A Practical Application of Modern Portfolio Theory to Capital Allocation

This paper presents and evaluates a capital allocation method that represents a significant part of a more complete modeling process required to fully allocate and release capital for application to pricing or profitability analysis. The complete process is also described at a more general level, including discussion of additional requirements for application to reinsurance. While the specific modeling presented is based largely on concepts from modern portfolio theory, the paper first compares alternative perspectives and practical considerations relevant to all methodologies. The perspective of a specific portfolio analysis is compared to a market equilibrium perspective adopted for risk load or capital allocation methods. The paper compares the differences in their assumptions and the intended interpretation of their indications. It is then described how both perspectives can add value to decisions by properly integrating them into pricing and financial risk management operations. The concept of economic valuation is introduced in establishing the total capital to be allocated. Implications of the market equilibrium perspective adopted by the methods proposed in the paper are discussed at the total capital level. These include the relationship between capital and expected loss exposure at the total industry level, as well as the use of required rather than actual capital of insurers. The proposed method for allocation of capital to segments of the portfolio is based on Capital Asset Pricing Model concepts with specific interpretation of the variances and covariance relationships between segments. Several numerical examples of the method are provided and practical application problems are identified and discussed. In conjunction with the capital allocated at inception, the release of this capital generates the total capital commitment needed to measure return on equity for application to pricing or profitability analysis. Finally, the paper describes extensions of the proposed methods to reflect excess layers, other contract provisions, and asset risk in a consistent manner.