General Cash Flows' Immunization

[LaGrandeFinale]

Schweser, Book-3, Pg-39 - General Cash Flows
“Let’s assume the manager expects to receive a cash flow in six months. Treating this like a zero, the duration of 0.5. To construct the portfolio to immunize a liability due in 1.5 years with a duration of 1.0, the managers could combine the cash to be received with an appropriate amount of bonds with duration greater than 1.0, so that the conditions for immunization are met, including weighted average portfolio duration of 1.0”
Please help with this puzzle?

 

[FRM2cfa]

The dur of zero coup bond is time till its maturity. if its is one year till maturity, the dur is 1.
since cash is expected to come in six months, which is half of one year, that is why cash dur in this example is 0.5.
1) meet the condition that Aggr dur of liability = aggr dur of assets. As per this you have to construct PF with aggr duration =1.
Why a zero has duration equal to its maturity is 1 ? because you do not receive anything in between apart from its maturity. If you receive any cashflow in between, the duration would be less than 1.
What the example says is that to make aggr duration 1, you can take a bond with duration greater than 1 say 1.5 (say this bond does not pay any cash flows in between). Now you add the exapected cash with duration 0.5 and treat this expected cash coming from the above bond with duration 1.5. Since you are receiving cash in between the duration would drop.
Is this clear.

 

[LaGrandeFinale]

Thanks bud! You explained it well.