Loss Development Factor Selection

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

Complex Calculations Made Easy to Understand

The loss development methodology is the most common actuarial reserving methodology around. It is usually the first actuarial method applied to losses to estimate ultimate losses and loss reserves. The loss development methodology requires the construction of a loss triangle and a loss development triangle. If you need a refresher, please click on the links. In this post I’ll be referring to the triangles constructed in the prior two posts.

The first step in loss development factor selection is to add some more features to the loss development triangles such as the average loss development factor for each age and the ultimate loss development factor. Averages are calculated for each particular age down many accident years. These averages represent a first estimate of the number that paid losses must be multiplied by to equal paid losses at the next age. Actuaries base their selections on the average, industry numbers, and their actuarial judgment. Below is our loss development triangle with averages and loss development factor selections:

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
All yrs. Avg. 1.614 1.126 1.057 1.090 1.026 1.038
Industry 2.050 1.221 1.096 1.045 1.034 1.023
Prior 1.750 1.190 1.130 1.070 1.050 1.020
Selected 1.800 1.190 1.130 1.070 1.050 1.020
Cumulative 3.217 1.787 1.502 1.329 1.242 1.183
7th to Ultimate           1.160

 

This loss development factor presentation shows the average factor for the client, the average factor for the industry, and the average factor selected in the prior actuarial review for the client. Actuaries usually consider all three of these factors when selecting loss development factors for the loss development methodology. In the example above, the actuary selected the same loss development factor as used in the last actuarial report for all but the first year. The actuary likely believed that the new information contained in the lowest diagonal of LDFs was not different enough to warrant a change in his loss development factor selections.

In addition to LDFs, the actuary must also select an “ultimate loss development factor” this is the actuary’s estimate of the loss development factor that will result from developing losses from the latest age (age 7 in the example) to the end of time. Another way of looking at it is estimating the number that you will have to multiply age 7 losses to get the ultimate value of paid losses for all claims for that accident year. The example above estimates the ultimate paid loss development factor for age 7 to be 1.160. This ultimate loss development factor generates an estimate of ultimate losses (total losses that will ever be paid) for accident year 2008 to be $1,167,216 x 1.160 or $1,353,971.

Now that a set of loss development factors have been selected, cumulative LDFs can be calculated. These factors are just the product of the selected LDFs going from right to left. For example the age 7 cumulative LDF is 1.160. The age 6 LDF is 1.183= 1.160 x 1.020; the age 5 factor is 1.242 = 1.183 x 1.050. These cumulative factors are used in the loss development methodology and shown below the selected development factors. Read on to see how we use these factors in the loss development methodology.

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Complex Calculations Made Easy to Understand