum of the dollar durations of each bond. (Dollar duration for a bond = bond value X duration X 1.00%). What is the bond portfolio’s initial dollar duration?
Please Show Work and Explain!
Bond
Coupon
Maturity
Price/Value
YTM
Duration
Dollar Duration
Bond X
3.00%
2
$ 1,000,000
3.00%
1.93
Bond Y
4.00%
5
$ 1,000,000
4.00%
4.49
Bond Z
5.00%
10
$ 1,000,000
5.00%
7.79
$ 3,000,000
Explanation / Answer
a) since the bonds are equally weighted i.e have same value, portfolio duration is the average
portfolio duration = (1.93 + 4.49 + 7.79)/3 = 4.74%
b. duration of portfolio = 1,000,000*0.01*(1.93+4.49+7.79) = 142,100