Description: A central problem for regulators and risk managers concerns the risk assessment of an aggregate portfolio defined as the sum of d individual dependent risks Xi. This problem is mainly a numerical issue once the joint distribution of (X1,X2, . . . ,Xd) is fully specified. Unfortunately, while the marginal distributions of the risks Xi are often known, their interaction (dependence) is usually either unknown or only partially known, implying that any computed risk measure of the portfolio is subject to model uncertainty. Previous academic research has focused on the maximum and minimum possible values of a given risk measure of the portfolio, in the case in which only the marginal distributions are known. This approach leads to wide bounds, as all information on the dependence is ignored. In this paper, we integrate in a natural way available information on the multivariate dependence and provide easy-to-compute bounds for the risk measure at hand. We observe that incorporating the information of a well-fitted multivariate model may, or may not, lead to much tighter bounds, a feature that also depends on the risk measure used. We illustrate this point by showing that the Value-at-Risk at a very high confidence level (as used in Basel II) is typically prone to very high model risk, even if one knows the multivariate distribution almost completely. Our results make it possible to determine which risk measures can benefit from adding dependence information (i.e., leading to narrower bounds when used to assess portfolio risk), and, hence, to identify those models for which it would be meaningful to develop accurate multivariate models.

Description: This report reviews the academic literature on risk aggregation and diversification as well as the regulatory approaches. We will point out the advantages and disadvantages of the different approaches with a focus on model risk issues.

Description: In a well-designed enterprise risk management (ERM) program, the firm integrates risk management into the strategic planning process, addressing strategic risk, financial risk, operational risk and hazard risk under a single overarching process. This is particularly important to large financial firms, such as property and casualty (P&C) insurers, which face a diverse set of risks. In contrast to previous studies that document a significant product line and geographic diversification discount relative to more focused competitors, our analysis suggests that firms with effective ERM programs exhibit a performance premium. Using the Standard and Poor’s (S&P) ERM ratings from 2006 to 2012, we find that product line diversification has a significant positive effect on value for more diversified firms with well-implemented ERM programs, as compared to those with weak ERM.