Adjexpectile风险测度的性质、优化及资产配置的应用

doi:10.16381/j.cnki.issn1003-207x.2018.05.006

摘要/Abstract

摘要： 金融风险的度量和识别是风险管理的重要内容，常用的风险度量工具是标准差、VaR、ES，但存在很多缺陷，expectile的提出弥补了这些不足，在理论界得到广泛的讨论和应用。本文扩展了expectile进行资产配置，提出Adjexpectile的概念，并讨论和分析了Adjexpectile的一致性风险度量、随机占优性、凸性，与标准差、VaR、shortfall的关系，风险贡献及风险分解的性质。通过对六个资产指数：上证国债指数、上证企业债指数、上证180指数、深圳100指数、深成长40p指数和黄金现货指数的复合周收益率数据进行组合优化配置，发现Adjexpectile在非对称性收益数据、组合前沿、风险分散方面具有一定的优越性。

关键词: Adjexpectile, Expectile, Shortfall, VaR, 资产配置, 非对称最小二乘

Abstract: A suitable financial risk measure is especially important. Distinct risk measures have different impacts on asset pricing, portfolio hedging, capital allocation, and investment performance evaluation. Standard deviation、VaR and ES are commonly used risk measurement tools,but there are lots of defects. For example, the standard deviation makes the upside and downside movements of returns be same punishment; VaR depends only on the probability of more extreme realizations but not on their values, and is not subadditivity risk measure; Expected Shortfall(ES) is a conditional expected value below the quantile, which although overcomes VaR's drawbacks, but only depends on catastrophic loss, thus being more conservative. Newey and Powell (1987) define the "asymmetric least squares" (ALS) and put forward the concept of expectile. It has some excellent properties, such as:strictly monotone increasing; positive homogeneity; translation invariance; superadditivity; prudentiality and sensitiveness to tail events. What's more, it's an average that balances between conditional upside mean and conditional downside mean.In this paper, the expectile is extended to asset allocation, and put forward to Adjexpectile's concept based on Levy theorem. Its economic and financial meaning can be understood as follows:when the portfolio return is lower than its τ quantile, after trading off conditional downside mean punishment, the size of the losses below the expected return. The coherent risk measure of Adjexpectile is discussed. Generally Adjexpectile satisfies subadditivity and positive homogeneity, further meeting the convexity, providing a theoretical basis for Adjexpectile portfolio optimization. Also, the relationship between Adjexpectile and shortfall、VaR、standard deviation, as well as Adjexpectile risk contribution and Euler decomposition is discussed. To Adjexpectile portfolio optimization, the nonparametric method is used to convert Adjexpectile into a linear programming problem. In the empirical analysis part, six asset indexes are enployed to the optimization allocation. Because the characteristics of six indexes data are more complex, having left skewness, also having right skewness and leptokurtosis, so for a given τ value, the average of four CARE modeles is taken to estimate different index α value into portfolio optimization calculation. The conclusions are summarized as follows:(1) Portfolio efficient frontier areas:to standard deviation as a risk measure, 99% Adjexpectile portfolio frontier is better than 99% shortfall frontier, overlaps the mean standard deviation portfolio frontier; to Shortfall as risk measurement, 99% Adjexpectile portfolio frontier is better than 99% shortfall portfolio frontier. The charm of Adjexpectile as risk measure is shown. (2) Portfolio risk diversification areas:mean Adjexpectile asset allocation is more dispersed than the mean standard deviation and mean Shortfall. This further embodies its advantage.

Key words: adjexpectile, expectile, shortfall, VaR, asset allocation, asymmetric least squares

中图分类号:

F830.9

周静, 罗乐. Adjexpectile风险测度的性质、优化及资产配置的应用[J]. 中国管理科学, 2018, 26(5): 51-61.

ZHOU Jing, LUO Le. Adjexpectile as A Risk Measure: Properties、Optimization and Asset Allocation Applications[J]. Chinese Journal of Management Science, 2018, 26(5): 51-61.

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