Task 2 three bonds in equal par amounts of You are the manager of a portfolio co

Question

Task 2 three bonds in equal par amounts of You are the manager of a portfolio consisting of $1 mion each. The firs table below shows the market valuc of the bonds and their durations. (The price includes accrued interest.) The second table contains the market valuc of the bonds and their durations one vear later Initial Values urity Price Market Value Duration Dollar Duration Bond #1 Bond #2 Bond #3 $106.110 98.200 109.140 $1,060,531 981,686 1,090,797 5.909 3.691 5.843 Portfolio Dollar Duration = After 1 ycar PriceMarket Value Duratio Dollar Duration Security Bond $104.240 $1,042,043 Bond 2 Bond 3 106.93 1,068,319 980,461 2.817 5.125 98.084 Portfolio Dollar Duration maintain the portfolio's dollar duration at the initial As manager, you would like to level by rebalancing the portfolio. You choose to rebalance using the existing security proportions of one-third cach. Calculate A. The dollar durations of each of the bonds. ncing ratio necessary for the rebalancing. C. The cash required for the rebalancing.

Explanation / Answer

Soln : Dollar duration is the dollar value change in the bond price due to change in interest rate. We can calculate it by multiplying modified duration with the price of the security.

At t= 0

Bond1, dollar duration = 106.110*5.909/100 = 6.27

Bond 2, dollar duration = 98.2*3.691/100 = 3.62

Bond 3,dollar duration = 109.14*5.843/100 = 6.38

For portfolio the same can be calculated by adding the weighted value of the dollar duration, as 1/3 is the weighted value. Hence at t= 0 the dollar duration of portfolio = (6.27+3.62+6.38)/3 = 5.42

At t=1, dollar duration of portfolio = 4.55

B) Rebalancing ration can be calculated by using the old portfolio duration and new dollar duration

i.e. Rebalancing ratio = 5.42/4.55 = 1.19

C) So, 19% increment is required in the portfolio, Total cash required = addition of new market values of each security*19% = (1042043+980461+1068319)*0.19 = 587256.38

t=0 Price Duration Dollar duration Bond1 106.11 5.909 6.27 Bond2 98.2 3.691 3.62 Bond3 109.14 5.843 6.38 t =1 Bond1 104.24 5.177 5.40 Bond2 98.084 2.817 2.76 Bond3 106.931 5.125 5.48

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