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I’m trying to create the realized efficient frontier from a quarter period, with the daily closing prices of a hundred stocks, no short positions allowed.

The first step is to calculate the daily return for the period for each stock:

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

Then I used the portfolio.optim() function from the {tseries} to perform the quadratic programing and create the an optimum portfolio:

w2 <-portfolio.optim(as.matrix(returns),shorts=FALSE,riskless=FALSE)

But, when I run this function the following message appears: 

Error in solve.QP(Dmat, dvec, Amat, bvec = b0, meq = 2) : matrix D in quadratic function is not positive definite!

When I run the same code for fewer stocks, It seems to work well:

# 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

Anybody knows why I’m facing this problem? Thank you very much!

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  • Please provide a reproducible example Commented Mar 22, 2016 at 11:21
  • Have you tried running it with the second part of the data assets <- Quarter[,70:ncol(Quarter)] ? Maybe a data problem. Commented Mar 22, 2016 at 11:29
  • [1:n-1,] is not [1:(n-1),]! 1:n-1 is the same as 0:(n-1) because of operator precedence. Commented Mar 22, 2016 at 11:32
  • @jogo Just fix It, thank you! but the error was kept! Commented Mar 22, 2016 at 11:38
  • Not much help without seeing the data - can you share your 20153Q.csv somehow? Commented Mar 22, 2016 at 11:39

1 Answer 1

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OK, had a look at the data, and it's OK. The problem is, as the error says, that the covariance matrix is not a positive definite. A quick test confirms that (BTW - I'm using packages matrixcalc and 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))

gets

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

What you can do is adjust the covariance matrix to its nearest positive definite matrix by using Matrix::nearPD

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

which will then allow you to using portfolio.optim by explicitly specifying the covmat:

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

which works without error:

> sum(po$pw) [1] 1

and you can confirm that it has weights for each symbol:

> length(po$pw) [1] 99

EDIT Just to be sure, the adjusted covariance matrix is very close to the original covariance matrix, the diffs are miniscule:

> # 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
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thank you very much for your help! Really appreciated!

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