Maximum number of assets in R package 'performanceanalytics' optimizer

Question

This is just a general question regarding the maximum number of stocks I can use in the r performanceanalytics optimizer function.

My code works fine for optimizing anything up to around 110 assets but anything exceeding that gives an error. I couldn't find any documentation regarding limits around the actual number of assets. Any help is appreciated.

Further to the above, I have added reproducible code example below:

library(xts)
library(PortfolioAnalytics)
num_stocks = 300
num_periods = 200

rets = replicate(num_stocks, rnorm(num_periods))
colnames(rets) = paste0('stock', 1:num_stocks)

dates = seq(as.Date('2000-01-01'), by = 'month', length.out = num_periods) - 1




#100 stocks, returns optimal weights
equity.data = xts(rets, order.by = dates)[,1:100]

stocks <- colnames(equity.data)

# Specify an initial portfolio
portf.init <- portfolio.spec(stocks)

# Add constraints
# weights sum to 1
portf.minvar <- add.constraint(portf.init, type="full_investment")
# box constraints
portf.minvar <- add.constraint(portf.minvar, type="box", min=0.00, max=0.10)

# Add objective
# objective to minimize portfolio variance
portf.minvar <- add.objective(portf.minvar, type="risk", name="var")

optimize.portfolio(equity.data, 
               portfolio=portf.minvar, 
               optimize_method="ROI",
               trace=TRUE)


## 200 stocks, optimizer returns N/As for optimizes weights
equity.data = xts(rets, order.by = dates)[,1:200]

stocks <- colnames(equity.data)

# Specify an initial portfolio
portf.init <- portfolio.spec(stocks)

# Add constraints
# weights sum to 1
portf.minvar <- add.constraint(portf.init, type="full_investment")
# box constraints
portf.minvar <- add.constraint(portf.minvar, type="box", min=0.00, max=0.10)

# Add objective
# objective to minimize portfolio variance
portf.minvar <- add.objective(portf.minvar, type="risk", name="var")

optimize.portfolio(equity.data, 
               portfolio=portf.minvar, 
               optimize_method="ROI",
               trace=TRUE)

Answer 1

I think the problem arises because of issues with calculating covariance matrices where (num_stocks = 300) > (num_periods = 200).

If I increase the number of periods to say 1000, there is no error when optimizing for 200 stocks.

Thanks all for your time