Loss Development Methodology

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Loss Development Methodology as described by HB Actuarial Services, Inc.

Complex Calculations Made Easy to Understand

In this article, I perform the final step in the most commonly used actuarial method to estimate loss reserves – loss development. If you need a refresher of any of the preliminary steps–  loss triangle, loss development factor, or loss development factor selection, please review the appropriate article. This post assumes that you are comfortable with all of that already.

The final step of the loss development methodology is constructing a table that looks something like this:

  1 2 3 4 5
Accident Year Paid Losses Age in Years Cumulative Loss Development Factor Estimated Ultimate Losses
(1) x (3)
Estimated Ultimate Outstanding Losses
(4) – (1)
2008            1,167,216 7 1.160            1,353,917              186,701
2009              428,350 6 1.183              506,804                78,454
2010              393,186 5 1.242              488,460                95,273
2011              367,698 4 1.329              488,770              121,073
2012              445,860 3 1.502              669,716              223,856
2013              238,268 2 1.787              425,897              187,629
2014                40,913 1 3.217              131,635                90,722





This part is definitely not rocket science. It is just putting calculations from all the other steps together. Let’s go through it. Column 1 is the latest observation of paid losses. These values are the rightmost value for each row on the loss triangle. They form a diagonal line on the loss triangle and represent the data for the 2014 valuation year.

Column 2 is just the current age of the accident year. This report is using data through December 31, 2014, so the age of 2014 is 1 year and each year prior is a year older.

Column 3 is the cumulative loss development factor based on our selected LDFs in the table here.

Column 4 is just simple math. It’s column 1 times column 3 and represents an estimate of ultimate losses (all the losses that will ever be paid) for that particular accident year.

Column 5 is also simple math. Ultimate losses minus paid losses is outstanding losses. This is an estimate of reserves for the accident year. Based on this methodology, the actuary estimates that ultimately $4,065,200 will be paid for all accidents occurring between 2008 and 2014. Since $3,081,491 has already been paid for these accidents, $983,708 must be reserved for future claim payments.

The walkthrough I have provided during the past four articles shows how the paid loss development methodology can be applied to raw claim data to arrive at an estimate of ultimate losses and loss reserves. The loss reserve approach is also commonly applied to incurred losses (cumulative paid losses plus outstanding loss reserves). It is the same exact methodology except the loss development factors are smaller (because incurred losses are larger). There is still an “ultimate development factor” and a projection of ultimate incurred losses. It is important to be aware that ultimate incurred losses will always equal ultimate paid losses (because ultimately reserves = 0). As a result the paid loss development methodology and the incurred loss development methodology are different techniques used to project the same number.  The actuary may rely on the paid or incurred loss development methodology more depending on whether he believes recent paid or incurred patterns are more predictive of the future.

The final step for the actuary in a loss reserving study is to review the results for this method and other actuarial loss reserving methods and select a “best estimate” of ultimate losses and reserves. This “best estimate” will underlie the actuary’s loss reserve selection and actuarial opinion on loss reserves.

I hope you benefit from this background in the most commonly used actuarial reserving methodology. Your understanding of this methodology will allow you to better understand actuarial reports created for your company.

Find out more about us at www.hbactuarial.com.

Complex Calculations Made Easy to Understand