Calculate the rebalancing ratio and cash required for rebalancing to maintain do

Question

Calculate the rebalancing ratio and cash required for rebalancing to maintain dollar duration at the initial level.

A. Calculate the rebalancing ratio.

B. Calculate the cash required for this rebalancing

Please Show Work and Explain!

Intial

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

After Change

Bond

Coupon

Maturity

Value/Price

YTM

Duration

Dollar Duration

Bond X

3.00%

2

$     980,961

4.00%

1.92

Bond Y

4.00%

5

$     956,240

5.00%

4.46

Bond Z

5.00%

10

$     925,613

6.00%

7.67

$ 2,862,814

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

Dollar Duration (DD) = Value x Duration x 1%

Portfolio Dollar Duration = Sum of individual DD

Rebalancing Ratio = Old DD / New DD = 142,100 / 132,477.27 = 1.0726

Cash required = (rebalancing ratio - 1) x End Value

= (1.0726 - 1) x 2,862,814 = $207,945.70

Bond Old Value Duration Old DD New Value Duration New DD Bond X $ 1,000,000 1.93 $        19,300 $    980,961 1.92 $   18,834.45 Bond Y $ 1,000,000 4.49 $        44,900 $    956,240 4.46 $   42,648.30 Bond Z $ 1,000,000 7.79 $        77,900 $    925,613 7.67 $   70,994.52 $ 3,000,000 $      142,100 $ 2,862,814 $ 132,477.27

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