论文标题
脂肪尾部因素
Fat Tailed Factors
论文作者
论文摘要
由于资产回报的成对相关性的随机性质，标准，基于PCA的因素分析遭受了许多已知的问题。我们分析了基于ICA的替代方案，该替代方案是根据其非高斯性而不是其差异来识别因素的。投资组合构造对ICA框架的概括导致了两种半最佳的投资组合构造方法：一种胖尾的投资组合，可最大程度地提高非高斯式投资组合的回报，而混合投资组合则渐近地降低了差异和非高斯的差异。对于脂肪尾投资组合，与凯利投资组合线性缩放相反，投资组合权重尺度像$ 1/3 $的功率；这种投资组合的建设大大降低了投资组合的浓度，而凯利投资组合中固有的所有问题。对于混合投资组合，该方差的多样性与基于Kelly PCA的投资组合相同，但是与Kelly Portfolios的$ n^{ - 2} $相比，与Kelly Portfolios的$ n^{ - 1}相比，多样化的多元化速度要快得多，而$ n^{ - 2} $的速度越来越多。
Standard, PCA-based factor analysis suffers from a number of well known problems due to the random nature of pairwise correlations of asset returns. We analyse an alternative based on ICA, where factors are identified based on their non-Gaussianity, instead of their variance. Generalizations of portfolio construction to the ICA framework leads to two semi-optimal portfolio construction methods: a fat-tailed portfolio, which maximises return per unit of non-Gaussianity, and the hybrid portfolio, which asymptotically reduces variance and non-Gaussianity in parallel. For fat-tailed portfolios, the portfolio weights scale like performance to the power of $1/3$, as opposed to linear scaling of Kelly portfolios; such portfolio construction significantly reduces portfolio concentration, and the winner-takes-all problem inherent in Kelly portfolios. For hybrid portfolios, the variance is diversified at the same rate as Kelly PCA-based portfolios, but excess kurtosis is diversified much faster than in Kelly, at the rate of $n^{-2}$ compared to Kelly portfolios' $n^{-1}$ for increasing number of components $n$.
