Planning for the Variability of Future Losses

Lloyd Kelley

Decisions about risk financing are often made using one assumption about the retained losses, or at best, using a range of claims.  Claims costs for future periods are a forecast that will vary to some degree. The amount of that variation is measured by estimating the confidence interval based on the probability distribution calculated from the insured’s loss experience.  Based on this distribution, an array of random claims costs is estimated to make the decision based on a realistic range of future claims costs based on actual loss experience.Definitions

Since loss financing decisions effect the cost of risk over several years, especially for liability lines, the forecasted cost of risk is done for a five year period.

The subject of this blog is XYZ – a risk bearing entity writing workers’ compensation, general liability, and auto liability.  For purposes of this blog, a risk bearing entity can be a captive insurance company, a public entity pool, or a small limited purpose insurance company.  Also for this blog, let us assume, XYZ is considering an increase in the per occurrence retention for all lines of coverage.  XYZ’s board wants to know how the proposed increase will affect the solvency and liquidity of XYZ.

The first step in quantifying the future effect of the increased retention is to forecast the potential cost of retained losses.  Three sets of retained loss costs are used as the first step in the forecast.

  1. Base case – forecasts assuming claims costs in each year will be equal to the loss forecast or expected losses.  While we know that losses will vary to some extent, the benchmark case provides a base from which to measure the potential variability of other scenarios.
  2. High variable – in this scenario, claims costs are higher over the five year period than those in the base case.  The costs are not necessarily higher in each year because each year’s cost of claims is a random selection of pure loss rates.
  3. Low Variable – claims costs are lower over the five year forecast period than the base case and, of course, than the high variable.

The loss forecasts are done by estimating the variability of the claims forecast by line.  Then, a pure loss rate for each year is randomly selected for every line based on the insured’s variability pattern.

The loss forecasts are then input into a forecast of XYZ’s financial statements to produce a range of forecasts of the descriptive statistics by which the board measures the solvency and liquidity of XYZ.  The solvency measure is 2:1, net premium: surplus ratio.  The liquidity measure is liquid assets equal to at least 125% of the previous year’s cash outflow.

The charts and graphs embedded in the text show whether XYZ will meet its benchmarks with a range of anticipated claims costs.
The following graph and supporting chart show XYZ’s net premium: surplus for the years 2010-2014 compared to the goal of 2:1.

Graph 1.1

In the Base case and Low variable scenarios, XYZ meets the solvency goal of 2:1 Net premium: surplus. In the High variable case the goal is not met in any year. Based on these forecasts, the board needs to consider:

  • Are they willing to risk the chance of claims costs in the high variable scenario in return for the decreased cost of excess premium and the chance of surplus accumulation in Base case and Low variable?
  • Should they purchase aggregate excess coverage to protect against the loss potential of High variable losses?

The liquidity measure of 125% of the previous year’s cash outflow is shown in the following graph.Graph12

The goal is achieved in the Base case and Low variable scenarios. However, in High variable scenarios, XYZ’s liquid assets fall short of the goal in all years except 2011.

When deciding whether to increase retentions, the board should ask the following questions about the liquidity forecast:

  • Is the goal realistic? The goal of 125% of the previous year’s cash outflow is conservative, but it is set so that unexpected liability settlements or large property claims could be paid.
  • Should the board increase the retention, but arrange for a standby line of credit in case of a liquidity shortfall – High variable claims costs?

As demonstrated in the data above, the cost of risk can vary considerably when claims costs are not exactly as forecasted.

The risk profile of the insured will drive the variability of the claims costs. If an insured has large property or sexual misconduct retentions, the claims costs will vary considerably more than if their retention is limited to workers’ compensation or auto coverage.

These factors should be quantified and discussed in detail with the board and XYZ’s management to make the proper decision about retained risk.

We welcome your feedback by posting a comment, or contact Lloyd at
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© 2012 SIGMA Actuarial Consulting Group, Inc.

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