Convecuty

[cfahead]

Question 8 D of the 2013 morning session states that the duration of an immunize portfolio remains matched but that the convexity of the assets remains greater than the convexity of the liabilities. Explain the effect of the yeild curve shift on the economic surplus when the yeild curve shifts upwards by 75 basis points. The answer indicates rising surplus. I dont follow the way convexity works here and would appreciate some assistance. Thanks

 

[naren]

Duration is “pessimistic” - if you just use duration and ignore convexity, you will underestimate the rise in value when interest rates fall, and overestimate the fall in value when interest rates rise. Talking about positive convexity here (e.g. option-free bonds and callables far from being called).
Think of a curve that looks very roughly like the southwest corner of a circle, draw in the positive quadrant of X-Y axes. Duration is the slope of the tangent. But the curve goes up on either side.
If assets have greater convexity, their duration is overerstimating their fall in value more than for liabilities, when yields rise.