Random Sampler: Primum Non Nocere

Charles L. McClenahan

Primum non nocere or "First do no harm," is often referred to as the first rule of medicine. This rule requires of the physician that the expected outcome of the medical treatment should be no worse than the expectation without any treatment whatsoever. Good advice for doctors. And good advice for actuaries.

Over the years, and for various reasons, I have reviewed well over a thousand casualty actuarial analyses produced by peers, subordinates, competitors, litigants, M&A consultants, regulators, reinsurers, and brokers. To the credit of our profession, the vast majority of those analyses were of high quality and produced reasonable results. In some instances, however, I have observed certain aspects of the casualty actuarial practice that have introduced bias into the analyses.

I have considered writing a paper on this subject, but have recently decided that the principles involved are so simple that they can be demonstrated without the need for a scholarly treatment. So I will take advantage of the opportunity provided by The Actuarial Review and point out a few of the more obvious cases.

Average of Link Ratios Excluding High and Low Values - I list this first not because it is the most dangerous, but because it is the most prevalent. The technique rests upon the unstated assumption that link ratios are distributed symmetrically and that the elimination of outliers will improve the estimate. There are two problems with this, one theoretical and one practical. The theoretical problem is that the distribution of link ratios is not symmetric. While this can be demonstrated by simply looking at such distributions, it should be apparent that link ratios can be much higher above the mean than they can be below. The practical problem is that actuaries tend to apply this method where there is a single aberrant ratio, thus tossing out a ratio which would otherwise be included in the selection process simply because there is an unusual ratio on the other side of the mean.

Removal of Large Losses _ This technique involves simply removing "unusually large" losses from the losses to which the development factors are applied and then adding those losses back to the indicated ultimates. This is appealing because we can reasonably assume that the eliminated losses are not going to develop further, often because they are closed or already at policy limits. The problem is that we generally neglect to remove these and similar losses from the loss development history so that we have development factors appropriate for these "limited" losses.

Adding of Lows (and Highs) _ Among the most pernicious, and least excusable, practices that introduce bias into actuarial analyses is the summation of low (or high) estimates for individual lines or coverages in order to produce an aggregate low (or high) for the "range of reasonable estimates." This is based upon the erroneous assumption that standard deviations are additive. Even ignoring the very real question of independence, it is the variances, not the standard deviations that are additive, and the aggregate low should be greater than the sum of the lows. If this is unclear, consider ten tosses of a true coin. We might set our range at between 3 and 7 "heads" with there being a probability of about 5.5 percent that we will be below the low. Now, what if we had 10 people tossing true coins 10 times each. Would 30 (3 x 10) be a reasonable "low" for the aggregate number of heads? Since the probability of fewer than 30 heads out of 100 tosses is approximately 0.001 percent this would be unreasonably low. A more realistic "low" might be 42, since the probability of being below 42 is approximately 4.4 percent. By adding the lows we create an unrealistic low for the aggregate distribution.

Complement of Credibility _ Finally, I'll address an old adversary, the application of the complement of credibility to an unrealistic hypothesis. Most typically, the subject of such misuse is the "status quo" or "no change" assumption in ratemaking. By applying the complement of credibility to an indication of no change when we have identified underlying trends we introduce actuarial bias into the process.

These four examples have something in common: they are all simple. But, William of Ockham notwithstanding, just because something is simple doesn't make it right. Primum non nocere.