Coherent Capital Allocation

[td290]

Sorry, me again. Come back to have another rant about the "Incorporation of cost of return on capital calculations" chapter. Amongst the properties we are told a coherent allocation method should have is Symmetry:

If the risk of two sub-portfolios is the same (as measured by the risk measure), the allocation should be the same for each.

This is ludicrous! If, for example, our portfolio consists of three sub-portfolios, A, B and C, all with the same stand-alone risk but with A and B perfectly correlated and C completely independent of the other two, should we really be required to allocate the same amount of capital to each sub-portfolio? Honestly, who writes this stuff?!

The definition used by seemingly all other credible authors is far subtler an can be found in sources such as Denault, M. (2001) Coherent Allocation of Risk Capital (see http://www.risklab.ch/ftp/papers/CoherentAllocation.pdf).

 

[td290]

Apologies for the somewhat intemperate tone of my previous post. For what it’s worth, I’ve now found the source that the definition in the Core Reading (an much of the rest of the chapter) was almost certainly taken from, namely the following paper by Paul Kaye: http://www.casact.org/pubs/dpp/dpp05/05dpp1.pdf. Interestingly though, this paper incorrectly claims to be using the definitions from the Denault paper I mention above.

It’s this kind of thing causes so many actuarial terms to have several different definitions. We start off with one generally accepted definition that somebody paraphrases carelessly, altering it subtly in the process. Several others then copy the paraphrased definition without verifying it. Confusion ensues.

In this case, Denault’s definitions are clearly preferable since many widely accepted results, some of which are even quoted in Kaye’s paper (e.g. coherence of Aumann-Shapley allocation used with TCE), depend on us accepting them. Please could the Profession and ActEd will give careful consideration to this when preparing the 2013 study materials?

 

[td290]

One other thing: on page 24 of Chapter 7, the ActEd write-around wrongly states that 2^n is being used as an approximation for n! See Definition 9 of the Denault paper for an explanation of why this is. I’ve reproduced the links to both papers below since one of them seems to be broken in the original post.

Denault, M. Coherent Allocation of Risk Capital http://www.risklab.ch/ftp/papers/CoherentAllocation.pdf
Kaye, P. Risk Measurement in Insurance http://www.casact.org/pubs/dpp/dpp05/05dpp1.pdf

 

[Ian Senator]

Hi td290

Thanks very much for pointing out these problems with this chapter. It certainly looks as if 'chinese whispers' have been a culprit when the Core Reading was put together (lots of Core Reading has been based on the CAS material for this subject). We'll discuss these points with the Profession and arrange for corrections and/or explanations to be made where necessary (although the 2013 material is already finalised now, so it may appear as a correction on our website for this year, and then get incorporated into the material for 2014, so please bear with us).

There is one bit of good news: the examiners have never examined anything from this chapter......yet!!!

Best of luck for the exam, don't dwell on all the maths for too long!

Ian