CFAI Mock 2018 PM Q35

Shouldn’t this be in reference to a liability? I mean, the convexity aspect, its so arbitrary to just choose a portfolio with lowest convexity. I thought we should have had the convexity for the liability also?

It is in reference to a liability (the $2.3mm payable in 6.5 years)… and the assumption is that the liability is a zero-coupon bond (which would have a convexity of zero because all the cash flows come at expiration at the desired amount). Therefore to eliminate dispersion around this zero coupon liability you want an asset with the lowest convexity.

Damn. Thanks, man

Single liability is always lowest convexity with matching duration. Multiple liabilities you want to have slightly higher convexity of assets vs. liabilities.

actually this is false as a zero coupon bonds do have convexity. In fact convexity increases as coupon size decreases.

Yes - you’re right. I was thinking dispersion and convexity were one in the same (which they’re not). Thanks for clarifying.

To be clear, minimizing convexity will help minimize dispersion, and therefore be better when immunizing a single liability. Is this the right way to think about it?