I agree the “portfolio optimisation good” is just not there in the book. To account for this you presumably need to get into individual utility maximisation, which would not lead to either loss coverage or coverage as a criterion. I’m not very enthusiastic about utility maximisation as a basis for public policy because the necessary assumptions (about utility functions) seem unknowable, but yes that is more the way an economist might think about it.

On further reflection I’m not discouraged by your p = 0.75 example, for which my interpretation is: to “break” the construct of loss coverage, you have to extrematise so far that you “break” the construct of insurance itself (i.e. loss coverage makes little sense at p = 0.75, but nor does insurance itself).

I don’t think that the scenario on Table 3.3 on p46, with severe adverse selection, itself “breaks” the construct of loss coverage. The main point of the book, as per the sub-title, is that insurance works better with SOME adverse selection, not with ANY AMOUNT of adverse selection. On this point, scenarios like Table 3.3 aren’t counter-examples; they just substantiate the word “some”.

Thanks Guy for the response and food for further thought. I assume Google Alerts is part of your toolkit too.

I revisited the sections you highlighted to see whether I missed anything. I have the kindle version so I hope the page numbers are consistent with your references.

• On page 52 where you differentiate between probabilistic and reassurance goods, you don’t, as far as I can tell, take the value of reassurance beyond intangible feel good into real world, hyper relevant for public policy of portfolio optimisation good. (I use your terms, they seem to do the job well and I’m also not aware of generally accepted terms here.)
• On page 54/55:

  Maximising loss coverage is equivalent to maximising premium income. If profit loadings are proportional to premiums, maximising loss coverage could be a desirable objective for insurers. Even from the insurer’s perspective, adverse selection is not always a bad thing! This might help explain why insurers often appear rather slower to make use of every scrap of marginal information for risk classification than economic theory predicts, even when information is observable at zero or at negligible cost and apparently relevant to the risk.

  • It seems optimistic to assume profit is a constant proportion of premiums since profit will often be the result of the balance between selection and anti-selection and the varying self-assessment of risk and risk appetite of prospective policyholders. With limited risk selection, the actual profit margin will depend on the mix of business within the broad risk categories allowed. I suppose this could stabilise at an equilbrium level, although experience of non-underwritten medical insurance coverage in at least two markets I’m aware of shows this to be a major change to prevent spiralling costs and premiums.
  • Further though, given Solvency II (and SAM in South Africa) capital requirements for underwriting risk are broadly going to be proportional to premium volumes, and with modern pricing factoring in the cost of capital and a hurdle rate, the waters are further muddied and possibly in favour of lower premium products from an economic value added perspective.
  • However, I have a simpler explanation for the practical under-utilisation of information by insurers – practical constraints such as quoting engines, desired simplicity for distribution channels, consistency with aggregator requirements, and in some cases, regulatory restrictions on risk selection(!). I think we may have similar thoughts on the complexity of fine-tuned risk ratings providing more opportunities for policyholders to game or exploit imperfections, but I want to do a more thorough post on that another time.
  • On a related note to the annuity post code impact, I read an article in a recent The Actuary magazine evaluating further geographical differences in mortality across England and Scotland. In South Africa, we have very marked differences in mortality across provinces, likely mostly a proxy for other underlying issues. This information isn’t used for non-underwritten products, even though it would be trivial to adjust prices based on distribution branch location. An interesting question has arisen whether this “known but not used” information will require insurers to separate these policies out into different cohorts under IFRS17 and therefore show many more policies as onerous from inception. If so, this might be another push towards more refined pricing, less cross subsidisation and maybe lower loss coverage. If your views are correct, this would be a push in the wrong direction.

I enjoyed engaging with your ideas. I hope my coverage and our discussion here may prompt some more interest from others. If you remember, for your next book, throw another comment in here to let me know and you’ll have at least one repeat customer.

Thanks for your interest in my book. Although you are critical, this is welcome sign that somebody has actually read the book (well some of it, anyway).

Re “reasons for insurers themselves to be wary of selecting too well”:
I do touch on this on page 55, where I note that maximising loss coverage = maximising premium income. So it could be optimal for insurers, if profit loadings are roughly proportional to premiums. Another possibility is that you add more classifications, you may think you are classifying better, when in fact you are just creating more opportunities for customers to game the classifications.

Re “limited view of the value of insurance”:
I do discuss insurance as a “probabilistic good” versus “reassurance good” on pages 52-53. However it is true that apart from that page, the book focuses solely on the probabilistic framing, which I think is the better framing for public policy, for the reasons given on p53. I note that you are arguing for a third concept – insurance as a “portfolio optimisation good” – which is different again. It would be useful to have a commonly agreed terminology around these three concepts (I had to make up the terminology in the book).

Re “should have been a paper”:
Well it was a 2008 paper in the Journal of Risk and Insurance – and several more recent follow-ups – but the trouble is nobody reads them! All the papers are here….

http://www.guythomas.org.uk/genetics/genetics.php

Thanks again for the interest.

Guy Thomas

PS There should be a review in The Actuary next month.