{'fraction_non_alphanumeric': 0.019417475728155338, 'fraction_numerical': 0.00529567519858782, 'mean_word_length': 5.554913294797688, '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}}
The Portfolio Properties of Large Returns

Extensive research has already been conducted on the distributional properties of asset returns. On the contrary, relatively little research has been done on the nature of large returns. In this paper, we focus on several aspects of large stock returns. Our findings indicate that 1) average correlations among stocks are an increasing function of market capitalization and are asymmetrically U-shaped in the level of market performance, as correlations for large negative returns are greater than for corresponding positive returns. 2) The diversification properties of stocks during large returns are considerably poorer than for unconditional levels. Also, the degree of diversification benefit lost is an increasing function of market capitalization; however, it requires fewer of the large-cap stocks to achieve 110 percent of the maximum diversification benefit. (3) For Value at Risk (VaR) calculations, use of the unconditional estimates systematically underestimates the level of risk while results derived during times of poor market performance provide more reasonable estimates.