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Risks 2014, 2(3), 260-276; doi:10.3390/risks2030260
Article

The Impact of Systemic Risk on the Diversification Benefits of a Risk Portfolio

1
,
1
 and
2,*
1 SCOR SE, 26 General Guisan Quai, 8022 Z├╝rich, Switzerland 2 ESSEC Business School Paris, CREAR, av. Bernard Hirsch BP 50105, 95021 Cergy-Pontoise Cedex, France
* Author to whom correspondence should be addressed.
Received: 2 December 2013 / Revised: 15 May 2014 / Accepted: 17 June 2014 / Published: 9 July 2014
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Abstract

Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all of the policies at the same time. We introduce here a probabilistic approach to examine the consequences of its presence on the risk loading of the premium of a portfolio of insurance policies. This approach could be easily generalized for investment risk. We see that, even with a small probability of occurrence, systemic risk can reduce dramatically the diversification benefits. It is clearly revealed via a non-diversifiable term that appears in the analytical expression of the variance of our models. We propose two ways of introducing it and discuss their advantages and limitations. By using both VaR and TVaR to compute the loading, we see that only the latter captures the full effect of systemic risk when its probability to occur is low.
Keywords: diversification; expected shortfall; investment risk; insurance premium; risk loading; risk measure; risk management; risk portfolio; stochastic model; systemic risk; value-at-risk diversification; expected shortfall; investment risk; insurance premium; risk loading; risk measure; risk management; risk portfolio; stochastic model; systemic risk; value-at-risk
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Busse, M.; Dacorogna, M.; Kratz, M. The Impact of Systemic Risk on the Diversification Benefits of a Risk Portfolio. Risks 2014, 2, 260-276.

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