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Allianz Annual Report 2012

Annual Report 2012    Allianz Group Diversification and correlation assumptions Our internal risk capital model considers concentration and correlation effects when aggregating results at the Group level, in order to reflect the fact that not all potential worst case losses are likely to materialize at the same time. This effect is known as diversification and forms a central element of our risk management framework. We strive to diversify the risks to which we are exposed in order to limit the impact of any single source of risk and help ensure that the positive developments of some busi- nesses neutralize the possibly negative developments of others. The degree to which diversification can be realized depends in part on the level of relative concentration of those risks. The greatest diversification is generally ob- tained in a balanced portfolio without any disproportion- ately large exposures to only a few risks. In addition, the diversification effect depends on the joint movement of sources of risks. One measure of the degree of the joint movement of two sources of risk is linear correlation, char- acterized by a value between “–1” and “+1”. Where possible, we derive correlation parameters for each pairofmarketrisksthroughstatisticalanalysisofhistorical market data, considering weekly observations over several years. In case historical market data or other portfolio-spe- cific observations are insufficient or not available, we rely on the professional judgment of experts for the respective risk categories. In general, we set the correlation parame- ters to represent the joint movement of risks under adverse conditions. Based on these correlations, we use an industry- standard approach, the Gaussian Copula approach, to deter­ mine the dependency structure of quantifiable sources of risk within the applied Monte Carlo simulation. We complement our diversification strategy with a compre­ hensive framework of limits for risks which can accumu- late. This framework limits our reliance on diversification or correlation assumptions (see section on Concentrations of risk). Non-market assumptions Our internal risk capital model also includes non-market assumptions such as claims trends, inflation, mortality, longevity, morbidity, policyholder behavior, expense, etc. To the extent available, we use our own internal historical data for non-market assumptions and also consider rec- ommendations from supervisory authorities and actuarial associations. Assessment of assumptions We consider the assumptions made for our calculations to be appropriate and adequate taking into account the poten­ tial impact on our internal risk capital. Comprehensive controls exist within our internal risk capital and financial reporting frameworks for analyzing the assumptions we make.1 1 For additional information regarding our internal controls over financial reporting, please refer to the chapter Controls and Procedures from page 214 onwards. 190