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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