Immunizing single liabilities

CFA Level III Fixed Income
#1

The three conditions listed in CFAI text are:

  1. has an initial market value that equals or exceeds the present value of the
    liability;

  2. has a portfolio Macaulay duration that matches the liability’s due date;

  3. minimizes the portfolio convexity statistic

On (3) - does the convexity have to be above the convexity of the liability as well? I know this is the condition for multiple liabilities.

Or is this not specifically required because convexity of a single liability is 0.

Many thanks in advance.

#2

No this would only be for multiple liabilities.