Grappling With the Inexact Science of Frequency-Based Retentions

What rule do experienced risk managers use most often to select retention levels? Retain frequent losses. It is easy to see that the crux of this simple rule is what we define as "frequent," and how we do it. By observation of real-world decisions, we notice that the cutoff for frequent losses is usually based on an annual probability level of about one in 10, maybe down to one in 20 or so.

In setting reasonable retentions, we attempt to "cut off" loss frequency based on a firm's loss characteristics only.

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Insuring losses that occur more frequently that this, we find we are using the fairly expensive mechanism of insurance, which must charge the long-run average cost of losses plus expenses to cover losses the firm could comfortably, and predictably, bear.

Losses occurring less frequently, while still affordable, begin to impart a choppy variability to our overall cost of accidental loss. The management of a firm should be judged on operating results that are not subject to random variations due to accidents.

Also, as losses get larger, insurer expenses may begin to seem like a reasonable cost for reducing variability.

For example, at an annual probability of one in 50, for a loss of $100,000, the pure average, or expected value of loss, is $2,000. At an expense load of 30 percent of pure premium, our total premium is $2,600. The $600 starts to look attractive as a price to pay for added stability in earnings when we consider we have reduced the absolute variability of loss by 700 percent. Insuring a $7,000 loss with a probability of three in 10 results in roughly the same premium and load, but variability is reduced less than 200 percent.

The word "frequent" also implies the rule of thumb is inexact. Due to the complexities of the situation, we can't specify any exact cutoff, based on any mathematical formulas or theories. In practice, we eyeball a reasonable retention level. The experienced risk manager formulates an intuition for this imprecise dividing line. As loss experience changes, so does the retention.

There are also computer programs available that can help evaluate retentions based on the frequency concept. They are based on the concept of expert systems: computer programs that emulate the thought process of human experts in a field. It looks like our simple little rule really says a lot about the complex process of retention selection!

March 1, 2006

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