ILF (Increased Limit Factors) for Liability Insurance
How increased limit factors are calculated and used in liability insurance pricing.
What Are Increased Limit Factors?
Increased Limit Factors (ILFs) express the relative cost of providing higher liability limits compared to a base limit, which is typically $100,000 per occurrence for general liability and $25,000 for auto liability. An ILF of 2.0 at the $1 million limit means that coverage at that limit is expected to cost twice the base limit premium. ILFs are derived from the size-of-loss distribution, which describes the probability and severity of claims at different dollar amounts.
ILFs are central to liability insurance pricing because they allow an insurer to price any limit of coverage from a single base rate. The base rate captures the expected cost of claims up to the base limit, and the ILF multiplies that cost to account for the additional exposure when higher limits are offered. Without ILFs, insurers would need separate rate filings for every limit they offered, which would be impractical given the range of limits available in the market.
The Size-of-Loss Distribution
The foundation of any ILF calculation is the size-of-loss distribution, which describes the probability of claims reaching various dollar amounts. Actuaries analyze historical claims data to fit a parametric distribution that characterizes the tail behavior of losses. Commonly used distributions include the lognormal, Pareto, mixed exponential, and Weibull distributions. The choice of distribution matters most in the tail, where data is sparse but the financial impact is significant.
A key property of liability losses is that they are heavily right-skewed. Most claims settle for modest amounts, but a small percentage result in very large payments. For general liability, roughly 80% of claims may settle below $50,000, while the top 1% of claims may account for 20% or more of total dollars. This concentration of cost in the tail is what makes ILF calculations both important and challenging.
Calculating ILFs
The basic ILF formula divides the expected limited average severity (LAS) at the desired limit by the LAS at the base limit. The limited average severity at limit L equals the expected value of losses capped at L. Mathematically, LAS(L) equals the integral from zero to L of the survival function S(x) dx, where S(x) is the probability that a claim exceeds amount x.
For example, if the LAS at the $100,000 base limit is $15,000 and the LAS at the $500,000 limit is $22,500, the pure premium ILF at $500,000 is 22,500 divided by 15,000, which equals 1.50. This means the expected loss cost at a $500,000 limit is 50% higher than at the base limit. Notice that even though the limit increased by a factor of five (from $100,000 to $500,000), the ILF only increased by 50%. This reflects the decreasing probability of losses in higher layers.
Adjustments to Pure Premium ILFs
Pure premium ILFs based solely on loss costs must be adjusted before they are used in practice. The most important adjustment is for allocated loss adjustment expenses (ALAE), which are defense costs and other expenses assignable to individual claims. ALAE tends to increase with claim size because larger claims are more likely to involve litigation, expert witnesses, and prolonged legal proceedings. Actuaries model the relationship between ALAE and loss using either an additive approach (ALAE expressed as a percentage of loss by size-of-loss range) or a multiplicative approach.
A risk load is also added to reflect the increased uncertainty associated with higher limits. Claims in higher layers are less frequent and more variable, so the insurer requires additional compensation for bearing that volatility. The risk load typically increases the ILF for higher limits by 5% to 15% relative to the pure premium ILF. Finally, expense loadings may be adjusted if certain fixed expenses do not scale proportionally with the limit of coverage.
Properties of ILF Tables
Well-constructed ILF tables exhibit several characteristic properties. First, ILFs increase as the limit increases because higher limits cover a broader range of potential losses. Second, ILFs increase at a decreasing rate, meaning the marginal cost of each additional dollar of coverage declines as the limit gets higher. This is because the probability of losses in successively higher layers decreases. Third, ILFs should be internally consistent, meaning the implied cost of any excess layer can be derived from the difference between ILFs at the top and bottom of the layer.
ISO publishes standard ILF tables for major liability lines, including general liability, commercial auto, and products liability. These tables are widely used as benchmarks, though individual insurers may develop proprietary ILFs that reflect their own claims experience and risk appetite. ILF tables are typically updated periodically to reflect changes in the severity distribution driven by inflation, legal environment changes, and shifts in the mix of business.
Common Pitfalls
One frequent mistake is using an ILF table that was developed for a different line of business. The severity distribution varies significantly across lines. General liability claims have a different tail than auto liability or professional liability claims, and applying the wrong ILF table can produce materially incorrect pricing. Another pitfall is failing to update ILFs for trend. As inflation and social inflation push claim costs higher, the size-of-loss distribution shifts, and ILFs developed from older data may understate the cost of higher limits.
Actuaries should also be cautious about the impact of policy provisions on ILFs. Defense costs may be inside or outside the policy limit, and this distinction significantly affects the ILF calculation. When defense costs erode the policy limit (defense inside limits), the effective limit available for indemnity payments is reduced, producing lower ILFs than a defense-outside-limits structure.
Study Tips
For exam preparation, practice calculating ILFs from a given severity distribution. Understand how to compute limited average severities using the survival function. Be comfortable explaining why ILFs increase at a decreasing rate and how this relates to the tail of the loss distribution. Know the adjustments applied to pure premium ILFs, including ALAE, risk loads, and expense modifications. Review the properties that a well-formed ILF table should exhibit and be prepared to identify inconsistencies. Finally, understand how inflation and changes in the legal environment affect ILF tables over time.