我正试图在一个季度内创建实现有效的边界,每日收盘价为100股,不允许空头头寸。
第一步是计算每只股票的期间的每日回报:
setwd("/Users/ClariceLoureiro/Desktop/COPPEAD/5th Term/Introducao ao Pacote estatistico em R/db")
getwd()
library(tseries)
Quarter <- read.csv2("20153Q.csv",header=T,dec=".")
assets <- Quarter
n <- nrow(assets)
returns <- (assets[2:n,])/(assets[1:n-1,])-1
然后我使用{tseries}中的portfolio.optim()函数执行二次规划并创建最佳投资组合:
w2 <-portfolio.optim(as.matrix(returns),shorts=FALSE,riskless=FALSE)
但是,当我运行此功能时,会出现以下消息:
Error in solve.QP(Dmat, dvec, Amat, bvec = b0, meq = 2) :
matrix D in quadratic function is not positive definite!
当我为较少的股票运行相同的代码时,它似乎运作良好:
# Choosing just 70 stocks out of 100
Quarter <- read.csv2("20153Q.csv",header=T,dec=".")
assets <- Quarter[,1:70]
#Calculating the returns
n <- nrow(assets)
returns <- (assets[2:n,])/(assets[1:n-1,])-1
#Portfolio optimization
w2 <-portfolio.optim(as.matrix(returns),shorts=FALSE,riskless=FALSE)
#Weights
w2$pw
[1] -3.644189e-19 2.390930e-18 1.156864e-01 -3.918512e-16 2.676315e-17 -3.136607e-16
[7] 3.158552e-16 3.901110e-16 -1.112018e-17 -1.927371e-16 1.264102e-19 9.040602e-17
[13] 4.881587e-02 2.291796e-17 -6.328846e-17 8.224983e-02 1.210207e-16 1.329818e-16
[19] 3.460248e-17 8.966350e-02 -4.929045e-17 1.689343e-17 -9.573418e-17 0.000000e+00
[25] -1.323861e-18 1.133006e-01 -1.896390e-17 -1.386383e-17 1.525087e-16 4.805648e-02
[31] -4.695605e-18 6.110056e-02 6.128005e-17 -1.042136e-17 9.100962e-03 1.846112e-17
[37] 5.128598e-17 -3.981178e-16 -4.379979e-16 1.936907e-17 4.694298e-02 2.676847e-18
[43] 8.752091e-18 4.121872e-02 2.970893e-17 6.871426e-03 3.612246e-17 4.217859e-17
[49] -4.834692e-18 3.071602e-17 -7.301697e-19 -1.309647e-17 2.034399e-02 4.689105e-03
[55] -6.014390e-19 6.389368e-02 7.511315e-02 -4.338530e-17 1.551683e-18 -6.838667e-20
[61] 1.445453e-18 4.783709e-17 4.803861e-17 1.866350e-02 -1.471388e-17 1.100957e-01
[67] 1.809216e-02 2.610136e-02 -2.751673e-17 1.393180e-18
# It must sum 1
sum(w2$pw)
[1] 1
有人知道我为什么会遇到这个问题吗? 非常感谢你!
答案 0 :(得分:6)
好的,查看了数据,没关系。正如错误所说,问题是协方差矩阵不是正定的。快速测试证实了这一点
(顺便说一句 - 我使用包matrixcalc
和Matrix
):
library(tseries)
prices <- read.csv2("20153Q.csv",header=TRUE,dec=".")
n <- nrow(prices)
returns <- (prices[2:n,])/(prices[1:(n-1),])-1
portfolio.optim(as.matrix(returns), shorts=FALSE,riskless=FALSE)
# cov(X) not a positive definitive
# check
matrixcalc::is.positive.definite(cov(returns))
得
> matrixcalc::is.positive.definite(cov(returns))
[1] FALSE
你可以做的是使用Matrix::nearPD
returns.nearest.PD <- Matrix::nearPD(cov(returns))$mat
returns.nearest.PD <- as.matrix(returns.nearest.PD)
然后,您可以通过明确指定portfolio.optim
:
covmat
(po <- portfolio.optim(as.matrix(returns),
covmat = returns.nearest.PD,
shorts=FALSE,riskless=FALSE))
无误地运行:
> sum(po$pw)
[1] 1
您可以确认每个符号都有权重:
> length(po$pw)
[1] 99
修改的 可以肯定的是,调整后的协方差矩阵与原始协方差矩阵非常接近,差异微乎其微:
> # the matrices are really close
> sum((abs(returns.nearest.PD - cov(returns)) > 0.000000001)==TRUE)
[1] 0
> # the matrices are really close
> sum((abs(returns.nearest.PD - cov(returns)) > 0.0000000001)==TRUE)
[1] 74