Convexity in Immunization

There’s a question which states that the duration of the assets and liabilities in a classical immunization strategy are the same, but the convexity of assets is greater than convexity of liabilities. There is a 75 bp parallel upward shift in interest rates.

Wouldn’t this mean the economic surplus of the plan is reduced, since the assets have higher convexity and thus will react more negatively to an upward shift in interest rates than liabilities?

The answer says the opposite ie. economic surplus increases because lower convexity liabilities decline in value more than the assets.

Help please.

As far as I’m aware, convexity has a positive relationship with interest rates. Therefore if rates increase this allows the asset to decrease by less than liabilities. Due to the positive convexity contribution.

We learned for level 2 or so that the loss when interest rates increase is duration minus convexity. So you loose less on your bonds if you have a higher convexity.

thanks!! I finally get it!!!

Negative convexity happens when a callable security ( like MBS ) has a high probability of being called back during periods of low interest rates.

In this case, the convexity is positive since interest rates went higher and hence the MBS will not be called back/prepaid. Hence Net A - L values will be positive.

PS - just my approach to the answer.