Academic journal article Journal of Risk and Insurance

Optimal Capital Allocation Principles

Academic journal article Journal of Risk and Insurance

Optimal Capital Allocation Principles

Article excerpt

ABSTRACT

This article develops a unifying framework for allocating the aggregate capital of a financial firm to its business units. The approach relies on an optimization argument, requiring that the weighted sum of measures for the deviations of the business unit's losses from their respective allocated capitals be minimized. The approach is fair insofar as it requires capital to be close to the risk that necessitates holding it. The approach is additionally very flexible in the sense that different forms of the objective function can reflect alternative definitions of corporate risk tolerance. Owing to this flexibility, the general framework reproduces several capital allocation methods that appear in the literature and allows for alternative interpretations and possible extensions.

INTRODUCTION

The level of the capital held by a bank or an insurance company is a key issue for its stakeholders. The regulator, primarily sharing the interests of depositors and policyholders, establishes rules to determine the required capital to be held by the company. The level of this capital is determined such that the company will be able to meet its financial obligations with a high probability as they fall due, even in adverse situations. Rating agencies rely on the level of available capital to assess the financial strength of a company. Shareholders and investors alike are concerned with the risk of their capital investment and the return that it will generate.

The determination of a sufficient amount of capital to hold is only part of a larger risk management and solvency policy. The practice of Enterprise Risk Management (ERM) enhances identifying, measuring, pricing, and controlling risks. An important component of an ERM framework is the exercise of capital allocation, a term referring to the subdivision of the aggregate capital held by the firm across its various constituents, for example, business lines, types of exposure, territories, or even individual products in a portfolio of insurance policies.

Most financial firms write several lines of business and may want their total capital allocated across these lines for a number of reasons. First, there is a need to redistribute the total (frictional or opportunity) cost associated with holding capital across various business lines so that this cost is equitably transferred back to the depositors or policyholders in the form of charges. Second, the allocation of expenses across lines of business is a necessary activity for financial reporting purposes. Third, capital allocation provides for a useful device of assessing and comparing the performance of the different lines of business by determining the return on allocated capital for each line. Comparing these returns allows one to distinguish the most profitable business lines and hence may assist in remunerating the business line managers. Finally, allocating capital may help to identify areas of risk consumption within a given organization and support the decision making concerning business expansions, reductions, or even eliminations.

There is a countless number of ways to allocate the aggregate capital of a company to its different business units. Mutual dependencies that may exist between the performance of the various business units make capital allocation a nontrivial exercise. Accordingly, there is an extensive amount of literature on this subject with a wide number of proposed capital allocation algorithms. Cummins (2000) provides an overview of several methods suggested for capital allocation in the insurance industry and relates capital allocation to management decision-making tools such as RAROC (risk-adjusted return on capital) and EVA (economic value added). Myers and Read (2001) consider capital allocation principles based on the marginal contribution of each business unit to the company's default option. LeMaire (1984) and Denault (2001) discuss capital allocations based on game-theoretic considerations, where a risk measure is used as a cost functional. …

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