Portfolio Rebalancing based on the dollar duration. Bond Coupon Maturity Price/V
ID: 2795580 • 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) As all the three bonds have equal value, the duration of the portfolio is an arithmetic average of three bonds.
Portfolio duration = (1.93 + 4.49 + 7.79) / 3 = 4.74
b) Dollar Duation of the portfolio
= (1.93 + 4.49 x 7.79) x 1,000,000 x 1%
= $142,100