The economic costs of natural disasters in the United States (adjusted for inflation) have been increasing in recent decades. The primary reason for this is more people living and working in hazardous areas—and where there are people, there is infrastructure, capital investment, and economic activity. Moreover, some speculate that as the climate changes, the magnitude and/or frequency of certain extreme events may increase, amplifying this trend. This raises important questions about our current and future ability to manage and insure catastrophic risks, such as hurricanes and flooding.
In new research, we have been examining the distributions of damages from natural disasters. These distributions are a joint product of nature (the severity of the hazard) and society (where and how we build).
Three aspects of historical damage distributions—often neglected in policy discussions—are confounding our ability to effectively manage and insure catastrophic risks. The first is fat tails, the fact that the probability of an extreme event declines slowly, relative to how bad it is. With fat tails, damages from a 1-in-20-year event are not simply worse than those from a 1-in-10-year event; they are much worse. Second is tail dependence, the propensity of severe losses to happen together. For instance, a strong earthquake can cause fires to break out, leading to losses from two events instead of one. And the third is microcorrelations, negligible correlations that may be individually harmless, but very dangerous in concert. Weather patterns can induce tiny correlations in weather events in disparate parts of the globe. If an insurance company buys many similar policies in each area, thinking it has diversified, the aggregation of these microcorrelations could come back to hurt it. Traditional statistical techniques do not do an adequate job of detecting, measuring, or analyzing these three phenomena. Our research aims to improve this.
Many distributions we encounter in everyday life—running speeds, IQ scores, height—are "thin tailed." This means that we do not observe really extreme values. Suppose the tallest person we have ever seen is 6 feet, 7 inches. The average person taller than that will not be that much taller: he might be 6 feet, 10 inches, but he will not be 14 feet. Damage distributions from many disasters, on the other hand, are "fat tailed," and there is a greater possibility of witnessing very extreme values. Consider hurricanes: the National Hurricane Center estimates that Katrina caused over $84 billion in damages, considerably more than the second-costliest hurricane, Andrew, in 1992, which caused $40 billion in damages (estimates in 2006$). With fat tails, the next hurricane that is at least as costly as Katrina is expected, on average, to cause much more damage.
One of the challenges associated with fat-tailed risks is that data from a short period of time is not enough to adequately evaluate the potential for and amount of damages. In 1981, the National Flood Insurance Program (NFIP) adopted the goal of becoming financially self-supporting for the "historical average loss year." Floods can be catastrophic, however, and without a catastrophe in the historical experience of the program, the NFIP was unprepared for Hurricane Katrina. Figure 1 shows premiums minus losses by year for the program. The dramatic losses in 2005 are apparent.
Current NFIP rates count only 1 percent of the 2005 losses in calculating the supposed "historical average." The claims in 2005 sent the program deeply into debt, and with a mere 1 percent weighting to 2005, the NFIP, by its own admission, will be unable to pay even the interest on its debt to the Treasury.
Tails can be so fat that the variance is infinite. When insurance policies are aggregated from a distribution that has a finite variance, the tails are thin. This is good news for insurance companies. The bad news is that if the variance is infinite—meaning as the sample size increases, the sample variance keeps growing—the tails stay fat. The tail behavior of natural disaster damage data we have studied points to infinite variance.
Distributions with infinite variance defy normal methods for analyzing risk. For such distributions, the average loss will not converge as we consider more data; instead, it will whiplash back and forth. For the NFIP, the average annual amount of claims before 2004 was $553 million. When 2004 and 2005 are included, the figure jumps to $1.18 billion (claims are in constant year 2000$).
When Bad Things Happen Together
Tail dependence refers to the tendency of dependence between two random variables to concentrate in the extreme high values. Simply put, this means bad things happen together. After Hurricane Katrina, Risk Management Solutions, a catastrophe-modeling company, found that lines of insurance that are usually independent all experienced very high claims simultaneously; for example, property, cargo, inland marine and recreational watercraft, floating casinos, onshore energy, automobile, workers' compensation, health, and life insurance all spiked at once. This demonstrates the ability of extreme events to correlate damages across lines of insurance, locations, and types. Failure to consider this tail dependence could lead an insurance company to underestimate its exposure and thus court insolvency.
Figure 1. National Flood Insurance Program premiums minus losses per year
Tail dependence can be seen in loss data. Wind and water damage are insured separately in the United States. The former is covered under homeowners' policies or state wind pools, while the latter is covered by the NFIP. Flood and wind damage are often independent; a rising river does not necessarily mean terrible winds, and a storm with high winds may not have enough rain to cause flooding. A hurricane, however, causes both. This suggests that wind and flood insurance payments may be tail dependent in a hurricane-prone state such as Florida.
Figure 2 shows this is indeed the case. Wind payments from the state insurer Citizens Property Insurance Corporation were grouped by county and month for the years 2002 to 2006, as were NFIP flood claims (all are in constant 2007$). Each damage dataset was ranked by the magnitude of the claims and the ranks plotted against each other. The abundance of points in the upper right quadrant of Figure 2 shows that high flood damage claims and high wind payments occur together, indicative of tail dependence.
When Negligible Still Matters
Microcorrelations are correlations between variables at or beneath the limit of detection even with lots of data. Suppose we look at the correlation in flood claims between randomly chosen pairs of U.S. counties. Neighboring counties will be correlated if they experience the same flood events, but most correlations are around zero. When we do this for 500 pairs of counties, the average correlation is 0.04 (a correlation of 1 would mean the two counties always flooded simultaneously; a value of -1 would mean whenever one flooded, the other was dry). Indeed, using traditional statistical tools, 91 percent of the correlations would not be statistically distinguishable from zero. But that does not mean they are zero.
Figure 2. Tail Dependence in Wind and Water Claims, Florida 2002–2006. Note: Points of zero damages were removed, so axes do not begin at zero.
When the correlations actually are zero, the correlations between aggregations of counties will also fluctuate around zero. This is seen in Figure 3, which plots correlations between individual independent variables (green) and between distinct aggregations of 500 variables (red). Compare this to Figure 4, which shows correlations in county flood claims. The green histogram shows the correlations between individual counties. As just discussed, most are around zero. The blue shows the correlations between groupings of 100 counties, and the red shows the correlations between groupings of 500. With microcorrelations, the correlation between aggregations balloons as seen by comparing the red and green histograms in Figure 4.
Ballooning correlations will put limits on diversification by insurance companies and are particularly alarming since they could so easily go undetected. One might not readily assume that fires in Australia and floods in California are correlated, but El Niño events induce exactly this coupling. Identifying this type of correlation and creating insurance diversification strategies across areas or lines that are truly independent is essential.
Is Federal Intervention Needed?
Insuring risks plagued by fat tails, tail dependence, and microcorrelations is expensive—often much more expensive—than insuring risks without these features. Because there may be many years without severe losses, this fact can be obscured. One or two bad years can wipe out years of profitability. For the years 1993 to 2003, the Insurance Information Institute calculated that the rate of return on net worth for property insurers in the state of Florida was 25 percent, compared to only 2.8 percent in the rest of the United States. But if you add in the terrible hurricane years of 2004 and 2005, the rate of return on net worth for insurers in Florida drops to -38.1 percent, compared to only -0.7 percent for the rest of the United States.
It has been noted by insurance scholars that state insurance commissioners tend to place more weight on low prices and availability of policies than on solvency considerations or management of catastrophe risk. Homeowners' unhappiness with high premiums has led state regulators to suppress rates (keeping rates lower than they would be otherwise) and compress rates (decreasing the variation in rates across geographic locations) rather than allow rates that would be truly risk-based.
For risks plagued by our three phenomena, rate suppression and compression could make it unprofitable for insurance companies to operate. If insurers cannot charge prices they feel are sustainable, they may leave the market, as has happened in Florida. This puts greater pressure on residual market mechanisms, namely programs set up by states to provide insurance policies to those people who cannot find a policy in the voluntary market. If rates in these programs are not high enough to cover costs, firms in the voluntary market are usually assessed a fee, and thereby subsidize the residual market. Just recently, Florida increased the rates in its state insurance program because they had previously been too low for the state to be able to pay claims should a major hurricane strike.
Some policymakers and scholars have called for federal intervention in these markets. The federal government can smooth losses over time in a way that is difficult for states or private companies. Several proposals have been advanced in Congress, from the backing of state bonds used to finance claims after a severe event to federal reinsurance for state programs. The difficulty with such proposals is the creation of moral hazard. If the federal government subsidizes state insurance programs, it could encourage the state to provide insurance at rates that are far too low to cover the risk. This encourages nonadaptive behavior such as building in risky areas under inadequate building codes. Taxpayers across the country would unwittingly be underwriting such behavior.
As an alternative to intervening so heavily in the insurance market, the federal government could allow insurance companies to create tax-deferred catastrophe reserves. Insurers could choose to allocate funds to a trust or to a separate account with a firm-specific cap, where funds would accumulate tax-free and be withdrawn only for payment of claims following predefined triggers. The trigger could be based on specific events or firm-specific catastrophic loss levels. Creation of such funds would ensure that more capital is available to cover claims in the event of a catastrophe, thereby potentially increasing the availability and affordability of insurance.
We believe the first step in addressing these risks, however, should be to promote more mitigating activities, which can thin and decouple tails. For example, homes can be built or retrofitted to withstand hurricane winds, rising floodwaters, and earthquakes. Such measures not only benefit the individual homeowner, but also the more mitigation that is done, the more community and economic activities will be able to continue postdisaster. Congress is currently debating legislation that would offer tax credits to homeowners who secure their homes against hurricanes and tornadoes. These measures can have high up-front costs, and the probability of a catastrophe occurring often seems remote to many homeowners. Tax credits could potentially overcome these two barriers and spur more investment in mitigation.
Finally, there are a few cases where we can effectively decouple losses. For instance, the 1906 San Francisco earthquake ruptured gas mains, causing fires, and also ruptured water mains, so the fires could not be put out. Now we can build earthquake-resistant pipes for water and gas lines to ensure that when we have a serious earthquake, we don't also have serious fire damage.
Fat tails, tail dependence, and microcorrelations raise significant challenges for the insurance and management of natural disaster risks. As we better understand the nature of these risks, however, we can design and implement insurance and public policy measures that do not unwittingly leave us exposed to the next catastrophe.
Figure 3. Independent, Uniform Variables. Figure 4. Flood Claims by County and Year.
A version of this article appeared in print in the Summer 2009 issue of Resources magazine.
