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Tail-correlation matrices are an important tool for aggregating risk measurements across risk categories, asset classes and/or business segments. This paper demonstrates that traditional tail-correlation matrices—which are conventionally assumed to have ones on the diagonal—can lead to substantial biases of the aggregate risk measurement’s sensitivities with respect to risk exposures. Due to these biases, decision-makers receive an odd view of the effects of portfolio changes and may be unable to identify the optimal portfolio from a risk-return perspective. To overcome these issues, we introduce the “sensitivity-implied tail-correlation matrix”. The proposed tail-correlation matrix allows for a simple deterministic risk aggregation approach which reasonably approximates the true aggregate risk measurement according to the complete multivariate risk distribution. Numerical examples demonstrate that our approach is a better basis for portfolio optimization than the Value-at-Risk implied tail-correlation matrix, especially if the calibration portfolio (or current portfolio) deviates from the optimal portfolio.
This paper shows that a capital budgeting process in which the division manager is required to engage in personally costly influence activities prior to a project approval has beneficial incentive effects: It provides the manager with incentives to acquire costly information about project prospects and helps to elicit the revelation of the acquired information. As a consequence, imposing influence costs on the manager can lead to improved capital allocations. The optimal level of influence costs, chosen by the firm, trades off ex ante incentives for information acquisition against efficient use of the acquired information ex post.