The Return Period
Jul 27, 2016
On 16th April 2016, a 7.8 earthquake hit north east Ecuador resulting in circa 660 fatalities, together with extensive infrastructure and property damage throughout the affected region. Since the initial earthquake, in excess of 500 aftershocks have been recorded a number of which exceeded 4.5 on the Richter scale, according to the US Geological Survey (USGS). The Ecuadorian President, Rafael Correa, has estimated rebuilding costs to be in the region of USD 3 billion. This type of catastrophic event, along with hurricanes, tsunamis, volcanoes, etc., always provokes concerns as to when an event of the same nature and intensity will reoccur. This is an issue that not only impacts the insurance industry’s interest but also governments’, companies’ and, in general, population’s.
The estimated frequency of a catastrophic event reoccurring is usually expressed as the ‘Return Period.’ This refers to the average amount of time that passes between events of a similar magnitude in a given location; it can also be defined as the expected time, or average time, between two events of low probability.
The Return Period, also known as the Recurrence Interval, is a statistical concept that aims to provide an idea of the extent to which an event may be regarded as rare or extraordinary. This value, generally stated in years, is usually calculated by the distribution of extremity values, on the basis of a series of extreme values recorded within equal and consecutive periods.
In the insurance industry, the Return Period is used for risk assessment in determining an insurer’s exposure to such rarely occurring events which have potential to cause severe damage and far reaching consequences in their wake. However, the infrequency of occurrence means that it is very difficult to construct a database that will allow an insurer to estimate losses empirically, as it is possible to do in other areas of risk. This lack of historical data means that statistical models become the only benchmarks used to predict the potential frequency of such events.
A common cause of confusion in interpreting the data derives from the fact that the Return Period relates to the “average time” associated with a probability. Thus it can be expressed as a percentage or in reference to units of time. As an example, the Return Period of an event such as a flood occurring, on average, every 100 years can also be expressed as a likelihood of occurrence of 1/100, or 1% in a given year. However, this does not mean that if a flood should occur then the next flood will occur in approximately 100 years. Instead, what it means is that in any one year, there is a 1% likelihood that a flood (or the type of event under examination) of the same intensity will occur, regardless of when the last similar event occurred. It is therefore 10 times more likely that a flood of the same magnitude will occur in an area with a Return Period of 10 years.
It is not uncommon to encounter problems with interpretation when expressing this frequency of event as a Return Period. Often, these values are interpreted in absolute terms instead of average values leading to an erroneous expectation of infrequency of events. For example, when it is stated that a loss is associated with a Return Period of 100 years, it is frequently assumed that a similar event will occur in 100 years. However, what the Return Period means is that the event can occur on average every 100 years. Should similar events occur in consecutive years and then not reoccur for 200 years, then the Return Period is still represented by an average frequency of 100 years.
The reliability of any current statistical calculation is dependent on the accuracy of the data input, including all available information on an event in estimating a Return Period. In any natural catastrophe there will always be a number of variants applicable to each event that may influence the outcome of any statistical measurement, as such an expressed Return Period should be considered as guidance and not absolute.
With advances in technology and sciences and more detailed record keeping, our knowledge base of naturally occurring events is growing. Our understanding and interpretation of this information is bringing more accuracy to predictions. Over time these predictions are likely to gain more accuracy, but it is probable that there will remain a margin of uncertainty in any quoted Return Period.
