Alter duration of portfolio

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aymane07

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Hello Guys,
can anyone explain why when you want to alter the duration of the portfolio with a future/swap or any derivatives, the weighted duration of the portfolio does not seem to hold, let me explain what i say:
swap value = ( (D_target - D_portfolio) / ( D_Swap) ) * Value_port
let’s say we have 100M portfolio with duration 3 and swap duration is 6 and target is 4.5.
the above equation will give us a 25M swap
if however you are given a portfolio with 100M bonds with duration 3 and 25M swap with duration 6 and asked to calculate the duration of the total portfolio than you will use the weigthed duration equation:
D_port = (100/125) * 3 + (25/125) * 6 = (80% * 3) + (20%*6) = 3.6 which is different from 4.5
thanks a lot for your help!!!!!!!
 
The error in your second calculation is that the denominator should not be 125; it should be 100. You don’t invest 25M in the swap; at initiation there is no cash flow. The same would be true if you’d used a future/forward instead of a swap.
 
I get it now! I was trying to derive the formula which very simply comes from the following:
100% * D_port + (V_swap / V_Port) * D_swap = D_Target
thanks a lot!
 
S2000magician, i wanna have your take on this subject (maybe not related to CFA):
what would be the duration of a forward IR swap starting in 1 year for 1 year (1 fixing at the end for the floating) ?
 
The duration of the floating leg is generally considered to be ½ of the time between payments, so 0.5 years.
The duration of the fixed leg will depend on the interest rate, but it will be slightly less than one year; say, about 0.9 years.
Thus, the duration of the swap will be -0.4 years to the fixed rate payer, floating rate receiver, and +0.4 years to the floating rate payer, fixed rate receiver.
 
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