# Distribution of durations of the assets vs. multiple liabilities

Why the range of distribution of the assets in portfolio must exeed the distribution of the liabilities?  Why it can not be same or less?

* Assuming parallel rate shift and high liquidity of the market.

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on the date that the liability is due - you need to have enough assets to be able to sell and satisfy the liability.

you need enough value - and have a sufficient enough cushion so that PV(Assets) on Liability Due date = PV(Liability Due)

And the Duration part being higher ensures that if there is an adverse interest rate movement - you still are covered.

CP

I understand the first (PV (assets) = PV( Liability) and second (same aggregate duration), but do not understand why the of distribution of the assets in portfolio must exceed the distribution of the liabilities.

If PV and Duration are same, the liability will be covered…

For the effective duration of the assets to equal the average maturity of the liabilities (which is stupid, by the way, but we’re stuck with it), the average maturity of the assets must be longer than the maturity of the liabilities.

To limit interest rate risk, the maturity of some assets should be shorter than the maturity of the liabilities.

Simplify the complicated side; don't complify the simplicated side.

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S2000magician wrote:

For the effective duration of the assets to equal the average maturity of the liabilities…

I’ll regret trying to correct you, but you meant “to equal the average McCaulay duration of the liabilities”. I hope I’m right or I look like a ****.

googs1484 wrote:

S2000magician wrote:

For the effective duration of the assets to equal the average maturity of the liabilities…

I’ll regret trying to correct you, but you meant “to equal the average McCaulay duration of the liabilities”. I hope I’m right or I look like a ****.

For bonds whose cash flows won’t change when their YTM changes, effective duration and modified duration are the same thing.

you should know this by now

googs1484 wrote:
S2000magician wrote:
For the effective duration of the assets to equal the average maturity of the liabilities…

I’ll regret trying to correct you, but you meant “to equal the average McCaulay duration of the liabilities”.

I was thinking of only bullet liabilities, but you’re correct: for more general liabilities it would be the average Macaulay duration.

googs1484 wrote:
I hope I’m right or I look like a ****.