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  2. Determining Risk
  3. Expected Annual Loss
  4. Historic Loss Ratio

Historic Loss Ratio

The historic loss ratio (HLR) is defined as a hazard- and county-specific estimate of the percentage of the exposed consequence type (building value, population, or agriculture value) expected to be lost due to a hazard occurrence. For example, building historic loss ratio is the estimated percentage of the exposed building value expected to be damaged by a hazard occurrence.

Historic loss ratio is a natural hazard consequence factor for Expected Annual Loss, the natural hazards component of the National Risk Index. A higher historic loss ratio results in higher Expected Annual Loss and Risk Index scores.

Source Data

Arizona State University’s Center for Emergency Management and Homeland Security’s Spatial Hazard Events and Losses Database for the United States (SHELDUS) loss data are used in the calculation of historic loss ratios for all hazard types, except Cold Wave. SHELDUS provides county-level data that correspond to nearly all the natural hazards represented by the National Risk Index. SHELDUS offers a further degree of description by identifying events by peril as well as hazard. SHELDUS aggregates property damage, crop losses, injuries, and fatalities due to a peril by month, year, and county. Because SHELDUS hazards do not directly map into the hazard types included in the National Risk Index, data were downloaded at the more granular peril level, and then mapped to the appropriate Risk Index hazard type. Cold Wave is the only hazard type that did not use SHELDUS and instead leveraged the National Oceanic and Atmospheric Administration’s National Centers for Environmental Information’s Storm Events Database, which provides consequence estimates from hazard occurrences.

Census data and various natural hazard-specific exposure and susceptibility data are also used in the calculation of historic loss ratio.

Historic Loss Ratio Methodology

To begin the determination of historic loss ratio, a Loss Ratio per Basis (LRB) was calculated for each loss-causing hazard occurrence using the following equation:

LRB = Loss / Exposure

  • LRB represents the ratio of loss to exposure experienced by a county from a hazard occurrence of a specific hazard type. This value is calculated for each relevant consequence type.
  • Loss is the loss, by consequence type, experienced from each hazard occurrence documented in the source data.
  • Exposure is the total value, by consequence type, estimated to have been exposed to the hazard occurrence.

Loss Ratios per Basis were calculated for each loss-causing hazard occurrence in the source data. However, hazards may occur without resulting in any recorded losses to buildings, population, or agriculture. For example, Lightning may strike with a high frequency, but have few loss-causing hazard occurrences. SHELDUS only documents events where losses occurred.

To ensure that the historic loss ratio is calculated more appropriately, zero-loss hazard occurrences were inserted into the set of Loss Ratios per Basis to make up the difference between known hazard occurrences (using the annualized frequency source data) and loss-causing hazard occurrences (using the historic loss ratio source data). The result is an historic loss ratio calculation that considers both loss-causing and zero-loss hazard occurrences.

Conceptually, a county’s historic loss ratio is the average of Loss Ratios per Basis from past hazard occurrences of a specific hazard type. But often there is wide variance in the Loss Ratios per Basis or not enough hazard occurrences in a community for a statistically significant average. To address this, the Risk Index applied a Bayesian credibility approach to balance accuracy with geographic precision for areas where small sample sizes result in volatile estimates. This approach blends historic loss estimates based on their credibility (a function of sample variance) to smooth the impact of local hazard occurrences over a broader geographic area. Specifically, the averages and variances of the Loss Ratios per Basis were calculated for each consequence type at four levels:

  1. County
  2. Surrounding area (196 km fishnet)
  3. Region (hazard-specific areas larger than states in size)
  4. Nation

Credibility increases as a function of sample size and decreased Loss Ratio per Basis variance. The higher the credibility at a geographic level, the higher the contribution that a geographic level’s value has to the county’s final, Bayesian-adjusted historic loss ratio. Consider these two examples:

  • County A, in a part of the country with high tornado frequency, had many Tornadoes over the period of record. While the Loss Ratios per Basis vary based on the severity and touchdown locations, there is a relatively high average historic loss and relatively low variance for the county. For County A, the county-level will be a significant contributor to the final, Bayesian-adjusted historic loss ratio for the county.
  • County B is in a low Tornado frequency area where a Tornado has not occurred during the period of record. County B’s Bayesian-adjusted historic loss ratio will rely on the values from higher geographic levels: surrounding area, region, and nation.

For comprehensive details about historic loss in the Risk Index, see the National Risk Index Technical Documentation.

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