# A new paradigm in P&C Industry Pricing

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3 taking into account the effects (interactions) that many different characteristics (variables) of a risk have on one another (thus the term multivariate approach vs the univariate approach typically employed by most insurers today) These techniques have been mastered by data miners across academic (e.g. scientific research) and business (e.g. marketing and risk management) environments as way to predict behaviour. Many companies use Predictive Modeling (a form of multivariate analysis) to create measures of the likelihood that a customer will purchase a particular product (e.g. magazine subscriptions); Banks use these tools to create measures (e.g. credit scores) of whether a client will be able to meet lending obligations for a loan or mortgage. Similarly, P&C insurers can use predictive models to predict claim behavior. Essentially, predictive models identify the characteristics that best predict risk; produce a scoring equation that can be maintained and updated; calculate a score that represents the expected losses for each risk in the portfolio; Chart 1 Expected Losses Highest Risk Lowest Risk The Scoring model or mathematical equation is comprised of the fewest number of characteristics (variables) possible (usually 10 to 15), each of which are responsible for a discrete amount of the expected loss behavior that when added together account for 100% of the expected losses for the risk. A simple way of looking at this approach is to consider each characteristic in a model equation like a different piece of a pie where the pie represents the total expected loss amount. In Chart 2 below the pieces (characteristics of a auto insurance risk identified by the model) fit together to form a whole, perfectly shaped pie; in other words, the set of variables in the equation are the optimal combination that provides the most accurate measure of the expected losses. Whereas it may appear that by adding more information (ie. another piece to the pie) one could generate an even more accurate assessment of the risk, the statistical processes account for the relationships between different characteristics such that the addition of another 3

4 characteristic to the pie would only distort its shape, and not add any additional value in accurately measuring risk. Chart 2 It is our experience that multivariate or predictive modeling techniques provide even more granularity and better understanding of the differences between individual risks than conventional approaches used by most insurers today. This is achieved as risk measures produced by predictive modeling outcomes are produced for each individual risk rather than by group differentials. In essence, the techniques enable more accurate matching of rate with risk. Those relatively few insurers in Canada employing these methods are able to acquire business by offering lower rates for risks that the general market is overpricing, and have higher prices to avoid taking on risks that the general market is underpricing. The overall benefits of this result include: Better risk selection and pricing Reduced underwriting expenses Improved underwriting results 4

5 Results from Case Studies Whether the application of multivariate analytical techniques can improve upon the rating accuracy is ultimately determined by how much better these measures predict losses compared to the premium assigned to a risk (vehicle or property) using conventional rate-setting paradigm. Presented below is an example of actual observed results for a portfolio of homeowner s policies: A Homeowners Claims Risk Scoring model was produced for a Canadian insurer Each policy in the portfolio was scored at its effective date. The score represented the expected losses on the policy in the policy year. Each policy was ranked from highest risk (score) to lowest risk (score). Chart 2 Homeowners Property Insurance Model Highest Scores Lowest Scores The Line Chart depicts the percentage of actual losses on policies in the portfolio that occurred after the policy effective date o Based on the model s prediction of losses, policies with the highest 20% of scores generated 46% of total losses while those policies in the lowest 20% of scores accounted for only 6.8% of losses o Based on the premium charged for each policy, the policies with the highest 20% of premium produced 32% of all losses and those policies with the lowest 20% of premium produced 15.2% of losses The shaded area represents the lift or increased accuracy in loss prediction produced by the model over the insurer s current rating structure, essentially representing losses not accounted for by existing rates. Conclusion 5

6 The application of data mining tools and multivariate modeling techniques can substantially improve current rating structures for Property and Casualty insurers. Because of this capability multivariate modeling techniques are gaining traction and becoming an industry standard. The primary challenge is to effectively action these tools; Insurers must become more familiar with these techniques and adopt them as a daily part of doing business. Data Miner s familiar with these tools can provide critical assistance to company Actuaries in this regard. This incremental level of accuracy in predicting losses enables insurers to price policies more accurately than competitors, improve portfolio profitability and provide substantial long term competitive advantage. 6

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