One of the most common metrics utilized in evaluating the profitably of a book of vehicle service contract (VSC) business is the earned loss ratio, calculated by dividing the current cumulative losses paid or incurred by the earned premium-to-date. Earnings curves help a company appropriately match revenue with expected VSC liabilities by providing the percentage of premium that should be recognized as revenue at each point throughout the life of a VSC.

In our previous article, we examined the impact of cancellations and refunds on earned premium and we recommended an alternative approach to developing earnings curves which incorporate the impact of cancellations in an effort to produce stable earned loss ratios throughout the terms of the VSCs. However, as we noted, there is likely constant shifting in the mix of business underlying a given earnings curve, i.e., the distribution of loss and refund dependent variables within the applicable segment is changing from one year to the next. Because of this, maintenance of the earnings curves and monitoring of the loss and refund emergence patterns by the company’s actuary is required.

In this article, we will review a method of testing the appropriateness of the utilized earnings curves. First, however, we will examine various methods to review the experience which are entirely independent of the earnings methodology.

### Written Loss Ratio Development

Developing the optimal set of earnings curves is no easy task. Inappropriate earnings curves distort earned loss ratios and can mask problem areas of the VSC book. In addition, earned loss ratios for the most recent contract years can be highly leveraged resulting from few expected claims and a relatively smaller percentage of the premium earned. But what if we could examine the experience while removing the reliance on the earnings curves all together? One way we can do this is to observe the development of the *written* loss ratio, that is, the ratio of cumulative losses to net written premium as the book matures, as displayed in the following graph:

*Note the amounts provided in the graph above were developed for illustrative purposes only and do not represent actual results.

The above graph provides a comparison of cumulative *written* loss ratio development for each contract posted year as of each calendar month-end. As expected, each curve varies in length and increases from inception of the contract year until all contracts expire. For example, the 2011 curve extends to 48 months of age (12/31/2014), while the 2014 curve extends to only 12 months of age. Assuming each contract year performed identically, the curves would be on top of one another. However, we can see that each year is quite different. For example, the 2012 year (green line) has grown to a 61.3% loss ratio as of 36 months whereas the 2011 year (red line) had a 53.4% loss ratio as of the same age. This may be an indication that the 2012 year will ultimately have a loss ratio significantly higher than the 2011 year. In addition, the 2013 (orange line) and 2014 (blue line) years have significantly higher loss ratios than previous years at the same age, but why?

When building and examining this type of graph, it is desirable to achieve an appropriate balance of credibility (data volume) and homogeneity (similar characteristics across the years). At some point, as we filter the data down to a smaller segment of the overall book, homogeneity may increase, but we will have lost too much credibility to rely on the results. So we must try to find the delicate balance between the two.

The smoothness (or lack thereof) of the lines will give a quick indication of the volume of data behind the graph. Regarding homogeneity, one must be mindful of the underlying mix of business across the years. For example, if all term lengths are aggregated and we know that the more recent contract years have a significantly higher percentage of shorter term business, this type of graph may show the more recent contract years performing worse than older years at the same relative points in time. However, this conclusion may be the result of a misinterpretation.

Since the average term of the more recent years is shorter, the loss ratios will develop to their ultimate values faster and will initially appear less profitable than prior years. To help avoid misinterpretation of the results due to shifts in the underlying mix of business, we must compare year-over-year results by filtering to a level of sufficient homogeneity. However, if we were not aware of shifts in the VSC book toward shorter term contracts, this graph may help uncover the shift and we can now drill deeper into the data and review each term separately.

Reviewing at this more granular level may then uncover another trend across the years and a mix shift of another variable. We may never uncover all underlying mix shifts, possibly due to the capture of insufficient variables or lack of credibility at a sufficiently granular level, but understanding the shifts and results at a granular level will help us explain trends at a more aggregated level.

### Building the Graph

As discussed earlier, the graph of cumulative written loss ratio development is built by using purely raw data and is not dependent on any earnings curves. We can break it down into its components of loss development (numerator) and net written premium development (denominator).

*Note the amounts provided in the graph above were developed for illustrative purposes only and do not represent actual results.

The above graph shows how the cumulative net written premium for each contract posted year has developed as of each calendar month-end. Each year’s curve rapidly increases through 12 months of age as additional new business is written. After the peak at 12 months, the negative development is due to premium refunds on canceled contracts.

*Note the amounts provided in the graph above were developed for illustrative purposes only and do not represent actual results.

The above graph shows how the cumulative paid losses for each contract posted year have developed as of each calendar month-end.

The first step to building premium and loss development graphs is capturing the data. At a bare minimum, we need the appropriate dates (contract posted date, cancelation posted date and the claim payment date) and the appropriate measures (original written premium, premium refunded and claim amount paid). Contract and cancelation posted dates are typically used to be more consistent with the accounting aspect of the contract and will freeze each data point into the future. The contract purchase/effective date, cancellation reported date and claim reported date could be used, but the points of each line — especially the end points — may change when the graph is refreshed in the next period due to posting and payment lags.

You may be asking, “Do we need a data warehouse that captures a snapshot of our entire database at each calendar month-end?” The answer is ”No.” These graphs can be built with your current inception-to-date database. Without going into the details, all it takes is some creative arranging of your data, some fairly sophisticated database programming and data visualization software. (Tableau is used here.) This can be done utilizing Excel, but data visualization software will make these graphs much easier to build and refresh. Additionally, data visualization software can help you quickly dive into the data to identify unusual data points and understand the origin of trends. This type of analysis can be built one time and requires little maintenance on a regular basis.

### Development of Other Measures

Since loss ratios are dependent on premium levels, varying premium levels may cause differences in written loss ratio development curves even if the mix of business and loss levels were identical across all years. However, we can remove the impact of changing premium levels by building development graphs on other measures that are independent of premium such as claim frequency (claim count per contract) and loss costs (losses per contract). Similarly, we can evaluate cancellation activity by graphing cancellation frequency percentage of contracts cancelled per original contract) and refund ratio (percentage of premium refunded per original premium).

### Earned Loss Ratio Distortion

So how distorted are the earned loss ratios? Unfortunately, we can really only test this in hindsight since no contract year’s business is created equal. However, as long as mix shifting is gradual, we can get a reasonable idea of the appropriateness of the current earnings curves by observing the *earned* loss ratio development as displayed in the following graph:

*Note the amounts provided in the graph above were developed for illustrative purposes only and do not represent actual results. Amounts in this graph are not consistent with amounts in previous graphs.

The above graph shows how the cumulative *earned* loss ratio for each contract year has grown as of each calendar month-end. In a perfect world, the earned loss ratio for a given contract year would be the same at 12 months of age as at 120 months of age. However, even if perfect earnings curves were used for all segments, any difference in profitability between shorter and longer term contracts will result in an increasing or decreasing earned loss ratio as the contract year matures. So once again, homogeneity and the mix of business must be considered not only when comparing one contract year to the next, but also when examining the development of a given contract year. In general, to appropriately examine the earned loss ratio development of a given contract year we must filter the data to a level that we believe will not lead to misinterpretation due to differences in profitability among the rating variables — especially term length.

Utilizing graphs of earned loss ratio development can assist in further refining the earnings curves, but building these graphs takes sophisticated database programming and substantial computing power and space. Do you need a data warehouse that captures a snapshot of the entire database at each calendar month-end to build earned loss ratio development graphs? The answer is still ”No.” The current inception-to-date database can be used. However, since we need the earned premium for each month-end, we need to build a table with a separate record for each month in the life of each contract. Said differently, a 36-month contract occupying a single record in your database would need to be expanded into 36 records in this table. For a database with hundreds of thousands of contracts, populating a table with tens of millions of records to build the above graph could easily require tens of gigabytes of space.

### Conclusions

The graphs presented in this article can help us identify problem areas early, compare contract years without the distortion of earnings patterns, identify shifts in the mix of business, break down the experience into its components and help us make sense of the earned loss ratios.

Are these perfect tools? No. All methods of evaluating experience have strengths and weaknesses, but there are other useful tools to monitor experience without the dependence on or distortion of earnings curves. There are many variables driving loss and premium development, only some of which can be captured in the data and possibly used as rating variables.

Being able to explain every difference between point X and point Y is impossible. However, in our experience, these development graphs are helpful in showing that something has changed and provide some indication of the significance of the change. After a difference has been found, the next step is to figure out what has changed and why the results were impacted.

In our next article, we will examine various ways to visualize data in an effort to investigate and quantify the impact and cause of mix shifts and unprofitable outlier segments.

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