Tag Archive | "Ryan Hartman"

Staying Ahead of the Earnings Curve: Alternative Methods of Examining VSC Experience


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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Earnings Curves: Matching Premium with Losses…and Refunds?


With vehicle service contracts (VSCs) extending coverage over multiple years and premiums collected at the beginning of the contract, it is extremely important to have a benchmark to assess the profitability of the contracts that have been issued. Recognizing profitability (or lack thereof) early in the life of the contracts will assist a company in making sound financial decisions and can help keep profitability or adverse selection problems from getting worse. This article will assist readers in understanding the importance of earnings curves and the careful consideration that should be involved in deciding how to recognize revenue over the life of a service contract. We will focus on VSCs but the methodology could extend to other types of service contracts or long durational contracts where the exposure to loss may vary throughout the term of the contract.

Current Approaches

Earnings curves provide a company with the percentage of premium that should be recognized as revenue at each point throughout the life of a VSC in order to appropriately match revenue with expected VSC liabilities. Simplistic approaches commonly used, especially for financial reporting purposes, are Pro Rata, Rule of 78s and Reverse Rule of 78s. Pro Rata earns premium evenly over the life of a contract, which assumes that losses are expected to occur evenly throughout the term of the contract and does not reflect important factors such as the underlying manufacturer’s warranty or that a vehicle may exceed the VSC’s mileage term before it exceeds the time term. The Rule of 78s method of earning premium is commonly used as a benchmark when losses are expected to be weighted toward the beginning of a contract such as with Used vehicles or Guaranteed Asset Protection (GAP) coverage. The Reverse Rule of 78s is commonly used as a benchmark to earn premium for VSCs on New vehicles where the exposure is weighted toward the end of the contract after the manufacturer’s warranty has expired. In general, these benchmark curves have the benefit of being easy to calculate and understand but rarely provide an accurate expectation of the VSC liabilities throughout the term.

Ideally, earnings curves are based on an individual company’s historical experience and reflect the underlying characteristics of a particular block of contracts. Where credible data is present, earnings curves reflect the expected loss emergence pattern of a certain type of contract. The earnings patterns are typically determined by the company’s actuary based on the loss development factors obtained from actuarial loss development triangles.

Earnings curves typically state the earned percentage of premium for each month of age and vary by vehicle age group (New vs. Extended Eligibility vs. Used) and time term length. Companies with more refined methodologies and credible experience may have earnings curves that vary by a number of other factors including, but not limited to, product type, coverage level, manufacturer’s warranty term, beginning vehicle mileage, term mileage and distribution channel (dealer, internet, telemarketed, etc.).

The standard earned premium calculation in the service contract industry is as follows:

Earned Premium = [Written Premium on non-cancelled contracts * Earned %]

+ Written Premium Net of Refunds on cancelled contracts

where Earned % = 1 / Cumulative Loss Development Factor

The above approach utilizes the expected loss emergence patterns based on historical loss experience. However, the earned premium for cancelled contracts is equal to the retained portion of premium not refunded, which is independent of the selected earnings pattern. This can result in misleading calculated earned loss ratios.

Impact of Cancellations

Upon cancellation, VSCs typically refund the Pro Rata unearned premium based on time or miles, whichever is less. VSCs purchased on new vehicles have significantly lower exposure to loss during the manufacturer’s warranty and losses tend to be weighted toward the end of the contract. Therefore, upon cancellation, a New VSC may experience a significant increase in earned premium. Conversely, for used vehicles, where losses are weighted toward the beginning of a contract, the VSC may experience a significant decrease in earned premium upon cancellation. In other words, the change in earned premium due to the cancellation is negative. As the gap between the refund provision and the loss emergence pattern grows, so does the impact to earned premium at the time of cancellation.

As a result, the application of earnings factors developed solely on loss emergence patterns to premium amounts will likely produce inconsistent earned loss ratios throughout terms of the contracts, i.e., the ultimate profit will not be recognized in proportion to exposure over the terms of the contracts. Assuming the loss emergence pattern was known, using the known loss emergence pattern to earn premium will still lead to increasing loss ratios over the contract terms for Used VSCs and decreasing loss ratios over the contract terms for New VSCs as the loss and refund emergence patters ultimately converge.

To properly assess profitability, the company’s actuary must not only derive earnings curves from the loss emergence patterns but also project refund patterns to properly adjust those earnings curves to yield more accurate and more stable loss ratios.

The following graph provides an example of the impact cancellations can have on the earned loss ratio for a block of used, three year term, telemarketed VSCs evaluated at each 3 month interval.

*Note the amounts provided in the graph above were developed for illustrative purposes only and should not be relied upon.

In the example above, the earned loss ratio (utilizing an earnings curve based on loss emergence only) increases from 45% to 80% over the life of the contracts. Since the earned loss ratio increases over time, the implication is that the earnings pattern is too “fast” or too much premium was earned early in the contract term. Based on the loss and refund emergence patterns underlying this projection, an adjusted earnings curve can be derived which produces much more stable loss ratios. This adjusted earnings curve is applied to the active contracts only, just as in the formula previously stated. The effect of this adjusted curve is illustrated in the following graph:

*Note the amounts provided in the graph above were developed for illustrative purposes only and should not be relied upon.

Under both scenarios the loss emergence (green line) and earned premium associated with cancelled contracts (blue bars) are the same. The only difference is the amount of premium that is earned on active contracts (red bars) at each point in time and the resulting earned loss ratios. Since the adjusted earnings pattern accounts for both losses and cancellations, the projected earned loss ratio remains stable at 80% over the life of the contracts.

The earnings patterns utilized under both approaches are shown in the next graph. By slowing down the earnings on the active contracts, we have offset the effect that cancellations have on the earned loss ratios. As the cancellation rate increases, as is the case for direct marketed VSCs compared to dealer issued VSCs, so too will the discrepancy between an earnings curve based on loss emergence only and one which incorporates the expected refunds.

*Note the amounts provided in the graph above were developed for illustrative purposes only and should not be relied upon.

The above example represents a scenario where refunded amounts exceeded the unearned premium on cancelled contracts. A converse scenario could be imagined where refunded amounts are less than the unearned premium on cancelled contracts and a similar methodology for adjusting the earnings patterns could be utilized.

Maintenance and Monitoring

Loss and refund emergence, and therefore earnings curves, are influenced by many factors including manufacturer’s warranty terms, driving habits, economic conditions, vehicle quality, etc. 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 an analyzed segment is changing. Because of this, maintenance of the earnings curves and monitoring of the loss and refund emergence patterns by the company’s actuary is required. An annual actuarial review should include an evaluation of trends in the loss and cancellation patterns and as a result, the actuary can recommend modifications to the earnings curves in an effort to achieve an appropriate balance of credibility and homogeneity.

As a final note, adjusting your earnings methodology to incorporate refunds may not produce consistent earned, ultimate and future loss ratios in the aggregate for an entire book of business. The overall earned loss ratio is driven more by shorter term business and the future loss ratio is driven more by longer term business. To the extent that differences in profitability levels exist between shorter versus longer term contracts or between issue years, the earned, ultimate and future loss ratios will likely differ.

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