## Loss Development Factor Loss Development Factors as described by HB Actuarial Services, Inc.

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Loss development factors are typically organized in loss triangle format. If you aren’t familiar with loss triangles, please read our article on that topic.

Loss development factors are significantly relied upon in many actuarial loss reserving methodologies. They can be calculated entirely from loss triangle data– no additional data needs to be provided to the actuary to calculate loss development factors. A loss development factor is the loss value in a loss triangle divided by the value immediately before it in the loss triangle. For example in the loss triangle example, the first loss development factor for accident year 2008 is equal to \$688,542 divided by \$403,082 (the value right before it). That loss development factor (LDF for short) is 1.708. It is called the accident year 2008 age 1 to 2 loss development factor. Generally, the first thing that an actuary will do with a loss triangle is create a loss development triangle. Here is the one created from the loss triangle example.

 Accident Year 1-2 2-3 3-4 4-5 5-6 6-7 2008 1.708 1.174 1.135 1.166 1.051 1.038 2009 1.598 1.094 1.063 1.003 1.000 2010 1.734 1.147 1.023 1.103 2011 1.439 1.118 1.008 2012 1.471 1.099 2013 1.736

You probably notice a few interesting things with this triangle. First off, it is smaller than the loss triangle. There is one fewer row and one fewer column. Remember, an LDF is calculated from two numbers, so there is no loss development factor available for 2014 where there is only one loss observation. Also, there are only 6 loss development factors that can be calculated for the 2008 year.

The next point of interest to most people is that all of the factors are over 1. This isn’t a surprise as paid losses will generally be higher in each passing year as more and more losses get paid. For accident years that are very old and have no claim activity, the loss development factors will drop to 1.000 meaning that losses are unchanged between successive valuations.

A quick review of high school algebra will show that if you take the first number in a row of a loss triangle and multiply it by all the values in that row in the loss development triangle,  you will get the last number in the loss triangle. For example, for accident year 2008:  \$403,082 x 1.708 x 1.174 x 1.135 x 1.166 x 1.051 x 1.038 =  \$1,176,216. The loss development method, discussed in last post on this topic, assumes that future loss development factors for a particular age will be the same as those in the past. In other words, the loss development factors for a particular column in a loss development triangle will be the same.

Read our post on  loss development selection to learn how we take a triangle of loss development factors to determine factors that will be used in the loss development methodology.

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