CFA Exam Morning 2018 Q7A

Hi all

Quick question re immunising a single liability.

The answer to this question (CFA Exam Morning 2018 Q7A) says that for a single liability, PV(A) has to exceed PV(L).

My question is: why is that criterion different to multiple liabilities, where really what matters is that money duration (i.e. duration x PV) of assets and liabilities matches? Why can’t we just match money duration for a single liability as well?

For example, if the PV(A) is a tiny fraction less than the PV(L), but the Macaulay Duration of the asset portfolio is a bit higher than the MacDur of the liabilities, can’t we rely on the two to roughly cancel each other out as long as total portfolio duration (i.e. money duration) is roughly matched?

In the 2018 Q7A question specifically, the answer was Portfolio A for more reasons than just this but I didn’t exclude Portfolio B based on the shortfall of PV(A) vs. PV(L) because it was tiny (like 0.13%) and partially offset by the slightly higher MacDur.

Would be good to know how puritanical CFAI are on this - if PV(A) was $1 less than PV(L) does that make the portfolio unsuitable even if the MacDur is closer than alternatives?

Thanks