STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASURES

In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivari-ate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.     

STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASUREgS

In order to study the effect of different risk measures on the efficient portfolios （fron- tier） while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios （frontier） based on risk measures such as variance, value at risk （VaR）, and expected shortfall （ES） is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance （MV） efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.     

Robust portfolio choice with CVaR and VaR under distribution and mean return ambiguity

We consider the problem of optimal portfolio choice using the Conditional Value-at-Risk (CVaR) and Value-at-Risk (VaR) measures for a market consisting of n risky assets and a riskless asset and where short positions are allowed. When the distribution of returns of risky assets is unknown but the mean return vector and variance/covariance matrix of the risky assets are fixed, we derive the distributionally robust portfolio rules. Then, we address uncertainty (ambiguity) in the mean return vector in addition to distribution ambiguity, and derive the optimal portfolio rules when the uncertainty in the return vector is modeled via an ellipsoidal uncertainty set. In the presence of a riskless asset, the robust CVaR and VaR measures, coupled with a minimum mean return constraint, yield simple, mean-variance efficient optimal portfolio rules. In a market without the riskless asset, we obtain a closed-form portfolio rule that generalizes earlier results, without a minimum mean return restriction.     

不存在无风险资产的投资组合灵敏度分析

本文研究了M－V证券投资组合灵敏度分析方法。考虑了不存在无险资产时证券预睡益率和协方差矩阵存在扰动的情形，给出了最优投资组合有效边缘的漂移方程及组合扩展路径。     

基于几种风险测度的多阶段组合优化研究

基于均值-方差(MV)、VaR(Value at Risk)、CVaR(Conditional VaR)、HMCR(p=1,2,3)(Higher Moment Coherent Risk)几种风险测度进行多阶段组合优化研究。首先从一致性公理和随机占优一致性角度分析几种风险测度的风险识别能力,认为HMCR(p=2,3)的风险识别能力最高,然后给出静态和动态下的风险规避型的规划函数及多阶段CVaR和HMCR模型,最后依据单阶段和多阶段优化模型,对上证50指数成份股进行实证分析。对比单阶段和多阶段下几种风险测度优化组合的累计收益率及几种风险测度之间的关系,结合上证50指数收益率发现,多阶段优化组合要整体优于单阶段优化组合,且HMCR(p=2,3)要优于指数收益率和其它几种风险测度。从投资者投资决策方面来分析,HMCR(p=2,3)型积极投资策略比较适用于股市平稳期、顶峰期和下降期,被动投资策略比较适用于股市上升期。     

基于风险网络结构的资产分配策略研究

股票市场是一个高风险市场,如何在频繁发生的极端波动环境下进行有效的资产分配是当前热点问题。本文首次应用VaR模型构建股市风险网络,并基于风险网络模型进行最优投资组合成分选择,分析不同市场波动行情下最优资产分配权重和股票中心性的时变关系,融合风险网络时变中心性和个股表现提出新的动态资产分配策略(φ投资策略)。结果表明:在股市上涨和震荡期,股票中心性和最优投资组合权重呈正相关关系;股市下跌期,股票中心性和最优投资组合权重呈负相关关系;当φ>0.05时,投资者的合理投资区域向高中心性节点移动,反之。φ投资策略的绩效表现证明了风险网络结构能提高投资组合选择过程。此研究对于优化资产配置、提高投资收益、多元化分散投资风险具有重要意义。     

On minimizing drawdown risks of lifetime investments

Drawdown measures the decline of portfolio value from its historic high-water mark. In this paper, we study a lifetime investment problem aiming at minimizing the risk of drawdown occurrences. Under the Black–Scholes framework, we examine two financial market models: a market with two risky assets, and a market with a risk-free asset and a risky asset. Closed-form optimal trading strategies are derived under both models by utilizing a decomposition technique on the associated Hamilton–Jacobi–Bellman (HJB) equation. We show that it is optimal to minimize the portfolio variance when the fund value is at its historic high-water mark. Moreover, when the fund value drops, the proportion of wealth invested in the asset with a higher instantaneous rate of return should be increased. We find that the instantaneous return rate of the minimum lifetime drawdown probability (MLDP) portfolio is never less than the return rate of the minimum variance (MV) portfolio. This supports the practical use of drawdown-based performance measures in which the role of volatility is replaced by drawdown.     

损失厌恶偏好与资产组合选择研究

在不确定性条件下,期望的不可计算性、行动结果比较的局限性以及投资个体选择的非理性使理性假定的选择理论脱离现实,因此重新探讨决策选择准则是必要的.以行为金融理论中不确定性状态下的有限理性与满意准则为依据,引入与满意准则一致且体现损失厌恶偏好的VaR作为风险指标,构建行为资产组合模型,在一种简单新颖的M-V模型的矩阵解法基础上,探寻了正态与部分非正态性假设下VaR-BPT模型的显性最优解或有效前沿,解决了现实中最优投资组合选择的可操作性难题,并在中国股票市场验证了正态性转换方法是处理非正态分布下资产组合选择问题的一种优秀方法.     

An optimal investment and consumption model with stochastic returns

We consider a financial market consisting of a risky asset and a riskless one, with a constant or random investment horizon. The interest rate from the riskless asset is constant, but the relative return rate from the risky asset is stochastic with an unknown parameter in its distribution. Following the Bayesian approach, the optimal investment and consumption problem is formulated as a Markov decision process. We incorporate the concept of risk aversion into the model and characterize the optimal strategies for both the power and logarithmic utility functions with a constant relative risk aversion (CRRA). Numerical examples are provided that support the intuition that a higher proportion of investment should be allocated to the risky asset if the mean return rate on the risky asset is higher or the risky asset return rate is less volatile. Copyright © 2008 John Wiley & Sons, Ltd.     

Portfolio selection with a minimax measure in safety constraint

In this paper, we attempt to design a portfolio optimization model for investors who desire to minimize the variation around the mean return and at the same time wish to achieve better return than the worst possible return realization at every time point in a single period portfolio investment. The portfolio is to be selected from the risky assets in the equity market. Since the minimax portfolio optimization model provides us with the portfolio that maximizes (minimizes) the worst return (worst loss) realization in the investment horizon period, in order to safeguard the interest of investors, the optimal value of the minimax optimization model is used to design a constraint in the mean-absolute semideviation model. This constraint can be viewed as a safety strategy adopted by an investor. Thus, our proposed bi-objective linear programming model involves mean return as a reward and mean-absolute semideviation as a risk in the objective function and minimax as a safety constraint, which enables a trade off between return and risk with a fixed safety value. The efficient frontier of the model is generated using the augmented -constraint method on the GAMS software. We simultaneously solve the ratio optimization problem which maximizes the ratio of mean return over mean-absolute semideviation with same minimax value in the safety constraint. Subsequently, we choose two portfolios on the above generated efficient frontier such that the risk from one of them is less and the mean return from other portfolio is more than the respective quantities of the optimal portfolio from the ratio optimization model. Extensive computational results and in-sample and out-of-sample analysis are provided to compare the financial performance of the optimal portfolios selected by our proposed model with that of the optimal portfolios from the existing minimax and mean-absolute semideviation portfolio optimization models on real data from S&P CNX Nifty index.