戴维.鲁伯特的《统计与金融》第五章第五节有详细的理论推导
作为锦上添花,附上有效前沿的MC模拟
n<-4000
e<-c(0.04,0.05,0.045)
E<-matrix(e,nrow=3,ncol=1)#期望收益
s<-c(0.1,0.05,0.01,0.05,0.2,0.02,0.01,0.02,0.2)
S<-matrix(s,nrow=3,ncol=3)#协方差矩阵
xx<-numeric(n)
yy<-numeric(n)
for (j in 1:n)
{
x<-runif(3,0,200)
w<-matrix(x/sum(x),nrow=1,ncol=3)#随机生成头寸份额
xx[j]=as.numeric(w%*%E)
yy[j]=as.numeric(w%*%S%*%t(w))
}
plot(yy,xx,pch=20)