Loss development factors (a.k.a. LDFs or age-to-age factors and claim development factors ) are calculated by successive multiplications beginning with the tail factor and the oldest age-to-age factor and projects the total growth over the remaining valuations.
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.
To choose which development factor to use for projecting claims for future years, any of the following can be considered
- average of all the development factors can be taken or
- as a conservative measure, the largest development factor for any development year can be taken or
- weighted average can be taken.
Points to note in LDFs
You probably notice a few interesting things with this triangle in the exercise. 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