Allocating and forecasting changes in risk

Daniel Gaigall

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We introduce new axioms as a requirement on a useful allocation principle for the change in the risk of a portfolio and formulate conditions which are sufficient in this regard. We adopt established allocation principles and deduce that the conditions are satisfied by the covariance principle and the conditional expectation principle.
With the help of the allocation procedure for the changes in the risk, we introduce a new forecast problem for the changes in the risks of the components of the portfolio given the change in the risk of the portfolio.
We explain and demonstrate the implementation on the basis of the output of a simulation such as the new procedures would be putted in practice. We present an approximative procedure to ensure that we obtain (uniquely determined) forecasts for the changes in the risk of the components.

Abstract

We consider time-dependent portfolios and discuss the allocation of changes in the risk of a portfolio to changes in the portfolio’s components. For this purpose we adopt established allocation principles. We also use our approach to obtain forecasts for changes in the risk of the portfolio’s components. To put the approach into practice we present an implementation based on the output of a simulation. Allocation is illustrated with an example portfolio in the context of Solvency II. The quality of the forecasts is investigated with an empirical study.

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