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Brainstorms
From Triangle Offense to Triangulation
by Stephen W. PhilbrickAs I write this, I'm in the throes of basketball fever. I can't switch it off totally, so I'll see if I can find a business issue of interest to actuaries related to basketball. I jokingly proposed to a colleague that the stockmarkets moved more like the Poll rankings than the RPI ratings. Our discussion then extended to reserving and pricing, but I should recap the relevant attributes of the basketball ratings, for those who are not basketball addicts.
The RPI ratings are a pure mathematical calculation, based upon a team's win-loss record, the won-loss record of its opponents, and the won-loss records of the opponents of the opponents. The details of the calculations aren't important. The key features are that the ranking is purely mathematical (it doesn't depend on the opinion of a pollster) and the numbers are more or less continuously updated. Even if a team doesn't play on a particular day, if one of its earlier opponents plays, or its opponents' opponents play, the RPI number will change slightly, reflecting the tiny bit of new information.
In contrast, the Poll rankings are selected by people, either coaches or writers. Each week they rank the top 25 teams, and their collective rankings are combined. A team will move up or down in the rankings if, in the judgment of the person polled, they appear stronger or weaker than they were the week before.
An unwritten rule is that pollsters do not move a team down in the rankings unless they lose a game. If a pollster has decided that a team deserves, say, the number three position in the poll, plays an unranked team and just barely wins, it might be a sign that the team isn't as strong as originally thought. But such a result rarely results in a downgrade. If the team eventually loses, even to a good team, it might be moved further down the list than another team who had been winning by a large margin. In contrast, the RPI rating of a team could drop, even with a win, if, for example, some of the teams they had already played lost.
For this reason, I argue that the Poll rankings are "sticky." Conceptually, they can incorporate all relevant information up to the time of the decision, but in practice, a pollster will not move a team without some meaningful event.
These two types of systems occur in actuarial work. For example, companies setting reserves use mechanical methods as a start, but supplement it with judgment. Companies are understandably reluctant to report reserve strengthening in one month, then take it down the following month, then reverse it again in the next month. Even if the purely mathematical triangulation indicates such a pattern, a company will typically override what it perceives as noise in the system. This is perfectly justifiable, but it can lead to "stickiness" in reserve levels. Sometimes the raw calculations will indicate an increase, but there are no "meaningful events" to justify recommending a strengthening of reserves. Sometimes the situation continues to deteriorate until a point at which a major change in the reserves is required.
Pricing of certain lines also seems to follow a similar process. Companies have a sense that a certain line is underpriced, but it often takes a major event to trigger widespread price changes. This has an unfortunate effect, as consumers of insurance products are looking to replace uncertain financial outcomes with more certain premiums, but the variation in aggregate premiums sometimes exceeds the variation in aggregate losses.
The point of this observation is not to suggest that judgment-based reserving or pricing methodologies should be replaced by purely mathematical formulas. I've argued that the Poll rankings are better predictors of basketball results than RPI ratings, because they allow more subjective judgment, yet I recognize that the "stickiness" of Poll rankings creates a problem. The question in both cases is whether a better system can be devised that allows the key statistic, whether it be a reserve level, a pricing decision, or basketball poll rating, to reflect subjective judgment without becoming either too "sticky" or too formulaic.