CAJ | 학술논문

随着指数衍生产品日益受到重视,指数化投资组合常被传统的消极基金管理者或机构所采用,而用有限的资金按指数构成比例进行投资显然是不现实的,所以指数的最优误差追踪就显得更加重要。将追踪误差定义为证券投资组合收益率与所追踪的指数基准收益率之差的均值平方和的平方根,建立了基数约束（即总资产数不超过某个特定整数K）下考虑投资者损失规避决策偏好的跟踪误差最小化模型,并设计了一个粒子群算法求解模型。实际算例表明,所构建的模型和算法是有效的。
수착지수연생산품일익수도중시,지수화투자조합상피전통적소겁기금관리자혹궤구소채용,이용유한적자금안지수구성비례진행투자현연시불현실적,소이지수적최우오차추종취현득경가중요。장추종오차정의위증권투자조합수익솔여소추종적지수기준수익솔지차적균치평방화적평방근,건립료기수약속（즉총자산수불초과모개특정정수K）하고필투자자손실규피결책편호적근종오차최소화모형,병설계료일개입자군산법구해모형。실제산례표명,소구건적모형화산법시유효적。
As the index derivative production are paid attention to day and day,index portfolio are often used by investor or financial setup,but it is not realistic that investors invest index according to the proportion of index fund construction with limited fund in number.So the minimum tracking error of index is becoming increasingly important.In this paper,the tracking error is defined as the standard deviations of the returns＇differences（i.e.the root-mean-squared devia-tion） between the portfolio and the benchmark of index,and we model investor＇s preferences by introducing loss aversion to the index tracking objective function.Portfolio optimization model of the minimum tracking error is established with cardinality constraints.A particle swarm op-timization（PSO） algorithm is proposed to solve the tracking error minimization problem.The numerical results show that PSO approach is successful in portfolio optimization.