“双碳”目标下绿色双层投资组合研究

Research on Green Bilevel Portfolio under Carbon Peaking and Carbon Neutrality Goals

在绿色投资日益盛行和金融机构积极推进“双碳”目标的背景下,越来越多的投资者在估值、产品和策略中考虑ESG因素。随着ESG投资理念的深入,如何在投资组合中合理纳入ESG因素成为学界的研究热点。本文从预期效用理论出发,针对效用函数中风险厌恶系数和ESG偏好系数的估计困难以及投资组合规模缺乏限制等现实问题,提出了绿色双层投资组合模型。其中上层规划是决策效用函数系数的稀疏优化问题,下层规划是构建绿色投资组合的二次优化问题。在求解层面,针对不同约束情形,利用下层问题的最优性条件将双层规划问题转化为混合整数二次规划。研究结果表明:第一,通过模拟真实市场环境验证了模型的数值有效性,针对不同偏好的基准指数,模型可以准确估计隐含的参数水平;第二,通过验证2015—2021年间编制ESG100指数和上证50指数的341个投资组合,研究发现金融市场上的绿色指数隐含正向的ESG偏好,绿色指数相比于收益更加偏好资产的绿色属性;第三,以上证50和ESG100指数为基准构造的静态和动态投资组合在2015—2021年间不仅较好地实现了对基准的追踪,更获得了稳定的超额收益,从夏普比率,信息比率以及Omega比率等指标来看,普遍战胜了基准指数以及1/n策略。本文提出的绿色双层投资组合模型加强了绿色投资领域和现代投资组合理论的联系,对发展绿色指数型基金、扩大绿色金融市场直接融资规模具有重要的借鉴意义。

In the background of the growing popularity of green investment and the active implementation of“dual carbon”goals by financial institutions,more and more investors are considering ESG factors in their valuations,products,and strategies.The traditional Markowitz portfolio theory lacks attention to non-financial effects.It cannot directly guide the construction of green investment portfolios,resulting in the separation of investment practice and theory.With the deepening of ESG investment concepts,how to reasonably incorporate ESG factors into portfolios has become a research hotspot in the academic community.Most existing green portfolio models incorporate ESG factors based on the Markowitz mean-variance model by introducing ESG objectives,ESG constraints,or ESG utility functions.This paper proposes a green bi-level portfolio model for practical problems such as the difficulty in estimating the risk aversion coefficient and ESG preference coefficient in the utility function and the lack of restrictions on the size of the portfolio.The upper-level decision variables are the risk aversion coefficients of investors’green utility function regarding returns and ESG,as well as the sparse position of the portfolio.The lower-level variables are the green portfolio weights.At the solution level,for different constraints,the optimality condition of the lower-level problem is used to transform the bi-level programming problem into a mixed integer quadratic programming.When the upper and lower levels are unconstrained optimization problems,the bi-level programming can be simplified into an unconstrained optimization problem through the KKT condition of the lower level.Then the closed-form solution can be obtained.The model can not only estimate a portfolio’s implied ESG preference and risk aversion but can also be used in the construction of green index funds.The research indicates:First,the numerical validation of the model is verified by simulating the natural market environment.The model can accurately estimate the implicit parameters for benchmark indices with different preferences.Second,by verifying 341 portfolios that compiled the ESG100 Index and the Shanghai Stock Exchange 50 Index(SZ50)from 2015 to 2021,the study found that the green index in the financial market implies a positive ESG preference,and the green index prefers the green attributes of assets to income.Third,the static and dynamic portfolios constructed based on the SZ50 and ESG100 indices tracked the benchmarks well and achieved excess returns from 2015 to 2021.From the Sharpe ratio,information ratio,and Omega ratio,these portfolios generally beat the benchmark index and the 1/n strategy.The following investment recommendations are put forward based on the above research conclusions.For regulators,it is necessary to accelerate the relevant policies to support the establishment of financial products such as open-ended traded index funds of green financial indices.Institutional investors can use the green bi-level green portfolio model to construct green index funds,effectively avoiding the complex parameter decision-making process.Our model strengthens the connection between the green investment field and modern portfolio theory and has important reference significance for the construction and development of green index funds.