On the Diversification Benefit of Reinsurance Portfolios
SCOR Paper no 40 - Diversification Benefit
33 Pages Posted: 31 Oct 2017
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: Suggested Citation