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.
Sorry to bump this up, but had an issue with this very topic.
To aid my understanding, the reasoning behind why the range of distribution of the assets in portfolio must exeed the distribution of the liabilities is the same as saying we want the asset portfolio to have higher convexity isn’t it? Thus, for any increase in rates, the value of assets will not go down as much, and with any decrease in rates, the value will go up more, compared with the liabilities.