带有交易费用及风险厌恶系数的投资组合有效边界研究
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摘要
有效边界是投资组合的一个重要研究内容,用来判断投资组合的有效性.研究含有无风险资产投资组合的有效边界并推导出相关数学表达式.同时,交易费用又是投资者需要考虑的一个重要因素,在此基础上,考虑投资者对风险的厌恶程度,引入了风险厌恶系数,推导出带交易费用及风险厌恶系数的投资组合的有效边界.结果表明,交易费用增大,有效边界向下移动;交易费用减小,有效边界向上移动;而投资者对风险厌恶程度并不影响有效边界.用实例分析了2种投资组合模型的有效边界.
Effective frontier is an important part of the portfolio and is used to determine the effectiveness of a portfolio.Studies the effective frontier of portfolio with riskless assets and deduces the relevant mathematical expressions.At the same time,the transaction cost is an important factor that investors need to consider.On this basis,considering the degree of risk aversion of the investor,the risk aversion coefficient is introduced,and the effective frontier of the portfolio with transaction cost and risk aversion coefficient is deduced.The results shows that the effective frontier moves downwards when the transaction costs increase,the effective frontier move upward when the transaction costs are reduced,investors′ risk aversion does not affect the effective frontier.Finally,effective frontiers of the two portfolio models are analyzed by examples.
Effective frontier is an important part of the portfolio and is used to determine the effectiveness of a portfolio.Studies the effective frontier of portfolio with riskless assets and deduces the relevant mathematical expressions.At the same time,the transaction cost is an important factor that investors need to consider.On this basis,considering the degree of risk aversion of the investor,the risk aversion coefficient is introduced,and the effective frontier of the portfolio with transaction cost and risk aversion coefficient is deduced.The results shows that the effective frontier moves downwards when the transaction costs increase,the effective frontier move upward when the transaction costs are reduced,investors′ risk aversion does not affect the effective frontier.Finally,effective frontiers of the two portfolio models are analyzed by examples.
引文
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[12]姚海祥,李仲飞.最低投资比例约束下的证券组合模型及有效边界解析式[J].运筹学学报,2009(2):119-128
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[14]谢军,杨春鹏,闫伟.含有无风险资产的情绪最优投资组合[J].系统管理学报,2012(4):540-545
[15]尹楠.投资组合最优化有效边界绘制的实证分析[J].财会月刊,2015(11):69-71
[16]周伊佳,于波.几种最优投资组合在有效边界上相对位置[J].大连理工大学学报,2016(4):420-426
[17]郝玉芹.马可维茨模型与单因素模型有效边界比较分析[J].科技视界,2016(27):186,213
[18]唐小我,曹长修.组合投资证券有效边界的研究[J].预测,1993(4):35-38
[19]唐小我.组合证券投资决策的计算方法[J].管理工程学报,1990(3):45-48
[2]Sharpe W F.A simplified model for Portfolio Selection analysis[J].Management Science,1963(9):277-293
[3]Ross S A.The arbitrage theory of capital asset pricing[J].Journal of Economic Theory,1976(13):341-360
[4]Mao J C T.Models of capital budgeting,E-V versus E-S[J].Journal of Finance and Quantitative Analysis,1970(5):657-675
[5]Swalm R O.Utility theory-insights into risk taking[J].Harvard Business Review,1966,44:123-136
[6]Konno H.Piecewise linear risk functions and portfolio optimization[J].Journal of the Operations Research Society of Japan,1990,33:139-156
[7]Speranza M G.Linear programming models for portfolio optimization[J].Finance,1993(14):107-123
[8]柏林,房勇.基于模糊回归分析的投资组合选择模型[J].系统工程理论与实践,2015(7):1770-1776
[9]张鹏,张卫国,张逸菲.具有最小交易量限制的多阶段均值-半方差投资组合优化[J].中国管理科学,2016(7):11-17
[10]唐小我,曹长修.组合投资证券有效边界的研究[J].预测,1993(4):35-38
[11]陈收,赵禹骅.证券组合投资有效集与有效边界的研究[J].湖南大学学报,1995(2):123-128
[12]姚海祥,李仲飞.最低投资比例约束下的证券组合模型及有效边界解析式[J].运筹学学报,2009(2):119-128
[13]夏江山,荣喜民.具有交易成本的组合投资有效边界的研究[J].天津轻工业学院学报,2003(18):37-39
[14]谢军,杨春鹏,闫伟.含有无风险资产的情绪最优投资组合[J].系统管理学报,2012(4):540-545
[15]尹楠.投资组合最优化有效边界绘制的实证分析[J].财会月刊,2015(11):69-71
[16]周伊佳,于波.几种最优投资组合在有效边界上相对位置[J].大连理工大学学报,2016(4):420-426
[17]郝玉芹.马可维茨模型与单因素模型有效边界比较分析[J].科技视界,2016(27):186,213
[18]唐小我,曹长修.组合投资证券有效边界的研究[J].预测,1993(4):35-38
[19]唐小我.组合证券投资决策的计算方法[J].管理工程学报,1990(3):45-48