Insurers Can Recalculate Terrorism Risk

Statisticians describe such events as independent, meaning that if one event occurs, there is no change in the probability of the other event occurring. On the other hand, two adjacent homes are viewed as being positively correlated in terms of the fire risk. A fire in one could spread to the other, or a common cause, such as a brush fire or urban conflagration, could cause fire damage to both.

Now lets consider the implications of independence or positive correlation. To make the analogy closer to terrorism risks, lets view the properties in question as large trophy buildings, such as the Sears Tower in Chicago, or the Empire State Building in New York.

If the two buildings are separated by hundreds or thousand of miles, then we can assume that fires due to normal causes, such as gas leaks or faulty wiring, are independent–they have zero correlation. From an insurance companys point of view, independent risks and risks that have low positive correlation are attractive, since the probability of both buildings burning down is relatively low.

Turning now to the capital issue, insurance companies need to assign capital for the risks that they are taking on. For large risks, such as trophy buildings, probabilistic methods tend to be used.

For example, an insurance company providing $100 million in fire coverage to a trophy building will make some assessment of the probability of various levels of loss associated with this risk. Thus, a fire causing $1 million in losses might be viewed as having a probability of 1:20. At the other extreme, a fire causing a total loss of $100 million might be assessed as having a probability of 1:2000. The insurance company most likely will set aside at least $1 million in capital to cover this risk, but, not the full $100 million.

Typically, an insurer will follow some rule in deciding the amount of capital to set aside. Let us say it follows a rule to set aside capital for risks with a probability below 1:100. To see this in our example, let us assume that the probability of fire loss above $2 million is 1:100, then the company will set aside $2 million in capital to cover the risk.

For independent risks–say, two large buildings hundreds of miles apart–the capital charge, assuming the same probabilities of loss, will be double, or $4 million for our example. If the buildings are adjacent, then there is a higher probability of loss as indicated earlier, and the capital charge will be higher than $4 million.

Now lets move to terrorism risk and consider trophy buildings, particularly those separated by many hundreds of miles. Given the difficulty of destroying a trophy building, it is easy to accept the hypothesis that in a given policy year, the probability that terrorists can muster the resources to destroy more than one non-adjacent trophy buildings is extremely low. Further, if one incident occurs, the reaction by law enforcement would likely be such that the probability of a second event in a short time frame would be reduced significantly.

Put another way, what is being hypothesized is that the terrorism risk for the two buildings geographically separated is almost totally negatively correlated–an attack on one in a given year will mean that there will be almost no chance of an attack on the other. This would be 100 percent negative correlation. The implication for the capital of the insurer is then that both buildings can be insured with only a single capital charge.

If we transfer the arithmetic of the fire example above to terrorism risks, then a single capital charge of $2 million would be incurred. This is the extreme case of 100 percent negative correlation. In the case of negative correlation below 100 percent, the capital charge would be higher, but not as high as $4 million for independent risks.

Examples of negative correlation are not unique to the terrorism risk. For example, a term-life policy can be negatively correlated with a pension-type annuity. If the subject person dies, the insurance company has a loss of the term-life amount, but gains the discounted value of the annuity payouts.

This article is not concerned with making actual projections of future terrorism events. Indeed, the simultaneous attack on Sept. 11 of two geographically separated buildings–New York's World Trade Center and the Pentagon in Washington–would appear to counter the main argument proposed here.

However, it is easy to extend the argument so that the negative correlation begins at three or four buildings.

The more general point is that we need to think about terrorism risk outside the box of most other insured perils. While there are clear problems with the insurability of this risk, there are some positive aspects of the risk compared with many other property exposures.

Sean F. Mooney, CPCU, is senior vice president, research director and economist at Guy Carpenter & Company in New York.

Reproduced from National Underwriter Property & Casualty/Risk & Benefits Management Edition, April 29, 2002. Copyright 2002 by The National Underwriter Company in the serial publication. All rights reserved.Copyright in this article as an independent work may be held by the author.