均值-方差模型具有一般不确定性下的最优资产组合选择

引入以记忆系数和无差异系数表征的随机变量测度均值-方差模型的一般不确定性特征,反映投资者的模型信任程度,研究均值-方差模型具有一般不确定性下的最优资产组合选择问题。基于资本市场线理论,构建最优资产组合选择是模型信任程度和基于均值-方差模型的传统资产组合选择的线性函数;基于记忆系数和无差异系数的不同组合,运用基于事例推理的方法求解二次效用投资者的最优模型信任程度,获得均值-方差模型具有一般不确定性下的最优资产组合,并以上证综指1997年1月-2014年8月的月度收益数据形成两个研究样本予以实证比较研究。结果表明,较大风险规避投资者,在较大记忆系数和较小无差异系数下,其模型信任程度调整较快、资产组合调整幅度大,表现出可获得性和代表性行为偏差,通常采取积极资产组合策略;反之,其模型信任程度调整渐进、资产组合调整幅度小,表现出锚定性和保守性行为偏差,通常采取消极资产组合策略;模型一般不确定性对最优资产组合选择的影响强于股票市场记忆性的影响。研究体现了投资者的有限理性,将传统的资产组合选择问题延伸至行为金融学领域。

Optimal Portfolio Choice under the Mean-Variance Model with General Uncertainty

The problem of model uncertainty is the model's basic characteristic in the system of society and economy, the portfolio choice often studies the characteristic of investment decision under a specific environment based on an asset return model that describs the process of asset price. Since the investor is often hard to imagine all states of nature relevant to his portfolio choice problem which causes an uncertainty concerning an asset return model, the uncertainty is characterized as general uncertainty where neither states of nature nor their probabilities are known. So, in this paper, the problem of optimal portfolio choice is studied under the mean-variance model with general uncertainty by introducing a stochastic variable to measure its general uncertainty, which is characterized by the memory and indifference parameter, and reflects the investor's model belief degree. Based on the theory of capital market line, it builds that the optimal portfolio choice is a linear function of the model belief degree and the conventional portfolio choice based on the mean-variance model; based on the different pairs of memory and indifference parameter, the method of case-based reasoning is applied to determine the optimal model belief degree of the investor with quadratic utility function, obtain the optimal portfolio choice under the mean-variance model with general uncertainty, and do an empirical study based on the sample of Shanghai Exchange Composite Index monthly returns from January 1997 to August 2014. Empirical results show, the investor with a large risk aversion, characterized by high memory parameter and small indifference parameter, quickly adjusts its model belief degree and the portfolio choice. Such an investor may exhibit availability and representativeness biases, and often take the active portfolio strategy; on the contrary, the model belief degree and the portfolio choice is gradually adjusted, the investor may exhibit anchoring and conservatism biases, and often take the passive portfolio strategy; the effect of the nearer stock market information on optimal portfolio choice is stronger than that of the farther stock market information on optimal portfolio choice, but the effect of model general uncertainty on optimal portfolio choice is strongest. This study reflects the investor's bounded rationality and extends the problem of portfolio choice to the field of behavioral finance.