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[知识整理]【2015年财管知识点总结】第四章:投资组合的风险计量 [复制链接]

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只看楼主 倒序阅读 使用道具 0楼 发表于: 2014-12-02
1.相关系数与协方差:衡量两种证券收益率之间共同变动程度(相关性)的指标 \e:FmG  
  1)相关系数:-1≤r≤1(通常:0<r<1) I0l.KiBm  
  相关系数(r)= DAMpR3  
  ①r=+1:完全正相关,一种证券报酬率的增长总是与另一种证券报酬率的增长成比例,组合风险不变; _UBJPb@=U  
  ②r=-1:完全负相关,一种证券报酬率的增长总是与另一种证券报酬率的减少成比例,组合风险可以为0; ay:\P.`5)  
  ③若:-1<r<+1,则:0<组合风险<不变,即: 9S H<d)^  
  相关系数越接近于+1,风险分散效应越弱; Tt<-<oyU.  
  相关系数为正(正相关),相关系数绝对值越大,风险分散效应越弱; |T$a+lHMD  
  相关系数越接近于-1,风险分散效应越强; z<[.MH`ln  
  相关系数为负(负相关),相关系数绝对值越大,风险分散效应越强。 }`9fZK{. @  
      2)协方差 &Qq/Xi,bZ  
  ①公式:σjk=rjkσjσk oX 2DFgz  
  ②某证券与其本身的协方差等于该证券的方差 XuFm4DEJ  
2.投资组合报酬率的标准差 -wtTq ph'  
  1)计算公式: &FJU%tFA  
  投资组合报酬率的方差:组合内各证券两两配对组合(包括某证券自己和自己的配对)的协方差(n2个),再乘以两者的投资比重,加总的结果。 N}+B:l]Qy  
  2)协方差矩阵:组合内证券两两配对一共可得到n2个协方差项,构成协方差矩阵。 hDB`t $  
  以三种证券为例,协方差矩阵为: p~, 3A:i  
  σ1,1σ1,2σ1,3 ;H y!0n  
  σ2,1σ2,2σ2,3 EAC(^+15K  
  σ3,1σ3,2σ3,3 g~N ij~/  
  沿矩阵对角线共有3个方差项(即:某证券自己和自己配对的协方差),其他不在对角线上的配对组合的协方差共有6个,且两两相等(如:σ1,2=σ2,1)。 .}$`+h8W T  
      【结论1】 Ql#W /x,e  
  对于由n种证券构成的组合,两两配对的协方差矩阵共有n2项,其中包括n个方差项和(n2-n)个协方差项。 UYcyk $ da  
  【结论2】 M=\d_O#;Z  
  协方差矩阵中,方差项代表个别证券的风险,协方差项代表证券之间的共同变动程度(相关性)。 "lU]tIpCu  
  随着组合内证券数量的增加,方差项所占的比重越来越小,表明个别证券的风险对投资组合风险的影响越来越小,直至可以忽略不计;而协方差项所占比重越来越大,表明投资组合风险主要取决于组合内各证券收益率的相关性。 r\l3_t  
  因此,充分投资组合的风险,只受证券之间协方差(即相关性或共同变动程度)的影响,而与各证券本身的方差(个别风险)无关。 xyS2_Q  
      3)投资组合标准差的计算:协方差矩阵中的每一项(n2个方差及协方差),分别乘以两种资产的投资比重,再计算合计数,得到投资组合的方差,开方即得到标准差。 'TK$ndy;7}  
  以两种资产A和B为例,假设投资比重分别为:WA和WB,则协方差矩阵为: S& ,Ju%  
  σA,AσA,B tv@Z 5  
  σB,AσB,B ~b>nCP8q  
  两种资产组合的方差 yRq8;@YGY  
   rY[3_NG%  
  (类似于完全平方式) 1&8j3"  
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只看该作者 1楼 发表于: 2015-09-05
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