Loss simulations and confidence level analyses are important tools when budgeting for projected losses in the upcoming year. The projected loss pick determined by an actuary provides the expected or average value of losses, but it is also important to understand the volatility around the projected losses or to compare the effects of various per-occurrence and aggregate limits on the projected losses. For example, a confidence level analysis could assist in:

• Budgeting the self-insured or deductible portion of losses. Often, companies budget at a level higher than expected to minimize the impact of a bad year on their balance sheet.
• Determining the reasonableness of quoted premium compared to the company’s loss history.
• Determining the effect of various per-occurrence or aggregate limits on projected losses and appropriate risk margins at each scenario.

A confidence level analysis is a key component to a captive feasibility study. Information provided assists in making important decisions such as:

• Determining initial premium and capital contributions.
• Determining the potential impact of higher than expected losses in the first year(s) of the captive.
• Verifying to captive regulators that premium and capital contributions are reasonable and that risk transfer is taking place.
• Testing the effect on the stability of losses by adding new coverages or members to a captive portfolio.

One way the simulation process may work is by first selecting an average (or mean) frequency and severity for the projected year using traditional actuarial techniques, assuming sufficient historical data is available. Historical loss data is then reviewed to determine an appropriate distribution and other parameters such as standard deviation for both frequency and severity. A lognormal distribution is often used when simulating severity since it is positively skewed. A Poisson or negative binomial distribution is often used for frequency. Additional distributions may be used in other cases, such as a binominal distribution to simulate the frequency and a normal distribution to simulate the severity for a catastrophic claim or other low frequency and high severity exposure.

After initial parameters are determined, a software program can be used to generate a random frequency (or claim count) and a severity (or incurred claim value) for each of the claims based on the distributions selected. Simulated losses are capped at any per occurrence or aggregate limits and the total is recorded. The process is then repeated a large number of times (5,000 to 10,000 iterations). The law of large numbers implies that the average of simulated losses for a large number of iterations (or years) is a close approximation of the expected losses for the projected year. Total losses for each iteration are then ranked smallest to largest and estimates by confidence level are summarized. The estimate at each confidence level is the amount that should be adequate to fund losses x% of the time. This aggregate distribution provides an overall picture of the expected losses and confidence level estimates around the expected losses.

A limitation of the statistical model is that a concept known as parameter risk is often not included in the calculation of the aggregate distribution. Parameter risk is the risk associated with the possible incorrect estimate of the frequency and severity and other parameters used as input for the model. Additionally, company information, industry data or professional judgment are often used in selecting input parameters when sufficient historical loss data is not available. These limitations should be understood and considered when relying on the loss simulation and confidence level analysis.

For further reading, download our "Confidence Interval Analysis Snapshot" from our free resource portal at www.SIGMAactuary.com/resources.

SIGMA completes confidence level analyses for clients in a wide range of industries. Contact Lori Ussery at Lori@SIGMAactuary.com or our President, Al Rhodes at AL@SIGMAactuary.com.