Insurable and Uninsurable Risks

This is a post which isn’t really going to go anywhere, for which apologies in advance. But it’s just that I wanted to comment on this post on Mark Kleiman’s site, on the subject of the position of insurance companies with respect to health problems caused by alcohol. But as I was drafting an email to Mark, I realised that I was going wildly off onto tangents, and it really needed to be a post of my own. Then I had a few more thoughts about the generalisation of the problem of insurable and uninsurable risks, and how it could be used to make a few arguments I’ve been wanting to make anyway with respect to economic reasoning. And then this one came up on Brad DeLong’s site about the equity premium puzzle, which is all about the importance of unisurable shocks if you believe John Quiggin, so it was obviously important to include that, and by now we’re looking at a ten thousand word essay which is always a bit daunting to contemplate …. If you’re wondering how unplanned month-long hiatuses happen, by the way, that’s how they happen. So anyway, I think the best thing to do is to use this post to set out the core concepts of uninsurable risk, and then draw on it in two or three (or, realistically, somewhere between one and none) future posts on the substantial issues.

Basically, “insurability” and its opposite “uninsurability” are vague terms, defined by resemblance to the paradigm case of an insurable risk. A paradigmatically insurable risk is one which is accidental, small and actuarially well-behaved. Taking them in order:

Accidental: This is the category under which the well-known problems of “moral hazard” and “adverse selection” fall. If you’re insuring against an utterly random occurrence (paradigmatically, the weather), then you have no better information than the insurer about the likelihood that the insured event will occur in your case. Because of this, the insurer can quote a price for your risk without worrying about the possibility that he is dealing with someone who is trying to rip him off. As we move along the continuum of accidentalness, we reach motor insurance (where there is an asymmetry of information because you have better information than the insurer about whether you’re a crap driver or not), then professional negligence insurance (where the fact that you’re insured might mean that you take less care than you otherwise would), and finally we reach the provision of fire insurance to a small minority of proprietors of garment warehouses.

(By the way, a good way of testing whether you’re dealing with a sharp economist or not is to ask him whether fire insurance is a cyclical or countercyclical business. If he isn’t sharp, he’ll say that it’s neither; fires aren’t correlated to the business cycle. If he’s a bit more streetwise, he’ll realise that it’s a trick question and that the prevalence of fires in insured premises is actually quite strongly correlated to the degree of recession.)

There are things you can do as an insurer to try to make sure that you’re only exposed to the “accidental” component of the risks that you cover. You can use loss adjustment and claims investigation to cut down on fraud. You can put a hefty excess on your policies to deal with the adverse selection and moral hazard effects. Et cetera, et cetera. But it’s a real problem, and a quick glance at the two-and-eight that medical professional negligence has got into is enough to, is enough to make the hardiest of underwriters spend a while thinking about how much they like earthquakes.

Small: An easy one to understand; it’s not possible to write insurance against some kinds of events because the amount of the potential claim is too big a financial risk for the insurer. This is not a problem which can be solved by pricing the risk, by the way; remember the Alfred Hitchcock argument I used in the discussion of genetic testing. Just as Hitchcock’s hypothetical film about the Titanic could still be suspenseful because people wouldn’t know when it was going to sink, most of the variance of an insurance company’s profit and loss is related to the timing of claims rather than their size. For any realistic level of premium, if the insured event happens a couple of months after the policy is taken out you’re going to make a loss, and if that loss is big, you’re bust.

Note that “small” in this context refers to the risk rather than the event itself. Big hurricanes and earthquakes lead to big losses for the insurance industry, and it’s only through the careful use of reinsurance that it’s possible to manage these risks down to an insurable level. But the insurance industry is not just exposed to the risk of big things happening; things can be just as bad if a lot of small things happen at the same time. For example, if you were an insurer underwriting employers’ liability insurance in the 1950s, you’d probably think you were looking at a pretty insurable class of risks; each individual policy you were writing was pretty small relative to the whole. You wouldn’t have known that every single one of those policies was on a factory fitted with brown asbestos … and you certainly wouldn’t have written a policy for the general risk of asbestos if you’d known what you were doing. Small risks can become big in this way if they have long “tails”; if the liability extends out into the future. Another example of a risk of this sort was the guaranteed annuity issue that toppled the Equitable Life in the UK (basically, they’d implicitly written insurance against falling interest rates to a lot of policyholders). Each individual risk was small, but they were all related to a common factor, so the outcome was that Equitable was writing a much bigger single risk than would have been prudent given its capital base.

Actuarially well-behaved: Basically the requirement that it be possible for an actuary to say, with a degree of confidence which reflects his professional status, that he has determined both a premium at which the insurer can expect to write this business profitably in the long run and an amount of capital to be held against the insurance written which will provide reasonable confidence that the insurer will be able to meet claims. A risk which is paradigmatically “actuarially well-behaved” is one where there is a lot of data on past experiences of claims and where that data has the property that it can be fitted to a (possibly multivariate) probability distribution, and that this probability distribution remains stable over time. If you’re lucky enough to be writing insurance on deaths from horse kicks (the data which Poisson was investigating when he discovered the distribution that bears his name), then because you know that these events have a Poisson distribution over time, and you’ve got enough data to fit the parameters of that distribution (mean and moments), which will give you a clear picture of exactly what your risk of ruin is, at any given level of premium. If you’re dealing with subjects on which there is a patchy or inadequate dataset, then there is often a few statistical tricks you can pull (or educated guesses you can make) to quasi-fit a distribution of losses. Even for some kinds of nonergodic data (basically, those described by power laws), you can find actuaries who will go out on a limb and price a policy, even in the absence of a well-defined measure of central tendency and dispersion. But for some things (for example, the success or failure of a business and other “speculative” risks), the actuarial ill-behaviour of the data is bad enough to make it more or less impossible to write insurance.

More to come in this direction … in the meantime, an interesting factoid, backing up a few claims I made in the earlier “genetic discrimination” post (I was arguing that since timing is a much more important source of risk than probability, genetic discrimination in insurance premia would not have the effects many pundits have prophesied for it). Even given what we know about the relative importance of smoking habits, heredity, lifestyle and all the other questions you’re asked on forms, 95% of all UK life assurance policies are written on standard terms.


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