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The Cost of Financing Insurance - Version 1.0
The ABC Insurance Company is a sizeable commercial lines insurance company. Its goal is to obtain an above-average return on equity by setting profitability targets for each of its underwriting divisions that reflect the cost of capital needed to support each division's contribution to the overall underwriting risk.
While ABC's management recognizes the important role played by regulators and rating agencies in determining an insurer's capital, it feels that controlling the insurer's risk, as measured by its statistical distribution of outcomes, provides a meaningful yardstick that can be used to set profitability targets.
In addition, ABC's management wants to take the following considerations as input into its decisions.
How long must capital be held? The underwriting results for the typical liability line of insurance are not known for several years. As long as there is uncertainty in the final result, some capital must be held. The profitability targets for each line of insurance should reflect the cost of holding capital as the claims are being settled.
How much investment income is generated by the insurance operation? As the insurer is holding capital for the contingency of losses that are higher than expected, it is also earning investment income on its capital. The profitability targets for each line of insurance should also reflect the investment earnings generated by each line of business.
How closely correlated are the losses in the various lines of insurance? The textbook illustrations of the economic value of insurance often assume that insured accidents are independent events. Positive correlation increases the amount of capital needed and hence its cost. This cost should be reflected in the profitability targets for each line of insurance.
What is the effect of reinsurance? In place of raising capital, an insurer may rely on reinsurance to provide security for its ability to pay losses. The effect of reinsurance is to replace the ABC's cost of capital with the cost of reinsurance. The profitability targets should reflect both the cost and benefit of reinsurance on each line of insurance.
What is the effect of hedging losses with options on an insurance index? Hedging losses by buying options on an insurance index has many of the same costs and benefits of reinsurance. However these contracts involve basis risk. On the plus side, the sellers of the options could have lower operating expenses. The net effect might be that buying options could reduce the cost of capital and/or reinsurance.
The cost of financing an insurance company is defined to be the combined cost of capital, reinsurance and options on a catastrophe index. The ABC Insurance Company wants to allocate its cost of financing back to its individual underwriting divisions. A description of the methodology used for this allocation is given on the Methodology page. The final recommendations are given on the Summary page. Additional details about the implementation of the methodology are given on the Analysis page.
More about the ABC Insurance Company
ABC's market share has stayed relatively constant over the past several years, and it has no plans to grow. Its combined ratio has usually been in the 100 to 105 percentage range. Its projected premium writings for the year 2000 are:
Line of Insurance
Year 2000 Premium
Commercial Property
525,000,000
General Liability
1,500,000,000
Commercial Auto
225,000,000
Total
2,250,000,000
Reinsurance
ABC has reinsurance on commercial property that covers losses in excess of $1 million per occurrence. It has a separate catastrophe treaty that covers hurricane losses in excess of $50 million per storm. Half of ABC's general liability insureds have a policy limit of $1 million per occurrence, while the other half of its insureds have a policy limit of $10 million per occurrence. Currently, it reinsures its general liability losses in excess of $1 million per occurrence. All of its commercial auto insureds have a policy limit of $1 million per occurrence.
ABC's Operating Philosophy
The management of ABC recognizes the competitive nature of commercial lines insurance. It does not seek to interfere in individual underwriting decisions. Instead it gives considerable discretionary authority for pricing and underwriting to its underwriting division heads. In return, it expects them to meet annual profitability targets established at the beginning of the year.
If in the long run, an underwriting division cannot meet its profitability target, ABC's management feels it should get out of this line of business.
Capital management at ABC is a corporate function, and not an underwriting responsibility. The management of ABC views reinsurance as a substitute for capital, and subject to corporate control. If reinsurance is to be cost effective, the reinsurance transaction costs must be less than the cost of the capital it replaces.
ABC is also studying the use of options on a catastrophe index as a capital substitute to replace its catastrophe reinsurance. Although it believes the current market is not broad enough to use these instruments, it wants to be ready to move should conditions change. Should this happen, they are willing to use the market in these instruments provided it results in a lower cost of financing, i.e. the cost of capital and/or reinsurance and/or catastrophe options.
Once its capital management decisions are made, ABC's management will allocate the cost of financing back to the individual underwriting divisions.
The "To Do" List
ABC's management has asked for the following analyses.
Evaluate the cost effectiveness of its general liability reinsurance.
Find the cost of options on a catastrophe index that makes it competitive with its catastrophe reinsurance.
Allocate the cost of financing back to the individual underwriting divisions. Express the results in terms of both: (1) an "overall risk load" for each division; and (2) target combined ratios for each division.
While the analyses may take place throughout the year, ABC wants the ability to make quick decisions at year end as the reinsurance quotes come in.
This web site was written by and will be maintained by Glenn Meyers of Insurance Services Office, Inc..
Author's Statement - May 16, 2000
I view the "Cost of Financing Insurance" project as a serious attempt to apply the principles of Dynamic Financial Analysis to the pricing and/or underwriting of insurance. More work needs to be done and as the "Version 1.0" in the title implies, I plan to update this site from time to time.
I will now describe some of the strengths and weaknesses of the current version.
My purpose it to analyze the insurer's losses and to find how best to manage the cost of supporting these losses in the insurance company setting. I believe the overall methodology is sound.
A complete strategy for managing insurer capital would also consider the insurer's assets. For this analysis, I took a very simplistic view of insurer assets, namely that they are all invested in instruments that yield a fixed rate of return. While asset risk is not my area of expertise, I hope to include the work of others in future versions of this site.
The analysis makes use of the collective risk model, which derives the insurer's aggregate loss distribution in terms of the underlying claim severity and claim count distributions.
The underlying claim severity distributions, which vary by settlement lag, are real. They provide a way to reflect the uncertainty in loss reserves in our analysis.
This version of the collective risk model provides a way to incorporate correlations between lines of insurance. I believe the methodology for doing this is one of many ways to incorporate correlation. However I am not yet able to use sound estimates of key parameters in the model. I hope to fix this in future versions. My purpose now is to illustrate that correlation is an important consideration.
I hope these comments make it clear that I expect the methodology to continue developing. New ideas will come in and other ideas will become obsolete. My choice of media, a web site rather than the traditional paper, provides a way to update the state of the art as it happens, without sending the reader on a paper chase.
Last updated 05/16/00
