On the Diversification Benefit of Reinsurance Portfolios

SCOR Paper no 40 - Diversification Benefit

33 Pages Posted: 31 Oct 2017

See all articles by Jeta Limani

Jeta Limani

Swiss Financial Market Supervisory Authority (FINMA); SCOR

Régis Béttinger

SCOR

Michel M. Dacorogna

PRS Solutions

Date Written: October 30, 2017

Abstract

In this paper we compare the diversification benefit of portfolios containing excess-of-loss treaties and portfolios containing quota-share treaties, when the risk measure is the (excess) Value-at-Risk or the (excess) Expected Shortfall. In a first section we introduce the set-up under which we perform our investigations. Then we show that when the losses are continuous, independent, bounded, the cover unlimited and when the risk measure is the Expected Shortfall at a level · close to 1, a portfolio of n excess-of-loss treaties diversifies better than a comparable portfolio of n quota-share treaties. This result extends to the other risk measures under additional assumptions. We further provide evidence that the boundedness assumption is not crucial by deriving analytical formulas in the case of treaties with i.i.d. exponentially distributed original losses. Finally we perform the comparison in the more general setting of arbitrary continuous joint loss distributions and observe in that case that a finite cover leads to opposite results, i.e. a portfolio of n quota-share treaties diversifies better than a comparable portfolio of n excess-of-loss treaties at high quantile levels.

Keywords: Diversification benefit, risk measures, portfolio, excess-of-loss treaties

JEL Classification: C01, C02, C18

Suggested Citation

Limani, Jeta and Limani, Jeta and Béttinger, Régis and Dacorogna, Michel M., On the Diversification Benefit of Reinsurance Portfolios (October 30, 2017). SCOR Paper no 40 - Diversification Benefit, Available at SSRN: https://ssrn.com/abstract=3062199 or http://dx.doi.org/10.2139/ssrn.3062199

Jeta Limani

SCOR ( email )

92074 Paris La Defense Cedex
France

Swiss Financial Market Supervisory Authority (FINMA) ( email )

Einsteinstrasse 2
Bern, 3003
Switzerland

Régis Béttinger

SCOR ( email )

92074 Paris La Defense Cedex
France

Michel M. Dacorogna (Contact Author)

PRS Solutions ( email )

Raingässli 1
Zug, Zug 6300
Switzerland

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