Duration matching

[i-actuary]

Hi all,

i am reading the sp5 notes and i see that as a 1st step we can match the duration of the liabilities and the assets. I have 3 questions of more practical nature so to understand the process.
1. assume we have 1 bond and 1 liability (a specific product). If i want to calculate the duration of the liability what is the yield that i will use in the formula of let's say the macaulay duration? for the assets i think we know in advance that it will be the YTM or something similar.
2. If we assume that we have 2 bonds and 2 liabilities. are we going to use a single macaulay duration for the assets ? and if yes will it be a weighted average of the YTMs? Similarly for liabilities ?
3. Would you use expected Cash flows for liabilities or nominal ? and if expected would you use something equivalent for the assets ?

 

[Gresham Arnold]

Hi

I don't have any practical experience of this I'm afraid so I'm hoping that someone else will be willing to contribute.

However, thinking about this, I wonder whether it would be sensible to use the same discount factors for asset and liabilities to try to ensure consistency? Also in practice we probably ought to use a method which doesn't assume that the yield curve is flat. So maybe we should be using a yield curve to discount cashflows and perhaps the same yield curve for both asset and liability cashflows?

Speaking to one of my colleagues, they noted that in their experience some institutions want to be more closely matched than just by duration, so the focus may now be on holding assets that produce cashflows that match the timing and amount of the liability cashflows.

Hope that helps.