Property / Casualty Aspects of ERMReserve Risk for Property-Casualty Insurers

Presented byWayne Blackburn, FCAS, MAAAPrincipal and Consulting Actuary

April 30, 2009ERM Symposium

2 April 30, 2009

Loss and Loss Adjustment Expense Reserves for P/C Insurer (or Reinsurer)

Basic Definitions

The amount held by a property-casualty insurer’s to cover all future payments on insured claims that have already occurred as of a specified accounting date.

Depending on the type of business, a large portion of the reserves will be associated with claims that have occurred but aren’t known to the insurer at the time of valuation.

On the balance sheet:Loss and loss adjustment expense (LAE) reserves are net of reinsurance

Usually not discounted for the time value of money

3 April 30, 2009

An ERM Review for a P/C Insurer is Pointless Without Serious Consideration to the Variability of Loss Reserve Outcomes

On most P/C insurers balance sheets, the loss and LAE reserve approaches or exceeds the surplus of the company.

The future loss and LAE cashflows that the insurer has established the reserve for are subject to significant uncertainty.

There is no one set formula for estimating P/C reserves. Actuarial indications and methodology along with management booking decisions must be revisited at each valuation date.

In hindsight, a large proportion of P/C insurer insolvencies are due to inadequate loss and LAE reserves.

4 April 30, 2009

What are the sources of reserve uncertainty?Uncertainty inherent in the claim liability itself. How many claims will be reported? When will the claims will be reported? How much loss and LAE will be paid for any open or yet to be reported claim? And, what is the cashflow of these payments?

Uncertainty in the actuarial estimation process. Reserves are established based on the varying results of different methods. And, are the projection parameters for methods, which are usually based on average levels of historical loss emergence, applicable to future loss emergence?

Uncertainty of legal environment. Future precedent setting cases, changes in coverage interpretations, changes in benefit levels.

5 April 10, 2023

For ERM purposes, we seek the variability of outcomes, not the variability of actuarial estimates

Standard practice for a P/C actuary is to provide a reserve estimate based on different indications from a variety of projection methods. The variance of these indications does not establish a distribution for future possible outcomes.

Furthermore, when forming a dynamic financial / ERM model for a P/C company the actuary will want to simulate cashflows not just reserve variability.

6 April 10, 2023

Quantifying Reserve RiskExample of Measuring the Variability of Reserve Outcomes

General Liability Occurrence business

Historic development triangles of paid and incurred losses (focusing on paid losses for this example)

Net of reinsurance

Estimate a distribution of reserve outcomes using a simulation technique. The simulation process recreates 10,000 versions of data based on the actual historic loss data and the indicated variability of the loss emergence from that data.

7 April 30, 2009

Projected Variability of Runoff General Liability ReservesReviewing historical variability loss data ($000s)

Basic historical paid loss emergence (exposure year by maturity triangle format)

Scaled residual terms following from a static payment model

Uncertainty of loss emergence beyond maturity time frame of compiled data, too. “tail risk”

8 April 30, 2009

Projected Variability of Runoff General Liability Reserves

Tabular results based on 10,000 simulations of future loss cashflows($000s)

Expected mean that might be used to book reserves as of year-end 2007

Outcome distribution that needs to be considered for risk management

9 April 30, 2009

Projected Variability of Runoff General Liability Reserves

10 April 30, 2009

Most P/C insurers have multiple lines of business

Basic process: perform this type of analysis for each line / segment of business. Aggregate reserve distribution derived from correlated sums of individual line of business distribution estimates.

Try to estimate correlation from comparing historical loss cashflows between lines of business.

Reasonably dissimilar lines of business will yield narrower aggregate distributions (% variation from mean) than any single line of business which quantifies the benefit to reserve risk of diversification.

11 April 30, 2009

Practitioner’s point of view on quantifying reserve risk

1. When using historic data for modeling avoid smoothing over “outliers” unless clearly incorrect data compilation.

2. Try to compile as many years of historic data as possible.

3. Do not forget a source of uncertainty stated earlier – changes in legal environment.

Extremely difficult to quantify.Goes back to items (1) and (2) above, a long history of data has a better chance of exhibiting “real world” aberrations.

12 April 30, 2009

Connections Between Reserve Risk and Underwriting Risk

Indicated loss ratio variability following from the prior example

“Best estimate” reserve indications are usually dependent on prior pricing indications (expected loss ratios).

And these expected loss ratios are by no means certain.