2017 CFA exam morning session question 9. It says one condition that must satisfied to assure multiple liabilities immunization is: the distribution of the durations of individual portfolio assets must have a wider range than the distributions of the liabilities. Is it equivalent to convexity of portfolio must larger than convexity of liabilities?
Yes - higher dispersion = higher convexity
larger convexity for multiple liabilities, lower convexity for a single liability.
Don’t misunderstand this.
You need more dispersion for multiple liabilities because you want at least one bond with a maturity no longer than the maturity of your shortest liability, and at least one bond with a maturity no shorter than your longest liability. Having met those criteria, you still want to minimize the dispersion – and, consequently, minimize the convexity – of the portfolio.
Why is this rule (the rule regarding convexity) inversed for multiple and single liability immunization ?
It isn’t.
Read what I wrote, above.
sorry, i’m not sure I follow. I know that convexity adds structural risk to a portfolio, but to immunise a liability the portfolio should be structured so that:
-
single liabilities - minimise the convexity
-
multiple liabilities - the convexity needs to be greater than that of the liabilities.
is this saying, choose the bond with the lowest convexity for a single liability, and for multiple liabilities choose the portfolio with lowest convexity, subject to the constraint that convexity must be greater than the convexity of the multiple liabilities?
thanks, and sorry for all the confusion
No.
Subject to the constraint that the range of the durations of the bonds used in the portfolio encompasses the range of durations of the liabilities.
Which is the same constraint that you have for a single liability.
I was in agreement with Chris, so I went through the CFAI text on multiple liabilities and was focusing on Example 4. Basically:
-Like Magician suggested, it’s not that convexity of assets needs to be greater than convexity of liabilities. Check out part 2 of example 4. Even though Portfolio C’s convexity matches that of the liabilities, it was not chosen.
-The duration of concern in that example is money duration i.e. BPV
So thanks again Magician for your clarification. Fixed Income is a tough topic indeed!
For a single liability you have to:
-
match Maculay Duration
-
choose the min convexity ( which has a convexity greater than the zero-coupon bond that would provide perfect immunization)
For multiple liabilities when MV of liabilities is different from MV of asset you have to:
-
match BPV
-
and then choose the lowest convexity which satisfies Convexity Assets >= Convexity liabilities
This is also said in the bluebox you are referring to, you have to proceed in the correct order, first select the similar BPV and then between them choose the best convexity…
So you can see that the only difference between single and multiple liabilities is the MacDuration and the BPV, then the concept about convexity is the same.