基于非对称主动风险测度的增强型指数追踪模型及应用

本文以下方追踪误差测度非对称主动风险,构建了可以折衷超额收益和下方追踪误差的增强型指数追踪模型,给出了求解模型的广义最小角度回归(generalized least angle regression,简称GLARS)算法,并基于上证50进行了实证。GLARS算法可以给出超额收益在合理区间变化时,使得下方追踪误差最小的组合系数解路径,刻画投资组合的"超额收益—下方追踪误差"有效前沿。将模型应用于中国证券市场上证50指数,与基于"超额收益—追踪误差"的增强型指数追踪模型相比,得到如下实证结论:控制组合股票支数,本文组合的超额收益、单位风险收益更高,在承担相同风险的情况下,得到了更高的平均收益补偿;正下方离差中位数、最大回撤更小,右偏程度更高,表现出"守住下限,放开上限"的特质。本文组合在稀疏性要求下,样本外可以获得高于基准指数的累积收益,对机构和个人投资者具有参考价值,丰富了现有指数追踪研究。

An Enhanced Index Tracking Model based on Asymmetric Active Risk and Its Application

Enhanced index tracking problem is a bi-objective optimization problem of selecting a portfolio outperforming the benchmark index while subjecting to a limited additional risk. It receives extensive attention from both theoretical researches and financial practices. Considering that asymmetric risks coincide more with the investors' perception of risks, an enhanced index tracking model is constructed based on the asymmetric active risks measure in this paper. The asymmetric active risk is gauged by the downside tracking error, and at the same time the short-sale constraint is adopted that is more consistent with the Chinese stock markets. By transform of the constraints on excess returns, our model is equivalent to the non-negative weighted lasso problem; hence, sparse portfolios can be built. Further, the generalized least angle regression (GLARS) algorithm is proposed to solve the model. GLARS algorithm is able to provide the solution of portfolio's coefficients which minimize the downside tracking error when excess returns change within a reasonable range and then the effective frontier can be derived, depicting the trade-off of the portfolio's excess return and downside tracking error.The empirical analysis is conducted by daily closing prices of Shanghai Stock Exchange (SSE) 50 index and its constituent stocks from Jan.4^th to Dec.30^th in 2016. Comparing our model with the existing enhanced index tracking strategy based on the excess return-tracking error model, the following results are reached. Controlling the number of stocks, the portfolio based on our model can obtain higher unit risk-return. Moreover, the downside median deviation and maximum drawdown of our portfolio' excess return are both lower and the excess return is more right-skewed. Under the requirement of sparseness, the portfolio based on our model is able to obtain a higher accumulated return than the benchmark index in terms of out-of-sample performance, which is of great value for the both institutional and individual investors and enriches the existing research of enhanced index tracking model.