{'fraction_non_alphanumeric': 0.015555555555555555, 'fraction_numerical': 0.0, 'mean_word_length': 5.435714285714286, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Diversification vs. Contagion in Inter-Linked Portfolios

Inter-linkages between firms are a channel by which idiosyncratic shocks to one firm can affect the returns of linked counterparties. We extend a factor model of returns to allow for the transmission of idiosyncratic shocks between linked counterparties. We show that the structure of inter-linkages determines the rate at which idiosyncratic shocks are diversified away. Importantly we identify structures in which idiosyncratic shocks do not average out, even in large portfolios, but instead significantly affect returns. Simulations confirm that the structure of inter-linkages affects the rate at which return volatility decays as portfolio size increases. The results provide a theoretical basis for identifying assets, portfolios or markets in which returns are likely to be sensitive to idiosyncratic risk or susceptible to contagion.