Article Detail

A Risk-Based Risk Finance Paradigm

Journal 35: Zicklin-Capco Institute Paper Series in Applied Finance

Siwei Gao, Michael R. Powers, Zaneta A. Chapman

We propose an alternative to the conventional risk finance paradigm of enterprise risk management that accounts for not only a loss portfolio’s expected frequency and expected severity, but also its “risk” as captured by an appropriate measure of dispersion/spread. This new paradigm is based upon four distinct properties of a loss portfolio that enhance the benefits of diversification: (1) a high expected frequency; and (2) less-than-perfect positive correlations between individual severities; (3) light-tailed severities; and (4) a predictable (i.e. non-erratic) frequency.

The conventional risk finance paradigm
In enterprise risk management (ERM), the portfolio of total losses to which a firm is exposed in a given time period may be expressed by the sum where N denotes the frequency of loss events (taken as a random variable defined on the non-negative integers), and the Xi are individual severities (taken as positive, real-valued random variables). Such portfolios are commonly analyzed within a two-dimensional space spanned by expected frequency (E[N]) and expected severity (E[Xi]) [e.g. Zuckerman (2010)], with the most appropriate method of risk finance indicated by the placement of L within the matrix of Figure 1 [see, e.g., Baranoff et al. (2009)].

For the case of loss portfolios with low expected severities, the logic behind the conventional paradigm is fairly straightforward: portfolios with low expected frequencies are not very risky, and therefore can be financed as ordinary operational expenses; whereas those with high expected frequencies are best handled by pooling because they are amenable to risk reduction through diversification. For the case of loss portfolios with high expected severities, the rationale is somewhat different: portfolios with low expected frequencies are too risky to be handled by informal or formal retention and must be transferred through insurance or some other hedging mechanism; whereas those with high expected frequencies are simply too risky to be financed even by transfer, presumably because markets do not exist to accept such risks.

To enjoy the benefits of diversification, the random variable L must possess (at least) two salutary statistical properties: (1) a high expected frequency (i.e. a large value of E[N]), and (2) less than perfect positive correlations between individual severities (i.e. Corr[Xi, Xj] < 1 for all i not equal to j). For portfolios with low expected severities, the first of these properties is stated explicitly by the conventional paradigm, and the second is implied. What is left unexplained is why portfolios with high expected severities cannot benefit from diversification in the same way as those with low expected severities.

Resolving this issue, either by explaining the failure of diversification for portfolios of high expected severities or by revising the conventional paradigm to correct this inconsistency, requires that one examines statistical properties of L beyond simply the expected frequency and expected severity. In previous work the first two authors [Powers et al. (2012), hereafter denoted by PPG] began such a program by explicitly considering the impact of the severity distribution’s tail behavior on the benefits of diversification. In the present paper, we extend this work by offering a more comprehensive analysis of L.

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