论文标题
tsallis来自不对称分布的相对熵作为金融投资组合的风险措施
Tsallis Relative entropy from asymmetric distributions as a risk measure for financial portfolios
论文作者
论文摘要
在较早的研究中，我们表明Tsallis相对熵（TRE）是将Kullback-Leibler相对熵（KLRE）推广到非扩展系统的一般化，可以用作构建风险最佳投资组合的可能风险措施，其收益比市场收益均衡。在长期（> 10年）中，TRE的风险回收概况比风险度量的行为比常用的风险措施“ Beta”的行为更加一致，而资本资产定价模型（CAPM）则具有“ beta”。在这些研究中，从TRE得出的模型分布是对称的。但是，观察结果表明，金融市场和股票收益的分布在正面和负面回报中通常不对称。在这项工作中，我们通过将数据分布视为两个独立的归一化分布的线性组合来概括为不对称情况（ATRE）的TRE - 一个用于负回报，另一种用于正回报。这两个独立的分布中的每一个都是一半的Q-gaussian，具有不同的非扩展参数Q和温度参数b。使用ATR作为风险措施研究了风险回收（超过市场收益）模式。将结果与其他两种风险度量的结果进行了比较：TRE和Tsallis相对熵仅来自负回报。对数据的测试，包括互联网泡沫，2008年的崩溃和共同期限，长期（20年）和较短的期限（10年），表明所有三种风险措施的风险交通回报率都可以获得线性拟合。但是，使用S-在混乱的市场条件（崩溃）中创建的投资组合的适合，因为风险显示出更高的斜率指向给定风险价值的回报率更高。此外，在这种情况下，无论市场行为如何，即使是短期投资组合的超额回报仍然是积极的。
In an earlier study, we showed that Tsallis relative entropy (TRE), which is the generalization of Kullback-Leibler relative entropy (KLRE) to non-extensive systems, can be used as a possible risk measure in constructing risk optimal portfolios whose returns beat market returns. Over a long term (> 10 years), the risk-return profiles from TRE as the risk measure show a more consistent behavior than those from the commonly used risk measure 'beta' of the Capital Asset Pricing Model (CAPM). In these investigations, the model distributions derived from TRE are symmetric. However, observations show that distributions of the returns of financial markets and equities are in general asymmetric in positive and negative returns. In this work, we generalize TRE for the asymmetric case (ATRE) by considering the data distribution as a linear combination of two independent normalized distributions - one for negative returns and one for positive returns. Each of these two independent distributions are half q-Gaussians with different non-extensivity parameter q and temperature parameter b. The risk-return (in excess of market returns) patterns are investigated using ATRE as the risk measure. The results are compared with those from two other risk measures: TRE and the Tsallis relative entropy S- derived from the negative returns only. Tests on data, which include the dot-com bubble, the 2008 crash, and COVID periods, for both long (20 years) and shorter terms (10 years), show that a linear fit can be obtained for the risk-excess return profiles of all three risk measures. However, the fits for portfolios created during the chaotic market conditions (crashes) using S- as the risk show a much higher slope pointing to higher returns for a given risk value. Further, in this case, the excess returns of even short-term portfolios remain positive irrespective of the market behavior.
