Immunization of single liability

CFA Level III Fixed Income
#1

Characteristics of a bond portfolio to immunize a single liability are

  1. Initial MV >= present value of liability
  2. Macaulay Duration of portfolio=liability’s due date
  3. minimize portfolio convexity

I get point no. 2 and 3, but why is it necessary for condition 1 to be true? Even if – Initial MV < present value of liability, we can have a portfolio that can fund the liability in the future.

#2

Let’s say initial MV = $100 million and PV of liability = $120 million.

If the immunized return = 7% (say) and the MacDuration = 5 years, then will both asset and liability have the same future value at Year 5 (i.e. will you have enough assets in the portfolio to fund the liability)?

#3

But wouldn’t the outcome be dependent upon the discount rate we are using to get the PV of our liability?

#4

If the liability is immunized, the change in the mkt value of the asset will be close to the change in the present value of the liability, i.e. by the liability due date, the mkt value of asset will still be less than the liability value.

#5

I believe that the implication is that the present value of the liability uses as its discount rate the expected return on the immunizing asset(s).

Doing otherwise would be silly.