CFA Mock Exam Question 8D

[mp11932]

After further consideration, Bergen decides to maintain the classical immunization strategy. He
also decides to perform a scenario analysis that includes one scenario in which the yield curve
shifts upward in a parallel move by 75 basis points. During the analysis, Bergen notes that the
durations of the assets and liabilities remain matched but the convexity of the assets remains
greater than the convexity of the liabilities.

-Since the liabilities have a smaller convexity, why would the decline in value be greater for the liabilities?

 

[pokhim]

If you draw the assets and liabiltities convexity curve, you will see that liablilities fall faster than assets

 

[derswap07]

care to elaborate?

 

[whatsyourgovt]

basic convexity, for time purposes consider convexity a good thing for bond holders (relatively speaking that is). If rates fall, the bonds with higher convexity will increase more. If rates rise, the bonds with the higher convexity will decline less.

 

[Enemyofmyenemy]

Rate | L a(2)
| L a
| L a
| *(1)
| L a
| L a
| L a
_ _ _ _ _ _ _ _ _ _ _ _ _ _
Value

 

[Enemyofmyenemy]

Its a crude graph, but basically
a : represent assets
L: represent liabilities
Since assets are more convex, this implies that that the asset line (the ‘a’s’ above) are more curved (away from the axis). If we assume that at point ‘*(1)’ that assets = liabilites, we can see that when rates are moved up (2) that the ‘L’ is worth less than the ‘a’.
Make sense?