Using historical data to justify BI investments – Part II

May 15, 2011
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The earliest recorded surd

The earliest recorded surd

This article is the second in what has now expanded from a two-part series to a three-part one. This started with Using historical data to justify BI investments – Part I and will finish with the yet-to-be-published Using historical data to justify BI investments – Part III (once again exhibiting my talent for selecting buzzy blog post titles).
 
Introduction and some belated acknowledgements

The intent of these three pieces is to present a fairly simple technique by which existing, historical data can be used to provide one element of the justification for a Business Intelligence / Data Warehousing programme. Although the specific example I will cover applies to Insurance (and indeed I spent much of the previous, introductory segment discussing some Insurance-specific concepts which are referred to below), my hope is that readers from other sectors (or whose work crosses multiple sectors) will be able to gain something from what I write. My learnings from this period of my career have certainly informed my subsequent work and I will touch on more general issues in the third and final section.

This second piece will focus on the actual insurance example. The third will relate the example to justifying BI/DW programmes and, as mentioned above, also consider the area more generally.

Before starting on this second instalment in earnest, I wanted to pause and mention a couple of things. At the beginning of the last article, I referenced one reason for me choosing to put fingertip to keyboard now, namely me briefly referring to my work in this area in my interview with Microsoft’s Bruno Aziza (@brunoaziza). There were a couple of other drivers, which I feel rather remiss to have not mentioned earlier.

First, James Taylor (@jamet123) recently published his own series of articles about the use of BI in Insurance. I have browsed these and fully intend to go back and read them more carefully in the near future. I respect James and his thoughts brought some of my own Insurance experiences to the fore of my mind.

Second, I recently posted some reflections on my presentation at the IRM MDM / Data Governance seminar. These focussed on one issue that was highlighted in the post-presentation discussion. The approach to justifying BI/DW investments that I will outline shortly also came up during these conversations and this fact provided additional impetus for me to share my ideas more widely.
 
 
Winners and losers

Before him all the nations will be gathered, and he will separate them one from another, as a shepherd separates the sheep from the goats

The main concept that I will look to explain is based on dividing sheep from goats. The idea is to look at a set of policies that make up a book of insurance business and determine whether there is some simple factor that can be used to predict their performance and split them into good and bad segments.

In order to do this, it is necessary to select policies that have the following characteristics:

  1. Having been continuously renewed so that they at least cover a contiguous five-year period (policies that have been “in force” for five years in Insurance parlance).

     

    The reason for this is that we are going to divide this five-year term into two pieces (the first three and the final two years) and treat these differently.

  2. Ideally with the above mentioned five-year period terminating in the most recent complete year – at the time of writing 2010.

    This is so that the associated loss ratios better reflect current market conditions.

  3. Being short-tail policies.

    I explained this concept last time round. Short-tail policies (or lines or business) are ones in which any claims are highly likely to be reported as soon as they occur (for example property or accident insurance).

    These policies tend to have a low contribution from IBNR (again see the previous piece for a definition). In practice this means that we can use the simplest of the Insurance ratios, paid loss-ratio (i.e. simply Claims divided by Premium), with some confidence that it will capture most of the losses that will be attached to the policy, even if we are talking about say 2010.

    Another way of looking at this is that (borrowing an idea discussed last time round) for this type of policy the Underwriting Year and Calendar Year treatments are closer than in areas where claims may be reported many years after the policy was in force.

Before proceeding further, it perhaps helps to make things more concrete. To achieve this, you can download a spreadsheet containing a sample set of Insurance policies, together with their premiums and losses over a five-year period from 2006 to 2010 by clicking here (this is in Office 97-2003 format – if you would prefer, there is also a PDF version available here). Hopefully you will be able to follow my logic from the text alone, but the figures may help.

A few comments about the spreadsheet. First these are entirely fabricated policies and are not even loosely based on any data set that I have worked with before. Second I have also adopted a number of simplifications:

  1. There are only 50 policies, normally many thousand would be examined.
  2. Each policy has the same annual premium – £10,000 (I am British!) – and this premium does not change over the five years being considered. In reality these would vary immensely according to changes in cover and the insurer’s pricing strategy.
  3. I have entirely omitted dates. In practice not every policy will fit neatly into a year and account will normally need to be taken of this fact.
  4. Given that this is a fabricated dataset, the claims activity has not been generated randomly. Instead I have simply selected values (though I did perform a retrospective sense check as to their distribution). While this example is not meant to 100% reflect reality, there is an intentional bias in the figures; one that I will come back to later.

The sheet also calculates the policy paid loss ratio for each year and figures for the whole portfolio appear at the bottom. While the in-year performance of any particular policy can gyrate considerably, it may be seen from the aggregate figures that overall performance of this rather small book of business is relatively consistent:

YearPaid Loss Ratio
200653%
200759%
200854%
200953%
201054%
Total54%

Above I mentioned looking at the five years in two parts. At least metaphorically we are going to use our right hand t cover the results from years 2009 and 2010 and focus on the first three years on the left. Later – after we have established a hypothesis based on 2006 to 2008 results – we can lift our hand and check how we did against the “real” figures.

For the purposes of this illustration, I want to choose a rather mechanistic way to differentiate business that has performed well and badly. In doing this I have to remember that a policy may have a single major loss one year and then run free of losses for the next 20. If I was simply to say any policy with a large loss is bad, I am potentially drastically and unnecessarily culling my book (and also closing the stable door after the horse has bolted). Instead we need to develop a rule that takes this into account.

In thinking about overall profitability, while we have greatly reduced the impact of both reported but unpaid claims and IBNR by virtue of picking a short-tail business, it might be prudent to make say a 5% allowance for these. If we also assume an expense ratio of 35%, then we have a total of non-underwriting-related outgoings of 40%. This means that we can afford to have a paid loss ratio of up to 60% (100% – 40%) and still turn a profit.

Using this insight, my simple rule is as follows:

A policy will be tagged as “bad” if two things occur:

 

  1. The overall three-year loss ratio is in excess of 60%

     

    i.e. is has been unprofitable over this period; and

  2. The loss ratio is in excess of 20% in at least two of the three years

    i.e. there is a sustained element to the poor performance and not just the one-off bad luck that can hit the best underwritten of policies

This rule roughly splits the book 75 / 25; with 74% of policies being good. Other choices of parameters may result in other splits and it would be advisable spending a little time optimising things. Perhaps 26% of policies being flagged as bad is too aggressive for example (though this rather depends on what you do about them – see below). However in the simpler world of this example, I’ll press on to the next stage with my first pick.

The ultimate sense of perspective

Well all we have done so far is to tag policies that have performed badly – in the parlance of Analytics zealots we are being backward-looking. Now it is time to lift our hand on 2009 to 2010 and try to be forward-looking. While these figures are obviously also backward looking (the day that someone comes up with future data I will eat my hat), from the frame of reference of our experimental perspective (sitting at the close of 2008), they can be thought of as “the future back then”. We will use the actual performance of the policies in 2009 – 2010 to validate our choice of good and bad that was based on 2006 – 2008 results.

Overall the 50 policies had a loss ratio of 54% in 2009 – 2010. However those flagged as bad in our above exercise had a subsequent loss ratio of 92%. Those flagged as good had a subsequent loss ratio of 40%. The latter is a 14 point improvement on the overall performance of the book.

So we can say with some certainly that our rule, though simplistic, has produced some interesting results. The third part of this series will focus more closely on why this has worked. For now, let’s consider what actions the split we have established could drive.
 
 
What to do with the bad?

You shall be taken to the place from whence you came...

We were ruing a 54% paid ratio in 2009-2010. Using the same assumptions as above, this might have equated to a 94% combined ratio. Our book of business had an annual premium of £0.5m so we received £1m over the two years. The 94% combined would have implied making a £60k profit if we had done nothing different. So what might have happened if we had done something?

There are a number of options. The most radical of these would have been to not renew any of the bad policies; to have carried out a cull. Let us consider what would have been the impact of such an approach. Well our book of business would have shrunk to £740k over the two years at a combined of 40% (the ratio of the good book) + 40% (other outgoing) = 80%, which implies a profit of £148k, up £88k. However there are reasons why we might not have wanted to so drastically shrink our business. A smaller pot of money for investment purposes might have been one. Also we might have had customers with policies in both the good and bad segments and it might have been tricky to cancel the bad while retaining the good. And so on…

Another option would have been to have refined our rule to catch fewer policies. Inevitably, however, this would have reduced the positive impact on profits.

At the other extreme, we might have chosen to take less drastic action relating to the bad policies. This could have included increasing the premium we charged (which of course could also have resulted in us losing the business but via the insured’s choice), raising the deductible payable on any losses, or looking to work with insureds to put in place better risk management processes. Let’s be conservative and say that if the bad book was running at 92% and the overall book at 54% then perhaps it would have been feasible to improve the bad book’s performance to a neutral figure of say 60% (implying a break-even combined of 100%). This would have enabled the insurance organisation to maintain its investment base, to have not lost good business as a result of culling related bad and to have preserved the profit increase generated by the cull.

In practice of course it is likely that some sort of mixed approach would have been taken. The general point is that we have been able to come up with a simple strategy to separate good and bad business and then been able to validate how accurate our choices were. If, in the future, we possessed similar information, then there is ample scope for better decisions to be taken, with potentially positive impact on profits.
 
Next time…

In the final part of what is now a trilogy, I will look more deeply at what we have learnt from the above example, tie these learnings into how to pitch a BI/DW programme in Insurance and make some more general observations.