# Flood Risk in the U.K.: What Does Mr. Market Think? (Part 2 An Actuary’s Nightmare)

In my previous post, I noted that strange things were happening in the flood insurance market. In short, the insurance industry no longer wants to extend the status quo (here):

The current agreement under which insurers continue to offer flood insurance to their existing customers will expire on 30 June 2013. The insurance industry has proposed a new a scheme to ensure customers can still buy affordable flood insurance, after this date. We are currently in talks with the Government about taking this forward.

In truth, they want to move some flood risk from one actor in the market to another. But before I look at that issue, I want to ask the question “why do they want to change the status quo?”

To do this, we need to take a quick detour through the theory of insurance. There is a nice little eight-minute youtube video that explains the theory of insurance here:

The core message in the video is the same as the core message of this blog: risk is the probability of an event times the cost of the event. When we buy insurance, we generally are buying insurance for a low probability, high cost event. A horrible spiky risk; so if you are unlucky on the roulette table of life, a single event can rampage through your finances. But an insurer, by pooling hundreds of thousands of such single spiky risks, can make them smooth and well behaved.

As the video above notes, the insurer’s friend is the actuary, whose job is to calculate how those single spiky events look like when pooled together. If you like maths, then I highly recommend this short paper on Risk and Insurance published by the Education and Examination Committee of the U.S. Society of Actuaries (SOA). It takes the video above up a few levels.

Just to repeat, risk has two components. SOA calls these frequency and severity.

This random variable for the number of losses is commonly referred to as the frequency of loss and its probability distribution is called the frequency distribution……..The second random variable is the amount of the loss, given that a loss has occurred. The amount of loss is often referred to as the severity and the probability distribution for the amount of loss is called the severity distribution. By combining the frequency distribution with the severity distribution we can determine the overall loss distribution.

So the insurer is going to call in an actuary and ask two key questions: if I insure a bunch of homes for flood, how often are they going to get hit by floods, and when they are hit, how much will it cost? So how does an actuary answer these two questions? The first thing they will do is look at their database of past events. This will give them a first cut at the ‘frequency distribution’ (how often flood comes) and the  ‘severity distribution’ (how much flood costs).

As a blogger, I absolutely loath those bloggers who use full caps to put a point across. It seems shrill and crass to me. But today is an exception. The holy grail of every actuary are frequency and severity distributions THAT ARE STABLE. If the distributions are stable, you can use the past to tell you things about the future.

So back to the Environment Agency and the National Flood Risk Assessment (NaFRA). Note that NaFRA is a frequency distribution; it doesn’t say anything about the severity distribution. Is the frequency distribution as published by NaFRA stable? Unfortunately, no. Between each update of the NaFRA, homes move between the various risk categories, with the progression being from lower risk to higher risk. Moreover, as I noted in my previous post, the Environment Agency is not incorporating climate change into its risk assessment. So if you could ask them what your flood risk is currently, they will tell you what is was yesterday, not what it will be tomorrow.

Let’s now revisit some slides from Professor Arnell’s presentation that I talked about in my first post. These tell us that climate chance is, implicitly, going to move the frequency and severity distribution in future years.

As one of Arnell’s previous slides highlighted (in my previous post), you can get floods either through intense events or chronic events. So remember these are percent changes. Just because we have dry summers doesn’t mean we can’t get inundated in winter. So this says that the hoped-for-stable frequency distribution of the actuary will wonder around. But it gets a lot worse.

For a start, this is a ‘plausible scenario’. An actuary could just about stomach a frequency distribution moving from one stable state to another, but this is not what is happening. Professor Arnell has some other slides, which are what I would call ‘snap shots of climate change theory work in progress’. They show a jet stream that has become increasingly unstable:

And atmospheric rivers challenging moist air from one region to another:

This is climate change theory being put together in real time. For example, it was only in 2007 that Arctic sea ice extent drastically diverged from its expected path, in the process putting large swathes of sea into an ice free state at certain times of  the year. And it is only recently, that attention has focussed on instability of the jet stream, with a flurry of academic papers linking this to the warming of the Arctic.

That is at the macro level. At the micro level, Professor Arnell’s presentation brought home to me the sheer variability of flood risk at particular localities. The village of Pangbourne has a variety of catchments that all have different characteristics. Accordingly, slightly different permutations of rainfall intensity and perseverance in slightly different localities can give rise to very different flooding outcomes. The actuary really doesn’t like this. They want independent and identical random variables for the efficient modelling of risk. If they don’t get them, their overall loss distribution stretches out with big, fat risk tails. The type of tail that produced the £3 billion plus loss in 2007. And what to do in this situation? Easy: Cut that tail off. Don’t insure Mr. Angry of Pangbourne who we met at the beginning on my first post on the topic.

So what to do in this insurance game? Well, first recognise the asymmetry of information. The insurance companies are currently recognising that they don’t know the future shape of risk (and they don’t like it)—that is why they are so keen on passing the risk over to the government. By contrast, most home owners haven’t the faintest clue that they don’t know the unknowns.

In my next post, I want to drill down a little into that asymmetry of information between insurers and home owners, and how the insurance industry wants to change the rules.