One of the assumptions of the classical immunization theory is that if the interest rates change, the same changes by same quantum across all periods of maturities of bonds. However, at many a occasions, the change in interest rates may not be uniform across all the periods of bond maturities. Thus, equating the duration of maturity of bonds does not guarantee immunization.
Immunization risk is the measure of relative extent to which terminal value of the immunized portfolio may fall short of the target value of the arbitrary changes in the interest rates. Many bond portfolios could be constructed to immunize a given liability. Hence, the one that tends to minimize the immunization risk should ideally be applied in each case.
In general, immunized portfolios which have a cash flow well spread across the entire duration or tenure of the bond maturity around the investment horizon carries the maximum possibility of covering the immunization risk in an efficient manner rather than those who have cash flows coming in chunks only. In other words, the dispersion of cash flows across the duration is likely to prove to be the best bet for covering an immunization risk. Such a portfolio carries the lowest re-investment risk in the portfolio which is considered to be ideal for the immunization.
This implies that a portfolio comprising of zero value coupons maturing after a particular period has the advantage of zero re-investment risk.
If cash flows are accruing around or close to date of maturity, that is considered to be also having a low immunization case, since the coverage is high due to no re-investment in early part of the duration of portfolio/ bond.
However, for bonds where cash flows accrue frequently from an early date, changes in interest rates could aversely impact the immunization and should be last option. The risk in such cases is higher than other cases discussed.