Description: In this paper, we formulate the Capital Allocation problem as an optimization problem in which we seek the mix of business that maximizes an insurance company’s Expected Net After Tax Income subject to a constraint on the Tail Value at Risk TVAR. Using the method of Lagrange multipliers, we demonstrate that the returns on the respective TVAR contributions, so-called RORAC, are equal across all lines of business when the mix of business is optimal. Although the discussions in this paper center on the TVAR, the conclusions hold true for any conditional expected value measure. Presented at 2010 Enterprise Risk Management Symposium, Society of Actuaries, April 12-15, 2010.

Description: The Market Cost of Capital approach has emerged as the standard for estimating risk margins for insurers' fair value balance sheets. This paper takes some of the ideas developed for valuing life insurance liabilities and applies them to the problem of valuing credit risky bonds. The basic idea is that credit spreads should cover the cost a) best estimate defaults plus the cost of holding capital for b) contagion risk (e.g. a credit crunch) and c) parameter risk, this risk that the best estimate is wrong and must be revised. We argue that the margins required for parameter risk can capture liquidity issues. In addition, the models developed here allow the cost of capital rate itself to be a random variable which allows credit spreads to open and close stochastically. Finally, the paper argues that it is reasonable to include something like AA best estimate default rates and liquidity spreads when valuing insurance liabilities. The main rationale for doing so is the idea that there are elements of the total credit risk issue that can be hedged between the assets and liabilities.

Description: This paper addresses the allocation of solvency capital in multi- line financial businesses. Although this paper is uniformly applicable to financial enterprises of all types, the terminology in the paper is mainly that of insurance. The TailVaR risk measure is extended in a natural way to allocating capital to each of the business units. This method of allocation allocates capital in a way that is invariant over the method of decomposing the enterprise into business units. Analytic results are derived in the case of multivariate Normal risks. The key result of this paper is that the TailVaR-based proportional allocation of total required capital is identical to that based on mean-variance considerations analogous to the CAPM in the case of the multivariate Normaldistribution.

Description: Scenario analysis and stress tests based on consideration of shock events and their possible repercussions can provide useful information to management and regulators on a company’s resiliency through a chain of events, as well as support the consideration of a firm’s operations as an integral part of a wider financial system. We discuss how scenario analysis and stress testing can be used to define a company’s risk appetite, which is at the core of a well-embedded ERM framework. Presented at 2010 Enterprise Risk Management Symposium, Society of Actuaries, April 12-15, 2010.

Description: An insurance product’s return on required equity demonstrates how successfully its results are covering the company’s basic capital. Using some simplified assumptions, it is possible to calculate this return ratio and decompose it without a full projection of liabilities.

Description: This paper demonstrates the use of Quantile Regression in the development and understanding of conditional value at risk (VaR) models for enterprise risk management.

Description: Abstract: A model for analyzing the probability and severity of default of sovereign entities and banks. The methodology analyzes the risks inherent in the investment of debt of sovereign governments and large financial institutions side-by-side, taking into consideration macroeconomic interactions among the sovereign fiscal and monetary authorities, the financial institutions, and the real economy. The signature aspect of the methodology is that it adapts a Merton-style default model to use explicit measures of sovereign assets and asset volatility.

Description: This paper provides a novel approach to the valuation of the market value of economic surplus that is stable and immune from “market noise”.

Description: As an alternative to the widely-used 'return on economic capital' RAROC, this paper proposes a performance measure consistent with standard valuation models, and discusses its implications for prudential regulation. From 2007 Enterprise Risk Management Symposium, M-AS07-1.

Description: This monograph was presented at the 2011 Enterprise Risk Management Symposium, held March 14-16 in Chicago. The author, writing from a property-liability insurance perspective, notes that capital allocation is a theoretical exercise because all of a firm’s capital could be depleted to cover a significant loss arising from any one segment. However, firms do need to allocate capital for pricing, risk management and performance evaluation. In this paper, the cost of capital in financial markets is incorporated into the Ruhm-Mango-Kreps algorithm to yield one allocation that reflects the true cost of capital an insurer would face.