Fixed Income: Multiple Liability Immunization. Using Hedge Ratio of 75%

CFA Level III Fixed Income
#1

Solution to Example 8 as given in the curriculum

First calculate the notional principal needed to close the duration gap between assets and liabilities to zero using Equation 6.Asset BPV+(NP×Swap BPV/100)=Liability BPV
Asset BPV is USD 528,384; Swap BPV is 0.1751 per 100 of notional principal; and Liability BPV is USD 1.215 million.528,384+(NP×0.1751/100)=1,215,000A 100% hedging ratio requires a receive-fixed interest rate swap having a notional principal of about USD 392 million. For a hedging ratio of 75%, the notional principal needs to be about USD 294 million (= 392 × 0.75).

Why cannot we use
My calculation was based on the logic that, if the Plan Manager needs to Hedge only 75% of Liability, he can just take the 0.75 of Liabilities.
My solution comes to NP of 217,908,935.

Asset BPV+(NP×Swap BPV/ 100)=Liability BPV x ( Hedge Ratio of 75%) directly?

Is there something wrong in the way I am thinking?

Many thanks for helping clarify this topic.

Best Regards,
Dealdone

#2

The difference between the Asset BPV and the Liability BPV is what you need to hedge.

The hedging ratio of 75% means to hedge 75% of the difference which is 75%*(1,215,000-528,384).

PS. Hedge ratio is the ratio of an open position’s hedge to the overall position.

#3

Many thanks Okachiang.
That clarifies my faulty logic…