主管:中国科学院
主办:中国优选法统筹法与经济数学研究会
   中国科学院科技战略咨询研究院

Chinese Journal of Management Science ›› 2018, Vol. 26 ›› Issue (5): 51-61.doi: 10.16381/j.cnki.issn1003-207x.2018.05.006

• Articles • Previous Articles     Next Articles

Adjexpectile as A Risk Measure: Properties、Optimization and Asset Allocation Applications

ZHOU Jing, LUO Le   

  1. Huazhong University of Science and Technology, Wuhan 430074, China
  • Received:2016-12-20 Revised:2017-04-06 Online:2018-05-20 Published:2018-07-30

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

CLC Number: