Measuring Portfolio Risk under Partial Dependence Information
(2014) , 30 pages
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- Abstract
- There is a recent interest in finding bounds for risk measures of portfolios when the marginal distributions of its risky components are assumed to be known. This problem is well studied when the dependence among the risks is unknown, but the bounds obtained are too wide to be useful inpractice. Unfortunately, additional dependence information, such as knowledge of some higher-order moments, makes the problem hard to deal with. We motivate that replacing the knowledge of the marginal distributions by the knowledge of the mean of the portfolio sum does not result in significant loss of information, while making it possible to find explicit bounds if also higher-order moments as source of dependence information are available. Effectively, we propose an elementary derivation of bounds on various risk characteristics, including distribution functions and Value-at-Risk(VaR). Our results make it possible for supervisory authorities to assess the robustness of risk models used in practice and to identify issues of incomparability of risk models across different institutions.
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