Just started Fixed Income, so please bear with me 
Say I’ve got a liability with a horizon of 4 years. I understand to immunize this, one of the goals is to match the Mac Duration. Hence our assets should have a Mac Duration of 4 years too. To do this, I understand we could buy 2 bonds with a Mod Duration of 3.5 years and 4.5 years (bullet portfolio).
My questions are:
1.) Why are we matching Mac Duration and not Modified/Effective Duration ?
2.) What is logic behind averaging the duration of assets (3.5 and 4.5) to bring it to 4 years?
Macaulay duration gives us, amongst other things, the point-of-indifference: for a single, immediate, parallel shift in the yield curve, the Macaulay duration is the amount of time for the change in price and the change in reinvestment income to offset each other. Therefore, if the value of your assets equals the present value of your liabilities and their Macaulay durations match, then if there’s a single, immediate, parallel shift in the yield curve, they will again be equal after an amount of time equal to the Macaulay duration.
The Macaulay duration of a portfolio of bonds is equal to the weighted average of the Macaulay durations of the constituent bonds.
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Thanks a lot @S2000magician , very clear now!
Macaulay duration gives us, amongst other things, the point-of-indifference : for a single, immediate, parallel shift in the yield curve, the Macaulay duration is the amount of time for the change in price and the change in reinvestment income to offset each other. Therefore, if the value of your assets equals the present value of your liabilities and their Macaulay durations match, then if there’s a single, immediate, parallel shift in the yield curve, they will again be equal after an amount of time equal to the Macaulay duration.
Is this assuming a 1% parallel shift in the yield curve?
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It doesn’t have to be 1%; any immediate parallel shift will do, up or down.
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It doesn’t have to be 1%; any immediate parallel shift will do, up or down.
Thanks for clarifying that for me.
We should assume flat YC as well for Macaulay duration to work this way.