The Earnings Curve
For vehicle service contracts (VSCs), the earnings curve is a critical tool for financial reporting and experience evaluation. Typically, the earnings curve is a set of factors by month, which show how much of a contract should be earned.
When a company evaluates its financial results at the end of the year, each active contract will be aged from the months since purchase and the premium or reserve for that contract will be multiplied by this factor to calculate the earned reserve. For example, if the reserve on a contract is $400 and it is 12 months since purchase, the system will look up the factor for 12 months. If the factor is 20%, then $80 is earned and $320 is unearned.
It is important to realize that no earnings curve is perfect. It is always an estimate. Only in retrospect, by examining the claim pattern, will the true earnings pattern be known.
In the past, it was common to earn using a formula. Typical formulas were pro-rata (even earnings for each month) for used cars and Reverse-Rule-of-78s for new cars.
In Figure One are examples of various earnings curves. The “Actual Claims” curve is only known at the end of contract.Figure One
|Month||Reverse Rule-of-78s||Pro-Rata||Experience Based||Actual Claims|
The “Reverse Rule-of-78s” method uses a sum-of-the-digits method and the earnings are in proportion to the month. For example, for a 12-month contract in month 3, the earnings would be (1+2+3)/ (1+2+3+4+5+6+7+8+9+10+11+12) or 6/78 or 7.7%. So in month 3, a total of 7.7 percent would be earned.
While this method is easy to implement, it only does a fair job of approximating earnings. It tends to earn too fast early in the contract when there is very little exposure due the manufacturer’s warranty.
At the end of the contract, it earns too slow because many vehicles will “mile out” and expire the coverage before the end of the term. For example, if a contract holder with a 6-year/72,000-mile contract reaches 72,000 miles in year 5, the contract is completely earned at this point.
While many companies still use the Reverse-Rule-of-78s and other formulaic earnings, it is more common to base earnings curves on experience reviews.
In order to use claims experience, one must define curves based on the characteristics of the contract. For example, different terms require different curves. In addition, new, used and program cars will require segmentation. Losses are then examined by month since contract inception. Experience should be smoothed out where little data is observed.
While this type of analysis is preferable to formula curves since it covers actual claiming behavior, there are still some major shortcomings to this approach. First, notice that we needed to segment by new, used and program as well as term If we got more detailed, we would segment by coverage (exclusionary, powertrain and wrap) and manufacturer warranty. Also, we might see different earnings patterns between business produced by banks or credit unions, dealers and direct business.
If we chose to segment by all these variations, we could literally have hundreds of earnings curves to maintain.
Finally, there is no mechanism to model changes that would have a significant impact on earnings. One major problem is a change to the underlying manufacturer’s warranty. For example, an increase in the manufacturer’s warranty would have the welcome impact of decreasing claims. However, the claims we would see on VSCs would occur later in the contract. Our earnings pattern would “overearn” the contract at the midpoint of the contract and our profits would be overstated.
Another issue is mileage. If the driving habits of the contract holders change (for example, the contract holders begin to drive more miles), we would see an understatement of earnings since many of these contract holders will “drive out” or expire their VSCs prior to the expiration date.
In the past, mileage information has had to be estimated from claim or cancel records. However, new sensor technology is allowing odometer readings to be given in real time. We’ll return to this topic when we discuss the future of earnings curves.
The Difference between Financial Reporting and Experience Evaluation
While earnings curves are used for both purposes, it is important to realize that that there are different purposes for using earnings curves for financial reporting and experience evaluation.
Financial reporting, that is preparing financial statements for shareholders, regulators and participating dealers, may be subject to the Statutory Statement of Accounting Principles 65 (SSAP 65). In addition to other requirements, this statement says that unearned premium must be greater than or equal to the greatest of these three amounts:
- The amount of premium, which could be refunded if all contracts cancel,
- The portion of premium proportionate to future losses and expenses to total expected (past + future) losses and expenses,
- The present value of future losses and expenses.
The second goal is what we usually think when we think of earnings curves – that is, the premium will match the loss. However, in cases where the refund provisions are high, the company may earn the contract according to the refund provision
Earnings curves for financial statements should have the following goals (some of which are in conflict):
- The earnings curves should reflect the actual emerging experience of the book.
- The earnings curves should be simple and easy to reproduce to explain to stakeholders (auditors, regulators and shareholders).
- The earnings curves need to follow financial guidelines.
Because of the need for some simplicity and the requirements of SSAP 65, the earnings curve for financial reporting may not be the best for analyzing the experience.
The best curves for analyzing experience may need to be more sophisticated than those used for financial reporting. If there are issues between implementing a better earnings system and maintaining financial reporting standards, the administrator may need to create an earnings curve for financial reporting and another curve to analyze the experience.
What is the exposure base?
One of the implicit arguments in all types of earnings curves is that each month of coverage is an exposure. All insurance coverages usually have a common exposure base, which is used for rating. Common exposure bases are revenue (liability insurance), cars (auto insurance) and payroll (worker’s compensation).
A better exposure base for VSCs is an estimate of “months exposed.” By “months exposed” these are the months that the service contract:
- Is not covered by a manufacturer’s warranty
- Has not expired the VSC by driving out of the coverage
- Is covered under the contract (powertrain only, wrap or exclusionary)
Without knowing the mileage, it is impossible to know definitively the answer to whether the manufacturer’s warranty or service contract is still in effect (unless enough time has passed to expire the manufacturer’s warranty).
However, as explained above, new technology can allow us to know the current mileage on our exposures. Even if we don’t know the mileage, we can estimate this based on different driving patterns observed in our claims and cancel data.
Projecting the Losses
Statistical techniques, such as generalized linear models, can be used to model losses from the exposures developed above. An average “cost per month” can be calculated and the results can be varied using “relativity factors” derived for each of the characteristics of the contract. In our experience, contracts have typically varied on the following bases (this list is not exhaustive):
- Age of contract
- Mileage of vehicle at contract purchase
- Make and model of vehicle
- Source of business (dealer, direct, financial institution)
- Participation status of business source in underwriting gain
- Other (dealer, state, marketing group)
By combining the exposure base developed above with cost per exposure estimates from the characteristics of the contract, an estimate of the losses for each month of a specific contract may be formed.
The Future of Earnings Curves
This type of analysis implies a contract level earnings curve. When a contract is underwritten, a predictive model based on the term and the factors above can generate predicted claims by month. These “predicted claims” can be used to form an earnings curve for this contact. As the contract earns, the system can simply look up the earnings pattern for this specific contract.
If actual mileage is available, the curve can be adjusted by the specific driving patterns of the contract holder. The positives for this type of analysis are that it allows the most accurate earnings curve and it responds immediately to any changes in the underlying manufacturer’s warranty. In addition, it does not require the maintenance of hundreds of separate earnings curves.
One disadvantages is that it does require some front-end analysis (though likely less ongoing analysis than traditional earnings curves). In addition, it may be difficult to explain to stakeholders and does not guarantee that the contract is above the refund value (which may make a simpler curve for financial reporting advisable).
Administrators should consider the availability of new data and techniques to improve their earnings curves. By using a parameter-based model, administrators can address the many facets for their business without relying on formulas or earnings curves based on limited assumptions.