A Practitioner’s Guide to Adjusting for “Limits Drift” in Experience Rating

Eric Dynda; Neil Bodoff; Adam Carvalho

1. Introduction

1.1. Research context

Reinsurance pricing actuaries currently do not have a widely adopted approach to adjust for the impact of shifting policy limits over time on experience rating. This topic has become increasingly relevant following changes in policy limit appetites implemented by casualty insurance carriers during the late 2010s and early 2020s, with many market participants significantly altering the policy limit distribution of their portfolios. The shifts observed in the limit profiles of these portfolios negatively impacted pricing actuaries’ ability to accurately price excess of loss reinsurance layers using historical experience data. The increased uncertainty in pricing caused by the failure of existing experience rating techniques to account for shifts in policy limit profiles has created demand for alternative approaches. Appendix A contains a brief survey of previous literature on the topic.

1.2. Objective

This paper introduces an adjustment factor to incorporate into the experience rating process for casualty excess of loss reinsurance pricing that enables the pricing actuary to calculate a more accurate prospective experience loss cost for a given reinsurance layer.

1.3. Outline

The remainder of the paper proceeds as follows. Section 2 discusses the conceptual background of the traditional experience rating approach and its failure to properly address shifts in limits over time. Section 3 introduces the solution of limits drift factors to be added to the experience rating process. Section 4 explains the calculation and application of limits drift factors, and Section 5 provides a worked example. Section 6 covers some advanced considerations, including key assumptions and limitations of the approach. Appendix A discusses previous literature.

2. Background and failure of traditional experience rating

In the context of pricing excess of loss reinsurance layers, the fundamental goal of experience rating is to bring historical loss and premium to current level to estimate the prospective expected ultimate loss costs for a reinsurance layer. Actuaries have developed various techniques to accomplish the goal of bringing historical data to current level. Examples include the following:

Loss trending brings historical losses to current level by applying loss severity and frequency trend factors over time.
Premium on-leveling brings historical premium to current level based on changes in rating and the impact of exposure-base inflation over time.
Loss development factors account for future development on historical claims that have not yet been reported or fully reserved due to the lag in claims reporting, reserving, and settlements.

These techniques are all standard components of the traditional experience rating process in casualty reinsurance pricing. After these techniques have been applied, the historical data is assumed to be sufficiently transformed to the current level and therefore predictive of future results. These trended, on-leveled, and developed layer loss costs are then averaged across a set of historical years to obtain a final prospective expected loss estimate for the layer.

2.1. Failure of traditional experience rating under a limits drift scenario

The traditional excess of loss layer experience rating process described above works well for portfolios with consistent limit profiles over time, but it fails when limit profiles change significantly over time. Significant changes in limit profiles over time can result in a drastically different level of exposure, or the proportion of total ground-up expected loss, in a given layer under the current profile compared to the historical years being analyzed.

For example, consider a simplified scenario in which an actuary is seeking to derive an expected loss estimate for a $1 million excess of $1 million ($1M xs $1M) layer for a portfolio. The actuary has experience data from the most recent 10 years. For the early years in the experience dataset, the portfolio had a distribution of 50% policies at $1 million limits and 50% policies at $2 million limits. Recently, the insurer implemented a change in appetite for the portfolio, which resulted in a gradual move toward writing smaller limits, so that the current limit profile for the portfolio now consists of 75% policies at $1 million limits and 25% policies at $2 million limits. From the perspective of the $1M xs $1M layer, we can observe that the proportional percentage of policies with exposure to the layer (i.e., policies with limits greater than $1 million) has been cut in half, from 50% of the total to 25% of the total between an older historical year and the current year. All else being equal, this shift in limits will lead to a smaller proportional share of total ground-up loss breaching the $1M xs $1M layer, and, correspondingly, a greater share of total ground-up loss remaining below the layer.

In this scenario, because the excess layer experience of the historical years occurred under a historical limit profile that differs significantly from the go-forward limit profile, and because existing experience rating techniques used to bring the historical data to current level (loss trend, premium on-level, loss development) do not have a mechanism for adjusting for changes in policy limit profiles, the mechanical experience rating indication will be non-predictive. The fundamental premise of experience rating—that all historical data has been transformed to current level—will be violated unless the actuary also adjusts for changes in the policy limits utilization in the portfolio.

2.2. Common current approaches

Shifting limits exposure to an excess layer over time in insurance portfolios, which we refer to as “limits drift,” is a common phenomenon encountered in the world of casualty excess of loss reinsurance pricing. Historically, actuaries have often relied on makeshift or incomplete fixes to address the inaccuracy of traditional experience rating techniques under a limits drift scenario. For example, the actuary might adjust the selection period to give weight only to the most recent years, or they might apply varying credibility-weighting factors to older years versus more recent years. A second approach could be to extrapolate the time series of experience indications forward into the future, assuming a trend line can be fit from older years to newer years. These adjustments can help dampen the impact of limits drift, but they suffer from being ad hoc, and excess of loss data is often not robust enough to rely on a shorter-term view or properly fit an extrapolated curve. Another possible approach could be to restate historical policy limits to cap trended claims where these policies would now be written with lower (or higher) limits under the current appetite. This approach works best for full, “clean” shifts in limit appetite but is not fit for purpose for partial shifts in the portfolio in which some limits are still written at historical levels. Another approach involves accounting for the change in exposure by making an adjustment to the a priori estimate of expected loss when using the Bornheutter–Ferguson loss development method on the experience. However, the Bornheutter–Ferguson a priori will have negligible impact on the oldest, most developed experience years, which are often the most skewed by limits drift. This method too suffers from being ad hoc. Finally, the simplest approach is for the actuary to reduce the credibility given to experience rating in favor of exposure rating when selecting a final loss cost; this avoids rather than confronts the experience rating task of adjusting historical data to current level. While the above approaches can all help the actuary arrive at a more accurate final expected loss pick for the layer, they are indirect or incomplete solutions and are ad hoc, unreliable, and unquantifiable. The problem remains that, with the current actuarial toolkit, practitioners are not equipped to properly adjust for limits drift scenarios when bringing historical experience to current level in experience rating.

3. Solution: “Limits drift factors” as an additional tool in the experience rating toolkit

We propose adding a new technique to the actuary’s experience rating toolkit that explicitly accounts for shifting policy limits in an insurance portfolio. To do so, we start by measuring the portion of expected loss in the excess layer as a percentage of the total expected loss using exposure rating techniques. We can then measure how this layer’s portion of expected loss changes as the policy limit profile shifts over time. We call the parameters that measure this change “limits drift factors.” The proposed limits drift factors are derived by calculating the portion of expected loss in the excess layer for each historical year via exposure rating using both the historical limit profile and the current limit profile and then calculating a relativity, as described in Section 4. The resulting factors can be applied directly to the trended layer losses derived from traditional experience rating to bring the losses to the current limit exposure level for the layer. Limits drift factors are distinct from but complementary to the existing adjustment factors for loss trend, premium on-leveling, and loss development that are already used in traditional experience rating. The application of limits drift factors to adjust the historical layer losses to reflect the prospective view of limits exposure allows the actuary to transform the data to current level in a more complete way, increasing the historical year’s predictiveness of future results. The limits drift adjustment technique is a direct, versatile, complete solution: It can account for limits going in either direction (up or down), it can accurately account for both partial and complete shifts in the types of limits written over time, and it also accounts for changes in policy attachment points/self-insured retentions and share percentage changes over time to the extent that they are used in exposure rating.

4. Calculating and applying limits drift factors

Two key pieces of data are required to calculate limits drift factors:

Policy limit profiles evaluated as of each historical year being analyzed
The current exposure increased limits factor (ILF)/severity curve used for exposure rating the portfolio

With this data in hand, the calculation of limits drift factors follows two simple steps:

Use traditional exposure rating formulas and the current exposure ILF/severity curve to obtain the ILF allocated percentage share of total loss in the layer of interest for each individual historical year’s limit profile, and do the same for the prospective limit profile.
Calculate the ratio of the allocated percentage share of loss in the layer under the prospective limit profile to the allocated percentage share of loss in the layer under the historical year’s limit profile to obtain the limits drift factor for the historical year. This will be the adjustment factor applied to the historical year’s layer losses.

For step 1, we refer to the methodology and formulas for exposure rating described in Section 3A(b) of Clark’s (2014) Basics of Reinsurance Pricing paper, currently on the Casualty Actuarial Society (CAS) Exam 9 syllabus as of 2025. In the Clark paper, the calculated “exposure factor” is meant to represent the percentage of total expected ground-up loss allocated to the layer of interest for a given policy. This figure is derived using ILF relativities based on policy limit and attachment points and the layer of interest. If that exposure factor is multiplied by a ground-up expected loss ratio assumption, it equates to an exposure loss cost for the layer.

When adjusting for changes in policy limits, we seek to adjust for the portion of loss in the excess layer, which allows us to isolate the specific impact of policy limit changes independent of other changes such as trending losses and on-leveling premiums. Therefore, when calculating limits drift factors, we use the exposure factor as is, without converting it to an exposure loss cost. If we compare the exposure factor derived from a historical year’s limit profile to the exposure factor derived from the current year’s limit profile, we will obtain an estimate of how much the change in limit profiles over time has affected the expected percentage of total ground-up loss in the layer. Therefore, after the actuary has used the method described in Clark to obtain an overall exposure factor for the layer of interest as a percentage of ground-up subject premium based on the limit profiles of the years of interest and the current exposure ILF/severity curve, only one additional formula is needed to obtain the limits drift factor. The formula for the limits drift factor for a given historical year can be expressed mathematically as follows:

\[\mathbf{Limits\ Drift\ Factor_{hist} = EF_{proj} / EF_{hist},}\]

where EF_hist is the exposure factor for the historical year derived from exposure rating using the historical year’s policy limit profile and current ILF/severity curve, and EF_proj is the exposure factor derived from exposure rating using the current policy limit profile and current ILF/severity curve.

Once limits drift factors have been calculated for all historical years, they can be applied as a final adjustment to experience rating of the layer loss cost by multiplying them by the trended ultimate layer loss of the historical year. This adjustment culminates the process of transforming historical loss to current level so that not only are losses trended and developed and premiums on-leveled, but losses are also adjusted for changes in underlying policy limits utilization. The actuary can then divide the limits drift–adjusted trended layer losses by the on-leveled premium to obtain the final limits drift–adjusted experience loss cost for the layer indicated by that historical year.

5. Worked example

In this section, we will use a scenario similar to that described in Section 2.1 to illustrate the application of limits drift factors to a traditional experience rating analysis. Suppose we are pricing a $1M xs $1M layer for a portfolio. We have 11 years of historical premium and layer loss data for the portfolio. We also have historical data at the portfolio and/or industry level that has allowed us to make reasonable assumptions for on-level factors, loss trend, and loss development factors. Using these assumptions, we have performed a traditional experience rating analysis as expressed in Table 5.1. Excluding the newest policy year, the analysis results in a calculated expected loss cost for the $1M xs $1M layer of 13.5% using a 10-year average, or 9.0% using a 5-year average.

Table 5.1.Traditional experience rating analysis results for $1M xs $1M layer.

$1M xs $1M Layer Experience Rating
Policy Year	Written Premium ($000s)	On-Level Factor	On-Level Written Premium ($000s)	Reported Layer Loss ($000s)	Trend Factor	Trended Layer Loss ($000s)	Loss Dev’t Factor	Chain Ladder Trended Ultimate Layer Loss ($000s)	Chain Ladder Trended Ultimate Layer Loss %
	(1)	(2)	(3) = (1) * (2)	(4)	(5)	(6) = (4) * (5)	(7)	(8) = (6) * (7)	(9) = (8) / (3)
2015	10,000	1.34	13,439	3,400	1.36	4,614	1.00	4,622	34.4%
2016	10,500	1.30	13,700	760	1.32	1,001	1.00	1,005	7.3%
2017	11,025	1.27	13,966	2,500	1.28	3,198	1.01	3,221	23.1%
2018	11,576	1.23	14,237	1,200	1.24	1,490	1.01	1,512	10.6%
2019	12,155	1.19	14,514	2,100	1.21	2,532	1.03	2,605	18.0%
2020	12,763	1.16	14,796	1,700	1.17	1,990	1.06	2,107	14.2%
2021	13,401	1.13	15,083	750	1.14	852	1.12	956	6.3%
2022	14,071	1.09	15,376	1,650	1.10	1,821	1.26	2,289	14.9%
2023	14,775	1.06	15,674	300	1.07	321	1.58	508	3.2%
2024	15,513	1.03	15,979	400	1.04	416	2.50	1,040	6.5%
2025	16,289	1.00	16,289	100	1.00	100	5.00	500	3.1%
2015–2024	125,779		146,764	14,760		18,235		19,865	13.5%
2020–2024	70,523		76,907	4,800		5,400		6,900	9.0%

Separate from the historical experience data, we have received information on the exposure profile of the portfolio over time, including limit profiles for the past 11 years. Observing this data, we note that 11 years ago, the portfolio limit profile consisted of 50% policies at $1 million limit and 50% policies at $2 million limit. Since then, the insurer has implemented a change in appetite for the portfolio, which resulted in a move toward writing smaller limits, so that the current limit profile for the portfolio now consists of 75% policies at $1 million limits and 25% policies at $2 million limits. Table 5.2 illustrates the exposure profile limit distribution over time.

Table 5.2.Portfolio exposure profile.

Policy Year	Written Premium (WP) ($000s)	WP at $1M Limit ($000s)	WP at $2M Limit ($000s)	WP at $1M Limit %	WP at $2M Limit %
2015	10,000	5,000	5,000	50%	50%
2016	10,500	5,355	5,145	51%	49%
2017	11,025	5,954	5,072	54%	46%
2018	11,576	6,598	4,978	57%	43%
2019	12,155	6,807	5,348	56%	44%
2020	12,763	7,275	5,488	57%	43%
2021	13,401	8,711	4,690	65%	35%
2022	14,071	9,850	4,221	70%	30%
2023	14,775	10,638	4,137	72%	28%
2024	15,513	11,480	4,033	74%	26%
2025	16,289	12,217	4,072	75%	25%

Observing the trend in this exposure profile data leads us to believe that our loss cost derived from experience rating in Table 5.1 may be nonpredictive, especially when using the older years. The older years’ experience was based on a profile with significantly more exposure to higher-limit policies. At this junction, we consider the possibility of credibility weighting the historical years in our experience rating, giving relatively more weight to recent years than older years, or throwing out the older years entirely and just selecting the shorter five-year average experience rating indication. This would give more weight to years that are closer to the current limit profile and should dampen the impact of the limit shifts. But we run into several issues with this approach:

There is more uncertainty in the ultimate loss estimates for more recent years, which rely more heavily on development factor assumptions.
We observe a high amount of year-to-year volatility in the estimated layer ultimates in the historical results, decreasing our confidence in the robustness of a shorter-term view.
Credibility weighting of historical years requires judgmental assumptions regarding which credibility factors to use for each year.

The ideal method would instead (1) allow us to continue including older years in our analysis by increasing their predictiveness and bringing them closer to “today’s level,” (2) be a scientific adjustment without requiring judgmental assumptions, and (3) explicitly account for the changes in policy limits over time. The limits drift approach satisfies these criteria. So, we decide to move ahead with calculating limits drift factors to adjust the experience rating results.

First, we run each historical year’s limit profile through the exposure rating formulas using the selected ILF/severity curve to exposure rate the current profile and obtain the ILF allocated percentage of total loss in the $1M xs $1M layer for each of these profiles. Correspondingly, we calculate the exposure factor for the $1M xs 0 layer, which for a portfolio with limits up to $2 million is simply the remainder of the exposure not allocated to the $1M xs $1M layer. These ILF allocated percentages of total loss for each historical year’s profile, plus the current profile, are shown in Table 5.3. For calculation purposes in this example, we have used a Pareto curve with alpha parameter of 0.5 to obtain the ILFs.

Table 5.3.Allocated percentage of loss in $1M xs $1M layer via exposure rating.

ILF Table			Layer Exposure Factors (% loss allocated to layer)
Limit	ILF		Limit	$1M xs 0	$1M xs $1M
$1M	1.000		$1M	100.0%	0.0%
$2M	1.414		$2M	70.7%	29.3%
Historical Limit Profile – Exposure Factors
Policy Year	Written Premium at $1M Limit %	$1M xs $1M Exposure Factor for $1M Limit	Written Premium at $2M Limit %	$1M xs $1M Exposure Factor for $2M Limit	$1M xs $1M Portfolio Exposure Factor	$1M xs 0 Portfolio Exposure Factor
	(1)	(2)	(3)	(4)	(5) = (1) * (2) + (3) * (4)	(6) = 1 – (5)
2015	50%	0.0%	50%	29.3%	14.6%	85.4%
2016	51%	0.0%	49%	29.3%	14.4%	85.6%
2017	54%	0.0%	46%	29.3%	13.5%	86.5%
2018	57%	0.0%	43%	29.3%	12.6%	87.4%
2019	56%	0.0%	44%	29.3%	12.9%	87.1%
2020	57%	0.0%	43%	29.3%	12.6%	87.4%
2021	65%	0.0%	35%	29.3%	10.3%	89.7%
2022	70%	0.0%	30%	29.3%	8.8%	91.2%
2023	72%	0.0%	28%	29.3%	8.2%	91.8%
2024	74%	0.0%	26%	29.3%	7.6%	92.4%
2025	75%	0.0%	25%	29.3%	7.3%	92.7%

Note: $1M xs $1M exposure factor for $2M limit = (ILF_$2M – ILF_$1M) / ILF_$2M = 29.3%.

What is notable in Table 5.3 is that during, for example, 2016, the historical losses in the $1M xs $1M layer arose from a portfolio in which 14.4% of all loss exposure was allocated to this layer, but the current go-forward portfolio is clearly written such that loss exposure allocated to the $1M xs $1M layer is only 7.3%, which is profoundly different from the historical percentage. To not adjust for this fact would be a violation of the key principle of experience rating and actuarial pricing.

The next step is to convert these percentages into a limits drift factor for each historical year by calculating the ratio of the allocated percentage of total loss in the layer under the prospective profile to the allocated percentage of total loss in the layer under the historical profile, as shown in Table 5.4. We again calculate factors for both the $1M xs $1M layer and the $1M xs 0 layer to illustrate the reallocation of expected loss between the layers.

Table 5.4.Calculation of limits drift factors.

$1M xs $1M Limits Drifts Factors ($000s)				$1M xs 0 Limits Drift Factors ($000s)
Policy Year	$1M xs $1M Portfolio Exposure Factor (Historical)	$1M xs $1M Portfolio Exposure Factor (Current)	$1M xs $1M Limits Drift Factor	Policy Year	$1M xs 0 Portfolio Exposure Factor (Historical)	$1M xs 0 Portfolio Exposure Factor (Current)	$1M xs 0 Limits Drift Factor
	(1)	(2)	(3) = (2) / (1)		(1)	(2)	(3) = (2) / (1)
2015	14.6%	7.3%	0.500	2015	85.4%	92.7%	1.086
2016	14.4%	7.3%	0.510	2016	85.6%	92.7%	1.082
2017	13.5%	7.3%	0.543	2017	86.5%	92.7%	1.071
2018	12.6%	7.3%	0.581	2018	87.4%	92.7%	1.060
2019	12.9%	7.3%	0.568	2019	87.1%	92.7%	1.064
2020	12.6%	7.3%	0.581	2020	87.4%	92.7%	1.060
2021	10.3%	7.3%	0.714	2021	89.7%	92.7%	1.033
2022	8.8%	7.3%	0.833	2022	91.2%	92.7%	1.016
2023	8.2%	7.3%	0.893	2023	91.8%	92.7%	1.010
2024	7.6%	7.3%	0.962	2024	92.4%	92.7%	1.003
2025	7.3%	7.3%	1.000	2025	92.7%	92.7%	1.000

Note: $1M xs $1M limits drift factor for 2015 = EF₂₀₂₄ / EF₂₀₁₄ = 7.3% / 14.6% = 0.500.

Table 5.5 shows how these limits drift factors can then be applied to the trended ultimate layer losses of each historical year and how this translates into the new adjusted experience loss cost estimate for the layer. Note that on-leveled premiums are not adjusted. The goal of the limits drift method is not to adjust the total base of ground-up on-leveled premium and loss, but rather to adjust the allocation of the total ground-up expected loss between the reinsurance layer being priced and the retained layer; this need for reallocation of layer loss is caused by changes in the portfolio’s distribution of limits and attachments. In other words, the ground-up expected loss as a percentage of premium (ground-up loss ratio) is not being adjusted, but rather the proportion of ground-up expected loss that is projected to fall into the reinsurance layer.

Table 5.5.Limits drift factors applied to experience rating.

$1M xs $1M Layer Experience Rating with Limits Drift Adjustment
Policy Year	On-Level Written Premium ($000s)	Chain Ladder Trended Ultimate Layer Loss ($000s)	Chain Ladder Trended Ultimate Layer Loss %	Limits Drift Factor	Adjusted Chain Ladder Trended Ultimate Layer Loss ($000s)	Adjusted Chain Ladder Trended Ultimate Layer Loss %	Differential Adjusted vs. Unadjusted
	(1)	(2)	(3) = (2) / (1)	(4)	(5) = (2) * (4)	(6) = (5) / (1)	(7) = (6) / (3) – 1
2015	13,439	4,622	34.4%	0.500	2,311	17.2%	-50.0%
2016	13,700	1,005	7.3%	0.510	513	3.7%	-49.0%
2017	13,966	3,221	23.1%	0.543	1,750	12.5%	-45.7%
2018	14,237	1,512	10.6%	0.581	879	6.2%	-41.9%
2019	14,514	2,605	18.0%	0.568	1,480	10.2%	-43.2%
2020	14,796	2,107	14.2%	0.581	1,225	8.3%	-41.9%
2021	15,083	956	6.3%	0.714	683	4.5%	-28.6%
2022	15,376	2,289	14.9%	0.833	1,908	12.4%	-16.7%
2023	15,674	508	3.2%	0.893	454	2.9%	-10.7%
2024	15,979	1,040	6.5%	0.962	1,000	6.3%	-3.8%
2025	16,289	500	3.1%	1.000	500	3.1%	0.0%
2015–2024	146,764	19,865	13.5%		12,202	8.3%	-38.6%
2020–2024	76,907	6,900	9.0%		5,269	6.9%	-23.6%

Change in expected loss cost after limits drift adjustment = –38.6% in the 10-year average, or –23.6% in the five-year average.

Looking at both the 10-year and five-year average results of the adjusted experience rating, we observe that the adjusted experience loss cost estimate obtained after applying limits drift factors is significantly lower than that obtained by the original experience rating procedure. This reflects the dramatic shift toward lower limits. Generally, the magnitude and directional impact of the limits drift adjustment will be relative to the magnitude and direction in which the layer exposure has shifted over time in the portfolio. We also observe that the 10-year average and five-year average indications have come closer together as older years have been adjusted more than newer years, decreasing the differential of potential outcomes.

Ratio of five-year to 10-year average: Original analysis = 0.66; limits drift adjusted analysis = 0.82

As a final step, we can now bring this adjusted experience loss cost indication into our broader loss cost analysis for the excess of loss layer to make a final selection. For this exercise, we assume that an exposure rating analysis performed separately produces an expected loss cost of 8.8% and that a separate actuarial credibility analysis using the unadjusted experience produces a 55% experience credibility estimate for a 10-year average and a 35% experience credibility estimate for a five-year average. Comparing our unadjusted versus limits drift–adjusted experience loss costs, we see that the experience indication after adjustment now falls below the exposure indication (Table 5.6). In this scenario, the limits drift adjustment has brought us from a view where experience rating implies a credibility-weighted surcharge on exposure to one that implies a credibility-weighted discount on exposure.

Table 5.6.Final loss cost selection.

Analysis Version	Exposure Rating Loss Cost	Experience Rating Loss Cost	Credibility to Experience	Blended Loss Cost
	(1)	(2)	(3)	(4)
Unadjusted (10-year avg.)	8.8%	13.5%	55%	11.4%
Unadjusted (5-year avg.)	8.8%	9.0%	35%	8.9%
Limits Drift Adjusted (10-year avg.)	8.8%	8.3%	55%	8.5%

One could argue that applying a limits drift adjustment to historical data, while necessary, could make the historical data less credible; in this case, the actuary could use judgment to refine the selected credibility weight to apply to the adjusted experience rating, as illustrated in Table 5.7.

Table 5.7.Final loss cost selection with credibility refinement.

Analysis Version	Exposure Rating Loss Cost	Experience Rating Loss Cost	Credibility to Experience	Blended Loss Cost
	(1)	(2)	(3)	(4)
Unadjusted (10-year avg.)	8.8%	13.5%	55%	11.4%
Unadjusted (5-year avg.)	8.8%	9.0%	35%	8.9%
Limits Drift Adjusted (10-year avg.)	8.8%	8.3%	45%	8.6%

In Table 5.7, we judgmentally estimate that the significant changes in the policy limits utilization, which creates the need to adjust historical data via limits drift adjustment, leads us to reduce selected credibility slightly, to 45%, resulting in a final blended loss cost of 8.6%.

These final steps illustrate that if we were to have used the unadjusted analysis, any selection for credibility weighting between exposure and unadjusted experience would not be able to capture the full effect of limits drift, as even 0% weight to the unadjusted experience would still have produced a higher loss cost than the credibility-blended loss cost after limits drift adjustment. The most suitable approach is to explicitly calculate the adjusted experience rating via limits drift factors and then to apply credibility and judgment.

We also observe that the limits drift–adjusted 10-year average is close to, but still below, the unadjusted five-year average. The 10-year average after adjusting for limits drift gives us additional support and confidence in our pick compared to if we had used only the unadjusted five-year average, which is subject to a higher level of uncertainty as a shorter-term average.

6. Advanced considerations

6.1. Key assumptions and limitations

Mathematically, the limits drift adjustment approach relies on the implicit assumptions that the ground-up loss ratio and historical rate change are consistent across limits in the portfolio being analyzed. Reliance on these assumptions is not a major limitation of the method because these simplifying assumptions are common and widespread, and they are typically baked into most excess of loss reinsurance pricing analyses—historical rate changes and ground-up loss ratios are usually not split according to size of policy limit. Nevertheless, the savvy actuary should be aware of this limitation.

Another underlying assumption of the limits drift adjustment method is that the adjustment being applied to historical losses is representative of the policies that produced the claims in those historical years. If limits exposure over time for a subsection of the portfolio that has historically produced many layer claims is following a different pattern than another subsection of the portfolio that is loss-free, this may influence the actuary’s judgment of the appropriateness of an adjustment based on limits applied at the total portfolio level. The nature and source of known historical claims should be appropriately considered and allowed for when making any portfolio-level adjustments, such as adopting the limits drift approach proposed in this paper. Judgment should be used to evaluate whether different subsections of the portfolio are behaving differently than others; this should also be considered for experience rating generally when choosing the level of granularity at which to segment the portfolio.

6.2. Order of application of limits drift factors

Another issue to consider is whether it is more appropriate to apply limits drift factors to trended layer losses before or after developing the losses to ultimate. Under the simple chain ladder loss development method, these two approaches will produce identical results. However, if layer incurred but not reported (IBNR) claims are being calculated with a development method that uses an a priori estimate of expected loss, such as the Stanard-Buhlmann/Cape Cod method, then different choices of when to apply the factors can result in somewhat different final adjusted ultimate loss estimates. If the factors are applied to the trended ultimate losses after development, then IBNR will have been calculated on an unadjusted basis and then adjusted after the fact by the limits drift factor. If the factors are instead applied to the trended losses before development, then the calculation of the layer IBNR of the historical year and the a priori estimate used to derive that IBNR figure will incorporate the impact of the limits drift adjustment, and no further adjustment will need to be made to the ultimate loss estimate. The authors of this paper take the position that both methods can be appropriate. In our testing, the difference in results between the two approaches is minimal, but the actuary may wish to sensitivity test and choose the method they believe is most appropriate for the situation.

6.3. Other drifts

The authors of this paper acknowledge that there are other “drifts” that can potentially affect the accuracy and reliability of experience rating. These include changes in risk type, coverage, mix of business/industry appetite, etc., which are not explicitly adjusted for by traditional experience rating and therefore may prevent historical data from being brought fully to current level, similar to the impact of limits drift. We consider these other drifts to be outside the scope of this paper, which is focused only on adjusting for the impact of shifting limit profiles over time. We hope to inspire more research on ways to adjust for other drifts to further expand the actuary’s experience rating toolkit for additional scenarios.

A Practitioner’s Guide to Adjusting for “Limits Drift” in Experience Rating

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