Liability Driven and Index Based Strategies , effects of yield curve changes. The notes uses 2 sets of scenarios to demonstrate barbell strategies. Scenario one is a parallel shift of the curve, where the barbell strategy will benefit from structural risk due to positive convexity + unchanged IRR relative to liability; Scenario two demonstrate in a nonparallel reshape, portfolio could negatively exposure to structural risk due to uncertainty in change of IRR. Here is where i get lost. Why the change in portfolio IRR is the same with change in liability IRR in parallel scenario??? i did not do any match proveouts, but from a practical perspective it is difficult to understand…can someone share their insights ?