Risk‐Based Capital Allocation Using a Coherent Measure of Risk
This article outlines a procedure for quantifying risk‐adjusted capital reserves that may be used for both performance evaluation and capital allocation. The author identifies and quantifies the sources of risk capital that must be addressed, to cover current investment and withstand market shocks, for any business line that exhibits earnings volatility. The author classifies risk capital into two types: market‐risk capital and earnings volatility‐related capital. Market risk capital may be divided into two categories; risks due to “normal” or “diffusion” type price movements and catastrophic moves or “stress” events. In contrast, earnings volatility‐related capital is directly related to the firm's equity‐at‐risk, in the event that market shocks lead to sustained earnings volatility. The author suggests that these risk‐adjusted capital measures may be used as a benchmark, in conjunction with net earnings, to evaluate performance, or to allocate equity capital across different operations within a firm.
Measuring Investment Risk
LESLIE A. BALZER is manager of investment technologyfor Lend Lease Corporate Services Limited in Sydney, Australia. He was previously a principal of consulting actuaries William M. Mercer, and dean ofengineering at the Royal Melbourne Institute of Technology. Dr. Balzer holds a B.E. in mechanical engineering and a B.Sc. in mathematics and physicsfrom the University of New South Wales, Australia. In addition, he holds a Ph.D. from the Control and Management Systems Division of the University of Cambridge, England. Dr. Balzeer is a fellow of a number ofprofessional societies, and is vice president of the QGroup (Australia) and chairman ofits mrking Patty on Investment Risk.
AN EMPIRICAL METHOD OF COMPARING RISKS USING STOCHASTIC DOMINANCE
The need to evaluate risks, in either the investment or the insurance component of business, is a primary task of the actuary. Mathematical constructs for risk assessment using expected utility theory are problematic for practical use. One reason is that the elicitation of the utility function is difficult or impossible in most situations. Second, data related to risk choices contain noise that must be accounted for in the decision process. This paper presents a method of testing second-order stochastic dominance of risks. By using this methodology, risks can be partially ordered by value, with available data. The methodology developed here requires only that the risks have yields distributed as one of the location-scale family of distributions and that the actuary can specify that family. The paper presents the simulated power of the procedure. Risk assessment has three components: (i) analysis of the contingent event, (ii) evaluation of the contractual obligation associated with the event, and (iii) determination of the premium to be received for assuming the risk of the event. Assessing the value of the risks associated with either an investment or an insurance product is a fundamental task of the actuary. One appealing method of assessing the value of a specified risk is the use of utility functions. In this case, the value of a risk is assessed based on the expected utility of income or loss associated with the risk, calculated by using the probability density function of the risk. Those risks with higher