Abstract: Conditional skewness is one of the stylized facts in financial market. Its most widely used measure is the standardized third moment, but this moment based measure is very sensitive to outliers. In addition, as many previous works have shown, conditional skewness plays an important role in portfolio selection. The conventional portfolio approaches, which ignore the effect of conditional skewness, are often difficult to fully capture the "true risk" and cannot disperse financial risk efficiently. Thus, it is necessary to incorporate conditional skewness into the portfolio selection problem. In the presence of skewness, it is often introduced into the objective function of a portfolio selection model. This makes the portfolio optimization a challenging task, which needs to trade off the conflicting and competing objects simultaneously. To address the above issues, the combination of mixed data sampling (MIDAS) and quantile regression (QR), namely MIDAS-QR model, are first applied to improve the performance of conditional skewness measure. Then, the portfolio weights are designed as a linear function of conditional skewness and asset characteristics, and portfolio selection models are developed with the Constant Relative Risk Aversion (CRRA) utility. Furthermore, a two-step solution scheme is designed for its solution. Our approach has at least three advantages. First, the MIDAS-QR model makes full use of rich information contained in high-frequency data to estimate time-varying conditional skewness accurately and robustly. Second, the portfolio models we constructed not only take into account the investor attitude towards skewness, but also can be easily optimized as it reduces the numbers of parameters to be estimated. Third, the two-step solution scheme allows us to identify the specific role of conditional skewness in portfolio selection, including the significance, direction and magnitude of its impact. To illustrate the efficacy of our method, an empirical application on 10 typical stocks from the China Securities Index (CSI) 300 Index is conducted. The data is collected from the Genium Finance platform (http://www.genius.com.cn) and covers the period from Jan 1, 2006 to May 31, 2017. The rolling estimates of moment-based skewness and hybrid skewness are compared. Then, the proposed models are compared with the classical equal-weighted scheme and the mean-variance model in terms of expected return, standard deviation, downside risk, Sharpe Ratio, and Sortino Ratio. The empirical results are promising and show that compared with moment-based skewness, the rolling estimation distribution of hybrid skewness is more concentrated and less sensitive to outliers. This shows that hybrid skewness measure is an effective and robust method. Moreover, our proposed portfolio models with conditional skewness perform better than those competing models in terms of dispersing investment risk and improving portfolio performance. In practice, kurtosis is also concerned by investors. A rational investor will prefer to minimize kurtosis, which can be seen as a way to reduce the possibility of extreme events. To this end, it would be necessary to measure conditional kurtosis and incorporate it into the construction of optimal portfolio selection. This is an interesting topic and we leave it for future research.

Key words: conditional skewness, portfolio selection, MIDAS, quantile regression