The Value of Lift
By Glenn Meyers
A new word, “lift,” has become part of the standard actuarial vocabulary in the past few years. It is generally used in the context of evaluating the performance of predictive models in developing better risk classifications. Most of what I have seen on the subject treats lift as a statistical concept. In this column, I would like to explore ways of evaluating lift in a business context.
Before I make a proposal for evaluating lift, I would like to frame the discussion with a brief history of risk classification. In the early twentieth century, cartels dominated the insurance industry and risk classification was very coarse by today’s standards. With the breaking up of the cartels in the middle of the century, insurance became competitive and refined class plans were developed. Insurers who did not refine their class plans found that their most profitable business was taken away by their competitors and their profits were severely reduced.
The early class plans were based on cheap and readily available information. For example, consider auto insurance. Age, gender, garaging address, and vehicle type are easy to get, and through the ’50s, ’60s, and ’70s auto class plans were developed with hundreds of possible classifications. Then they hit what I call the credibility barrier. There was not enough data to reliably calculate the expected costs of further refinements.
Sometime in the ’90s, there were some new developments. First, there was an explosion of new and different kinds of data that could be used in ratemaking and underwriting. Credit data is probably the first example that comes to mind. Second, the widespread availability of personal computers made it possible to apply powerful statistical methods to predict the expected loss for better calibration and further refinements of the class plans. The generalized linear model (GLM) is the first example that comes to mind in this area.
As I am sure that anybody who has tried will tell you, these new methods are not easy to implement. Also, the existing class plans are not all that bad. The low-hanging fruit has been taken. Given that one has to invest both time and money to refine a class plan, how does one measure the return on that investment?
The following table shows a simple illustrative case of a class plan refinement.
This table describes a book of business consisting of four different risk classes. Based on the insurer’s expected loss estimates, each risk in the class is charged the same premium that is priced to yield a 10% expected profit as measured by the return on premium. On a per-risk basis, the profit is measured as the difference between the accurate expected loss and a calculated break-even loss amount.
Now suppose a competitor performs an analysis that accurately identifies which risks will have a lower expected loss. Based on this information, it lures these better risks away by competing on price, with the lost profit identified in the right-hand column of the table. In looking at the column totals, we see that the competitor can take away 80 of the original insurer’s expected profit of 120.
How much should the insurer invest to avoid adverse selection? Here I would like to coin a term called the “Value of Lift,” or VoL, which is the expected profit that would be lost from business that a potential competitor would take away with a more accurate classification plan. The VoL in the above example is 80.
The VoL should be thought of as an upper limit of cost that an insurer might pay to avoid adverse selection. In a well-run insurance company, there will be a number of policyholders that will not jump for the lowest price. In general I expect that the cost of introducing a new class plan would be noticeably less than the VoL.
The VoL should be compared to such expenses such as the following.
- The cost of obtaining information needed to determine the class. Examples of such costs include the cost of a credit report or a motor vehicle report.
- The amortized cost of the research and development needed to develop the class plan. This includes the cost of the predictive modeling unit plus the cost of developing the infrastructure needed to administer the plan.
Depending on the context, it may be appropriate to express the VoL as a percentage of premium or a dollar amount per policy.