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摘要翻译：
我们重新讨论了指数杠杆效应，它可以分解为波动性效应和相关性效应。我们使用矩阵回归分析来研究后者，我们称之为“主回归分析”(PRA)，并为其提供一些分析（使用随机矩阵理论）和数值基准。我们发现，指数向下的趋势增加了股票之间的平均相关性（用条件相关矩阵的最负特征值来衡量），并使市场模式更加均匀。另一方面，上升趋势也增加了股票之间的平均相关性，但使相应的市场模式偏离了一致性。与这些影响相关的时间尺度有两个，一个月（20个交易日）的短时间尺度，一个年的长时间尺度。我们还发现了部门相关性的杠杆效应的迹象，这在PRA的第二和第三模式中表现出来。
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英文标题：
《Principal Regression Analysis and the index leverage effect》
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作者：
Pierre-Alain Reigneron, Romain Allez and Jean-Philippe Bouchaud
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最新提交年份：
2011
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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英文摘要：
We revisit the index leverage effect, that can be decomposed into a volatility effect and a correlation effect. We investigate the latter using a matrix regression analysis, that we call `Principal Regression Analysis' (PRA) and for which we provide some analytical (using Random Matrix Theory) and numerical benchmarks. We find that downward index trends increase the average correlation between stocks (as measured by the most negative eigenvalue of the conditional correlation matrix), and makes the market mode more uniform. Upward trends, on the other hand, also increase the average correlation between stocks but rotates the corresponding market mode {\it away} from uniformity. There are two time scales associated to these effects, a short one on the order of a month (20 trading days), and a longer time scale on the order of a year. We also find indications of a leverage effect for sectorial correlations as well, which reveals itself in the second and third mode of the PRA.
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PDF链接：
https://arxiv.org/pdf/1011.5810
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