r - 使用portfolio.optim 函数在R 中进行二次编程时出错

Question

我试图从一个季度开始创建已实现的有效边界，每天收盘价为 100 只股票，不允许空头头寸。

第一步是计算每只股票当期的每日返回:

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() 函数来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，当我运行此函数时，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!

当我为更少的股票运行相同的代码时，它似乎运行良好:

# 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

有谁知道我为什么面临这个问题？
非常感谢你!

Answer 1

好吧，看看数据，没问题。问题是，正如错误所说，协方差矩阵不是正定的。快速测试证实
(顺便说一句 - 我正在使用包 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))

得到

> matrixcalc::is.positive.definite(cov(returns))
[1] FALSE

您可以做的是使用 Matrix::nearPD 将协方差矩阵调整为其最近的正定矩阵

returns.nearest.PD <- Matrix::nearPD(cov(returns))$mat
returns.nearest.PD <- as.matrix(returns.nearest.PD)

这将允许您通过显式指定 portfolio.optim 来使用 covmat :

(po <- portfolio.optim(as.matrix(returns), 
                covmat = returns.nearest.PD,
                shorts=FALSE,riskless=FALSE))

它可以正常工作:

> sum(po$pw)
[1] 1

并且您可以确认它对每个符号都有权重:

> length(po$pw)
[1] 99   

编辑
可以肯定的是，调整后的协方差矩阵非常接近原始协方差矩阵，差异很小:

> # 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