The limits of diversification when losses may be large

By Rustam Ibragimov, Johan Waldén. 2007

167 citations recorded by the source corpus.

Recent results in value at risk analysis show that, for extremely heavy-tailed risks with unbounded distribution support, diversification may increase value at risk, and that, generally, it is difficult to construct an appropriate risk measure for such distributions. We further analyze the limitations of diversification for heavy-tailed risks. We provide additional insight in two ways. First, we show that similar nondiversification results are valid for a large class of risks with bounded support, as long as the risks are concentrated on a sufficiently large interval. The required length of the support depends on the number of risks available and on the degree of heavy-tailedness. Second, we relate the value at risk approach to more general risk frameworks. We argue that in financial markets where the number of assets is limited compared with the (bounded) distributional support of the risks, unbounded heavy-tailed risks may provide a reasonable approximation. We suggest that this type of analysis may have a role in explaining various types of market failures in markets for assets with possibly large negative outcomes.

Subfields: Economics and Econometrics, Management Science and Operations Research, Soil Science

View Paper: https://www.semanticscholar.org/paper/46a3326bc7128178b547128634d5d13002ba3ddd

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Citations in the corpus

Multivariate extremes and the aggregation of dependent risks: examples and counter-examples (2009, unknown): “Since the marginal dfs have equal asymptotic behavior in the different infinite mean models in Examples 3.1 and 3.3, the asymptotic VaR behavior for the sum of the risks must follow from the different dependence structures (copulas, spectral measures).”
Robustness and sensitivity analysis of risk measurement procedures (2010, unknown): “Arguing in a diﬀer-ent direction, Ibragimov & Walden [14] show that for very “heavy-tailed” risks deﬁned in a very general sense, diversiﬁcation does not necessarily decrease tail risk but actually can increase it, in which case requiring sub-additivity would in fact be unnatural.”
Inhomogeneous Dependence Modeling with Time-Varying Copulae (2009, unknown): “Joe (1997); Cherubini, Luciano, and Vecchiato (2004); and Chen and Fan (2006) provide a detailed exposition of inference methods for copulae.”
On dependence consistency of CoVaR and some other systemic risk measures (2012, background): “, [10, 17], and attribution of systemic risk charges within a financial system, as discussed in [26, 25].”
Portfolio diversification and value at risk under thick-tailedness (2009, unknown): “…are particular examples of -symmetric distributions with ¼ 2 (that is, of spherical distributions) and (x)¼ exp( x ). xAs recently demonstrated in Ibragimov and Walden (2007), the conclusions in this paper also continue to hold for a wide class of bounded r.v.s concentrated on a sufficiently…”
Fat tails, VaR and subadditivity☆ (2013, unknown): “g Mandelbrot (1963), Fama (1965) and Jansen and de Vries (1991).”
Nondiversification Traps in Catastrophe Insurance Markets (2009, background): “In Ibragimov and Walden (2007), it is shown that similar U-shaped curves occur as a function of diversification when the VaR measure is used.”
Risk concentration and diversification: Second-order properties (2009, background): “More recently, Ibragimov and Walden (2007) and Ibragimov et al. (2009) have discussed diversification benefits linking heavy-tailed distributions to specific economic models.”
International diversification: A copula approach (2011, unknown): “Ibragimov and Walden ( 2007 ) examine distribu tional considerations that limit the optimality of diversification .”
Contagion as a domino effect in global stock markets (2009, unknown): “However, hedging is more difficult, and diversification opportunities diminish rapidly, when local crashes spread regionally or even globally (see Ibragimov and Walden, 2007).”
Extreme Downside Risk and Expected Stock Returns (2012, unknown): “Moreover, researches by Ibragimov (2009), Ibragimov and Walden (2007), and Ibragimov et al. (2008) provide theoretical evidence that diversification is not always preferable, especially for extremely heavy-tailed distributions.2 Recent empirical asset pricing studies have examined other risk…”