The 100-year Flood

The probability of a flood affects insurance and land values, and subsidies are wasteful and futile.

February 22, 2015

There is a concept in insurance and probability called the "100-year flood," or a "100-year recurrence interval." It is an event that occurs with a one-percent probability in a year. The "100 years" is just a round number for mathematical convenience. The concept assumes that the probability in each year is independent of that of the other years, so that the events are not correlated. It is also assumed that there is a stationary probability distribution, so that the deviations do not change year to year. Given the flowrate of a river and the volume of water, one can calculate the size of the floodplain, the areas that will be flooded.

The practical applications include insurance and investments in flood control. A policy implication is that the government should not encourage what is called "moral hazard," the tendency of people to take on more risks when the costs are subsidized. So, government should not bail out (financially) real estate owners who choose to live in a floodplain. If there is no subsidy, then the property owners will face insurance costs based on the expected damage.

If the annual probability of a flood is one percent, then how often would we expect a flood? The mathematical expected value of the number of floods within the 100-year period is 1 (one). But on the average, we would not wait 100 years for the flood. The annual probability of there not being a flood is 99 percent within a year. The probability of there not being a flood within two years is the .99 of the first year times .99 of the second year. For one hundred years, we multiply .99 together one hundred times, or .99 raised to the power of 100, which equals .366. There is a 36.6 percent probability of there not being a flood. Therefore the probability of there being a flood within 100 years is 1 - .366 = .634, or 63.4 percent. We get a 50 percent probability of both a flood and no flood with 69 years.

If there is no governmental subsidy, then the 100-year flood has implications for insurance and land value. If the building is expected to last over 100 years, then if the flood will completely destroy the building, the insurance would be based on the replacement cost. If the house owner is paying an annual insurance, the funds would obtain interest income during that time, so the insurance company will use that interest, and not have to charge the full replacement cost. Also, since only the building is insured and not the land, the insurance company will appraise the real estate with separate values for the land and for the vulnerable improvements. That provides a market-based reason for estimating land value separately.

The annual rent of flood-prone land will take into account the insurance costs, such as flood, fire, and earthquakes. The higher insurance costs are capitalized into lower land rents and land values. Any subsidy for insurance is capitalized into higher land values. Therefore ultimately it is futile for government to subsidize flood insurance. It not only wastes resources in excessive construction that gets destroyed, but does not serve a new buyer whose subsidy is offset by the higher price paid for the land. What looks like subsidized flood insurance is in reality a subsidy to landownership.

The avoidance of subsidy also extends to flood control. In a market, the costs of flood control are borne by those affected. A homeowners association, for example, invests in protection for its community. The residents and property owners can then weigh the cost of insurance versus the costs of prevention. If the flood control is provided by government, paid for by taxes other than on landowners, this is again a subsidy, which then gets capitalized into higher land values.

The 100-year flood concept shows that a small annual probability results in a substantial probability of the event occurring during several decades. We should not let small chances slide into a catastrophe. Therefore maintain your possessions and your body to make the annual probability of a disaster as tiny as feasible.

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Fred Foldvary, Ph.D.

Economist

**FRED E. FOLDVARY, Ph.D.**, is an economist and has been writing weekly editorials for Progress.org since 1997. Foldvary's commentaries are well respected for their currency, sound logic, wit, and consistent devotion to human freedom. He received his B.A. in economics from the University of California at Berkeley, and his M.A. and Ph.D. in economics from George Mason University. He has taught economics at Virginia Tech, John F. Kennedy University, Santa Clara University, and currently teaches at San Jose State University.

Foldvary is the author of *The Soul of Liberty*, *Public Goods and Private Communities*, and *Dictionary of Free Market Economics*. He edited and contributed to *Beyond Neoclassical Economics* and, with Dan Klein, *The Half-Life of Policy Rationales*. Foldvary's areas of research include public finance, governance, ethical philosophy, and land economics.

Foldvary is notably known for going on record in the *American Journal of Economics and Sociology* in 1997 to predict the exact timing of the 2008 economic depression—eleven years before the event occurred. He was able to do so due to his extensive knowledge of the real-estate cycle.