Abstract: Skewness and kurtosis are frequently utilized to describe stylized facts within the financial community. However, their conventional moment-based measures exhibit a high degree of sensitivity to outliers. To improve the deficiency of risk measurement and model optimization in the existing higher order moment portfolio selection model, this paper develops a parametric portfolio model, referred to as the B-S-K model, which incorporates dynamic higher moments risk. Specifically, we first apply the mixed data sampling quantile regression (MIDAS-QR) model to improve the timeliness, accuracy and robustness of dynamic higher moments risk measure by exploiting rich information contained in high-frequency data. Second, we develop a parametric portfolio method with characteristic variables, dynamic skewness risk, and dynamic kurtosis risk for utility-maximizing investors with an exponential utility function. This parametric method with conditional kurtosis not only takes into account the investor attitude towards kurtosis, but also captures implicitly the relation between the stock characteristics and investor expected utility which has been ignored in most of the literature. Furthermore, our approach greatly reduces the number of parameters and improves the solution efficiency. In this case, we only need to estimate the coefficients of variables that enter the portfolio weights instead of the weight coefficients of each stock at each time point. Third, a three-step solution scheme is designed for parametric portfolio with dynamic skewness and kurtosis risks via the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. In the first two steps, the coefficients of stock-specific characteristics and dynamic skewness risk are estimated separately. In the third step, we keep the coefficients in the first two step fixed at their values obtained, the remaining dynamic kurtosis risk coefficient is estimated by maximizing the investor’s expected utility. By comparing the estimation results of step 2 and step 3, the role of conditional kurtosis in allocating assets and improving portfolio performance can be investigated.
The empirical analysis is conducted on six single stocks and thirteen industry groups in China. There are at least three conclusions that can be drawn. Firstly, compared with moment-based skewness and kurtosis, the MIDAS-QR based dynamic higher moments risk measure is indeed robust and effective, which not only captures the time-variation in financial risk, but also shows much smoother and less sensitive to outliers. Secondly, price earnings ratio, book-to-market ratio and dynamic skewness risk are positively related to portfolio weights, while conditional volatility and dynamic kurtosis risk are negatively related to portfolio weights. The results provide evidence supporting the notion that investors exhibit a preference for stocks characterized by higher price-to-earnings ratio, higher book-to-market ratio, relatively larger skewness, lower conditional volatility, and smaller conditional kurtosis. Importantly, it is observed that stocks with higher conditional kurtosis are assigned smaller weights in the optimal portfolio selection. Once again, investor aversions towards minimizing kurtosis are confirmed. These findings offer rational mechanism explanations for investment decisions. Finally, the proposed B-S-K model, which incorporates dynamic higher moments risk, demonstrates significant and consistent superiority in terms of return, risk, and risk-adjusted return when compared to the equal weight scheme, M-V model, basic (B) model, and B-S model across various levels of risk aversion. These results highlight the necessity and benefits of incorporating dynamic higher moments risk into portfolio selection.
Considering the fact that portfolio selection is affected by many other factors, such as the market capitalization, the lagged returns, and so on, incorporating as many factors as possible to the model helps to improve the performance of portfolio selection. For future research, we will consider the impact of more factors on portfolio weights, and introduce dimension reduction techniques such as penalized variable selection to identify key factors. This will be helpful for producing sensible portfolio weights and providing a list of important factors for investment decision making.

Key words: higher moments risk, portfolio selection, parametric strategy, MIDAS-QR, CARA utility function

摘要： 针对已有高阶矩组合投资模型中风险测度与模型求解的不足,本文构建动态高阶矩参数化组合投资决策模型(B-S-K)并给出其求解方案。首先,运用混频数据抽样分位数回归(MIDAS-QR)模型,充分挖掘高频数据信息,提高动态高阶矩风险测度的及时性、准确性和稳健性;其次,采用参数化组合投资策略,将资产特征变量、动态偏度风险和动态峰度风险纳入组合投资权重函数,大幅缩减待估计参数数目,提高模型求解效率。分别对中国股票市场的个股和行业板块指数进行实证,研究结果一致表明:第一,基于MIDAS-QR模型的动态高阶矩风险稳健性测度,不仅充分考虑了金融风险的时变特征,而且测度结果受异常值影响较小,是一个稳健且有效的测度方法;第二,市盈率、账面价值比、动态偏度风险与组合投资权重显著正相关,条件波动率、动态峰度风险与组合投资权重显著负相关,这些为组合投资决策提供了较好的机理性解释;第三,与等权方案、M-V模型、基准(B)模型和B-S模型等相比,本文构建的B-S-K模型,在收益、风险和风险调整收益等三个方面均表现出显著且稳定的优势。

关键词: 高阶矩风险, 组合投资, 参数化策略, MIDAS-QR, CARA效用函数