Maximum Decorrelation portfolio optimisation

Question

Suppose that I have a data for U.S sector indices such as Non Durable, Durable, Manufacturing,..., etc and for the companies within each of these sectors. I am aiming to see if for the given sectors, does adding and increasing number of companies affect the portfolio risk adjusted return.

Is there a way in R that write a code to:

1- Obtain weights to be allocated for each of these sectors based on max decorrelation, 2- Create several portfolios based on investing for assets in these sectors. For example, a portfolio with 4 assets and measure its Sharpe Ratio, a portfolio with 8 assets,..., etc.

I have tried computing the max decorrelation weights for the sectors using RiskPortfolios package in the following code:

sigma =covEstimation(return_sectoral_data)

weights_max_decorrel<-round(optimalPortfolio(Sigma = sigma, 
                 control = list(type = 'maxdec', constraint = 'lo')),2)

print(weights_max_decorrel)

  Durable  Manufacturing   Energy        Tech                   NonDurable 
                  0.41                    0.06                    0.34                    0.00                    0.16 
             Tech                  Shops               Health 
                   0.00                    0.03                    0.00 

But after getting these weights, I am not sure how can I create different portfolios based on investing in the companies of the portfolios with Non-zero weights.

Answer 1

# Assuming you have the return_sectoral_data and weights_max_decorrel

library(RiskPortfolios)
library(PortfolioAnalytics)

# Set seed for reproducibility
set.seed(123)

# Number of portfolios to create with different numbers of assets
portfolio_sizes <- c(4, 8, 12)

# Initialize a data frame to store results
portfolio_results <- data.frame(Size = numeric(),
                                SharpeRatio = numeric(),
                                stringsAsFactors = FALSE)

# Loop through different portfolio sizes
for (size in portfolio_sizes) {
  # Randomly select 'size' number of assets from each sector based on weights
  selected_assets <- lapply(names(weights_max_decorrel),
                             function(sector) sample(names(return_sectoral_data[[sector]]), size, replace = FALSE))
  
  # Flatten the list of selected assets
  selected_assets <- unlist(selected_assets)
  
  # Extract returns for the selected assets
  selected_returns <- return_sectoral_data[selected_assets]
  
  # Calculate portfolio returns and covariance matrix
  portfolio_return <- colMeans(selected_returns)
  portfolio_covariance <- cov(selected_returns)
  
  # Calculate portfolio volatility
  portfolio_volatility <- sqrt(t(weights_max_decorrel) %*% portfolio_covariance %*% weights_max_decorrel)
  
  # Calculate Sharpe Ratio
  portfolio_sharpe <- SharpeRatio(portfolio_return, portfolio_volatility)
  
  # Store results in the data frame
  portfolio_results <- rbind(portfolio_results, c(size, portfolio_sharpe))
}

# Print the results
print(portfolio_results)