The curriculum states that to immunize a single liability, the duration of assets and liabilities must match.
However, for the multiple liabilities immunization, they say that the BPV of assets and liabilities must match. Also, the PV of Assets> PV of Liabilities.
Why can’t we just match the durations in the multiple liabilities case. What’s wrong in that?
Thanks.
Don’t quote me on this but this is how I understand it:
to immunize a single liability, the macaulay duration has to match.
for multiple liabilities you match the BPVs or the dollar duration (which are essentially the same thing in this context)
So you’re duration matching in both cases. Macaulay in one and dollar duration in the other
Matching dollar duration and Macaulay duration isn’t same. In the example in CFA curriculum text for multiple liabilities, the Macaulay durations dont match while the dollar duration matches.
My question is ehy don’t we do matching of dollar duration in both single and multiple liabilities.
Following up on this post.
CFAI says, “With multiple liabilities, matching money durations is useful because the market values and cash flow yields of the assets and liabilities are not necessarily equal.”
Why do we match MacDur for single liability but need to match BPVs for multiple liabilities? Why can we not just treat all the asset cash flows as one aggregate asset and all the liability cash flows as one aggregate liability and match the MacDur of those?
Hi
For a single liability, it is efficient to use MacDur because we have one instrument with specific risks.
Multiple liabilities consist of different instruments with different risks; treating all the cash flows as a single liability will oversimplify the analysis and not adequately account for the individual risks. Using the BPV approach considers the unique features and risk characteristics of each liability and optimises the asset allocation.