Contingent immunization: Explain the effect of the yield curve shift on the economic surplus

"…the yield curve shifts upwards in a parallel move by 75 bps. During the analysis, Bergen notes that durations of assets and liabilities remain matched but convexity of assets is greater than that of the liabilities.

“Explain the effect of the yield curve shift on the economic surplus.”

The answer says that the decline in value of liabilities is greater than the decline in value of the assets, thus increasing economic surplus.

I know that as a Level III candidate I should know what convexity is and its effects, but I cannot find the answer to this question in the CFAI or Schweser books and my brain is kind of fried, so I might need one of those magic S2000magician explanations. Please?

Just remember that convexity is good.

Assets with more convexity will improve the economic surplus whichever way the interest rate goes, all else equal.

Thanks MrSmart. Very smart :slight_smile:

I don’t know if this is the correct way to think about it, but if you think about the slope of a more convex line and follow it upwards, it goes up in value more for incremental yield curve shifts than a less convex line would. Likewise, it goes down in value less for incremental yield shifts versus a less convex line.

Right, a bond with positive convexity will experience less of a decrease in value than suggested by its duration for a given increasse in rates. For an asset (bond) that has greater convexity than a liability, the smaller price decrease will improve the surplus.