As leaders of property/casualty insurance carriers, you are routinely exposed to conversation about predictive models, along with assertions that the benefits realized by some carriers in auto insurance pricing can be replicated in other lines.
Executive SummaryTo make informed decisions about adopting predictive models, insurers must ask how implementation costs compare with model benefits. The author proposes a statistic called Value Of Lift, or VoL, to quantify the value of predictive modeling.
In the personal automobile insurance marketplace, the early adopters of predictive analytics—the extraction of meaningful, actionable insights from raw data—have gained significant competitive advantages over the past decade. Most notably, these personal lines insurers have used predictive models to develop more refined pricing by introducing credit reports, detailed vehicle classifications, and other predictors to a rating process that previously relied on variables like territory, age, gender and marital status. But even in this line, where the application of predictive modeling is relatively mature, new data sources such as vehicle telematics are emerging to form a whole new level of analytics.
Whether your company is poised to embrace new data to improve predictive models, or you are considering the possibility of embarking on a predictive modeling journey for the first time, one thing is clear: predictive modeling initiatives, like all forms of innovation, carry steep costs—measured in time as well as dollars.
Estimating the dollars you’ll spend provides only half the input to your decision-making process, however. To make a truly informed decision, you must ask how the cost of implementing a predictive model compares with the benefits it provides. We propose a statistic called Value Of Lift, or VoL, to quantify the value of predictive modeling.
Consider The Costs
Turning to the costs first, it has been our experience that it can take months, if not years, to develop a working predictive model from scratch and deploy it to refine risk classification systems. Gathering relevant data takes up the bulk of the time. If all relevant data is in place, the actual construction of the model can proceed quickly. But the modeling process often uncovers problems with the data, and fixing those problems is time-consuming.
Moving from a model to a product also takes time. If you want to file rates based on your model, you need to go through many steps to refine the presentation of the model to make it acceptable to regulators.
Maintenance costs then need to be considered once the model is up and running. Obtaining and updating the underlying data—and the systems cost to maintain the model—are some of the factors you must take into account.
Analyzing The Model; Valuing The Benefits
You must also evaluate how a predictive model would affect your underwriting and pricing decisions.
For example, if you use the model to change prices, how much would prices change? Can the model systematically identify risks that have lower or higher loss ratios under your current rating plan?
An illustrative example can help show one way to examine those questions. This example consists of 500,000 risks that have an overall expected loss ratio of 70 percent. As we shall see, the book of business has an existing class plan that already differentiates between good and bad risks. We also have a proposed class plan that refines the distinction between good and bad risks.
To address the first question, we define the relativity to be the ratio of the proposed premium to the current premium. Figure 1 shows that there are significant differences in the premiums indicated by the two competing class plans. The predictive model indicates minimal price changes (relativity is 1.0) for half of the risks. For risks on the left hand tail (relativity < 1.0), the predictive model indicates premiums should be at least 10 percent lower than current rate level. These are risks that are subject to adverse selection.
The right hand tail sees another 20 percent with indicated premiums 10 percent higher than current premiums. These are the less profitable risks and can be addressed through selective underwriting. On average, rate levels remain the same, but we see redistribution of premiums to adequately price each risk. This avoids having good risks subsidize bad risks and prices all risks to an accurate level.
The presence of different indicated premiums by itself, however, does not necessarily validate the model. We should check to see if the model allows us to differentiate good and bad risks relative to the current rating plan.
Figure 2 shows loss ratios for six equally sized premium groups ranked in order of their relativity. It shows that those risks with lower relativity have lower loss ratios, and those risks with higher relativities have higher loss ratios.
Figure 2 illustrates that the predictive model in our example identifies the most profitable risks. But it does not answer the overriding question: Is this model-building effort worth the expense?
Reframing the question slightly, we might ask: How much should the insurer spend on a predictive model to avoid adverse selection? In other words, what should the carrier invest to avoid the possibility that a competitor’s analysis accurately identifies the low relativity risks with the low expected loss ratios, and swoops in to lure that business away with lower prices?
To answer the question, we propose the summary statistic Value of Lift, or VoL, which is equal to the amount of potential lost profit due to adverse selection spread over all risks. Lift, or the incremental gain in accuracy, has become part of the standard actuarial vocabulary with the use of predictive modeling. Monetizing this increased predictive power is a challenge and the Value of Lift is one method of doing so. VoL measures the financial impact of losing customers due to adverse selection. This assumes your competitors have better tools and models to segment your book and have the ability to take your better risks which you cannot properly identify.
Figures 3a and 3b detail the calculation of VoL for a sample book of business with four risk classes, which is equal to $3.33 per car year. Therefore, if the amortized cost of producing the model is small compared with the $3.33 value of the VoL, you can reasonably conclude that the modeling exercise is cost-effective.
Three Dollars Per Exposure. Really?
While this example was produced to illustrate the concepts involved in evaluating a predictive model, the numbers are actually similar to real-world results we have derived for both liability and physical damage coverages based on a test of a suite of predictive models we developed for personal auto. After we produced the models, dozens of prospective users submitted premium and loss data for us to evaluate the performance. The analysis below comes from a combination of 10 separate insurers.
We produced separate models by coverage. The VoL per car year by coverage for the combined results of prospective users is shown in the following table:
Coverages which have historically garnered less attention tend to show the most value coming from predictive modeling. PIP and Comprehensive tend to show the most value since they are more often under/overpriced relative to larger coverages like Bodily Injury and Collision.
In one sense, the VoL might be thought of as an upper limit of cost that an insurer might pay to avoid adverse selection—because in a well-run insurance company, there will be a number of policyholders that will not jump for the lowest price.
On the other hand, we note that our calculations provide only a one-year view of competitor dynamics. As policyholders representing the best risks do move from the insurer’s book to lower-priced competitor in search of a lower price, the loss ratio of the remainder of the insurer’s book will rise—forcing the insurer to raise renewal prices on the remaining risks in order to maintain its expected overall profit margin. In this sense, the one-year VoL may underestimate the lost profit due to adverse selection.
While more complex multi-year calculations are possible, the VoL measure we have presented here serves its purpose. It provides a starting point for understanding the hidden costs of not adopting more refined ratemaking using a predictive model.
As for the costs of adopting predictive analytics, in some areas, those are declining. Importantly, for example, advances in technology and computing power in recent years have greatly increased our ability to collect and manage vast amounts of data. In measuring costs against the VoL, these technological advancements represent a key factor, since much of the expense of developing a predictive model is related data-gathering activities.
There is still much that our industry can learn from other industries that have been incorporating predictive modeling into their business processes for a longer period of time, such as financial services and marketing. While more and more property/casualty insurance actuaries are adding predictive modeling to their skill sets, we should also encourage analytical professionals with experience in other industries to join with us. The recruitment efforts within and outside the industry clearly represent another cost that should be measured against the VoL.
Although the development of a predictive model can be a lengthy and costly process in the short term, the long-term benefits of implementing advanced predictive modeling tools to streamline products, prices, and services can prove worthwhile, particularly in today’s demanding and interdependent economic environment.