Interest rate immunization as zero replication

To immunize a single liability has three conditions:

1, bond portfolio initial market value has to match or exceed the present value of zero coupon bond.

2, Macaulay duration of bond portfolio and zero coupon bond match.

3, minimize convexity.

But why there is no condition such that the cash flow yield of bond portfolio match the yield of zero coupon bond? If bond portfolio and zero coupon bond grow at different yield, the bond portfolio may not meet the future liability.

There is already a condition that make sures that bond will be able to meet future liability. If the present value of assets is greater than that of liabilities, the future value of assets will also be greater than the future value of liabilities.

True if the discount rate is the same for both; not necessarily true if they have different discount rates.

I think I got your point. Immunizing a single liability already assumes portfolio cash flow yield is the same as zero coupon bond yield.

Mark to remember to come back later

is there no way to save a post (bookmark) without commenting on it?

Got me.