We consider a portfolio of general defaultable assets with low individual default risk and study the probability of the portfolio default loss exceeding an arbitrary threshold. The latent variables driving defaults are modeled by a mixture structure that combines common shock, systematic risk, and idiosyncratic risk factors. While common shocks and systematic risk have been found by many studies to contribute significantly to portfolio losses, the role of idiosyncratic risks is often found to be negligible. Such conclusions are usually established under the assumption that the portfolio size tends to infinity and idiosyncratic risk factors are not dominant. We study under-investigated scenarios where the portfolio size is fixed and the idiosyncratic risk factors are heavy-tailed, exploring two distinct scenarios: an independence scenario and an asymptotic dependence scenario. The former is standard in the literature, while the latter is motivated by recent studies that have found the inadequacy of relying solely on common factors to capture default clustering. This consideration also reflects the possibility that idiosyncratic reasons can trigger contagion among firms with liabilities to each other. In the independence scenario, even with heavy-tailed idiosyncratic risk factors, the probability of a substantial portfolio loss remains low unless a single asset carries a disproportionately large weight. Conversely, in the asymptotic dependence scenario, the primary drivers of increased exceedance probability are the dependent idiosyncratic risk factors.

中文翻译：

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由特殊风险驱动的投资组合违约损失


我们考虑一个个人违约风险较低的一般违约资产投资组合，并研究投资组合违约损失超过任意阈值的可能性。驱动违约的潜在变量由混合结构建模，该结构结合了常见冲击、系统性风险和特殊风险因素。虽然许多研究发现，常见的冲击和系统性风险是导致投资组合损失的重要因素，但特殊风险的作用往往可以忽略不计。这样的结论通常是在投资组合规模趋于无穷大且特殊风险因素不占主导地位的假设下建立的。我们研究了投资组合规模固定且特殊风险因素粗尾的未充分研究的情景，探讨了两种不同的情景：独立情景和渐近依赖情景。前者在文献中是标准的，而后者的动机是最近的研究，这些研究发现仅依靠公因子来捕获默认聚类是不够的。这种考虑也反映了特殊原因可能引发彼此负债企业之间的传染。在独立情景中，即使存在重尾特殊风险因素，除非单一资产的权重过大，否则投资组合遭受重大损失的可能性仍然很低。相反，在渐近依赖情景中，超标概率增加的主要驱动因素是依赖性特质风险因素。