port_2_max_ret <- portfolio.spec(assets = colnames(returns_date_droped_dividened2)) # Add objectives - here we minimize risk (VAR) port_2_max_ret <- add.objective(portfolio = port_2_max_ret, type = "risk", name = "CVaR")#added #port_2_max_ret <- add.objective(portfolio=port_2_max_ret, type = "risk_adjusted_return", name = "SharpeRatio", risk_free_rate = risk_free_rate) # Add constraints - fully invested portfolio with no short sales port_2_max_ret <- add.constraint(portfolio = port_2_max_ret, type = "long_only") port_2_max_ret <- add.constraint(portfolio = port_2_max_ret, type = "full_investment") # Optimize the portfolio to minimize risk optimal_portfolio_2 <- optimize.portfolio(R = returns_date_droped_dividened2, portfolio = port_2_max_ret, optimize_method = "ROI") optimal_weights <- extractWeights(optimal_portfolio_2) asset_names <- names(optimal_weights) weights_df <- data.frame(Asset = asset_names, Weight = optimal_weights) plot_ly(data = weights_df, x = ~Asset, y = ~Weight, type = 'bar') %>% layout(title = "Interactive Portfolio Weights", xaxis = list(title = "Asset"), yaxis = list(title = "Weight"))

initial_portfolio <- portfolio.spec(assets = colnames(returns_date_droped_dividened2)) # Add objectives - here we minimize risk (VAR) initial_portfolio <- add.objective(portfolio = initial_portfolio, type = "risk", name = "VaR") initial_portfolio <- add.objective(portfolio = initial_portfolio, type = "return", name = "mean") initial_portfolio <- add.objective(portfolio = initial_portfolio, type = "risk-adjusted", name = "SortinoRatio") # Add constraints - fully invested portfolio with no short sales initial_portfolio <- add.constraint(portfolio = initial_portfolio, type = "long_only") initial_portfolio <- add.constraint(portfolio = initial_portfolio, type = "full_investment") initial_portfolio <- add.constraint(portfolio = initial_portfolio, type = "box", min = 0, max = 1) # Optimize the portfolio to minimize risk optimal_portfolio <- optimize.portfolio(R = returns_date_droped_dividened2, portfolio = initial_portfolio, optimize_method = "DEoptim") # View the optimal weights optimal_weights <- extractWeights(optimal_portfolio) asset_names <- names(optimal_weights) weights_df <- data.frame(Asset = asset_names, Weight = optimal_weights) plot_ly(data = weights_df, x = ~Asset, y = ~Weight, type = 'bar') %>% layout(title = "Interactive Portfolio Weights", xaxis = list(title = "Asset"), yaxis = list(title = "Weight"))

port_2_max_ret <- portfolio.spec(assets = colnames(returns_date_droped_dividened2)) # Add objectives - here we minimize risk (VAR) port_2_max_ret <- add.objective(portfolio = port_2_max_ret, type = "risk", name = "StdDev")#added #port_2_max_ret <- add.objective(portfolio = port_2_max_ret, type = "return", name = "mean") # Add constraints - fully invested portfolio with no short sales port_2_max_ret <- add.constraint(portfolio = port_2_max_ret, type = "long_only") port_2_max_ret <- add.constraint(portfolio = port_2_max_ret, type = "full_investment") port_2_max_ret <- add.constraint(portfolio = port_2_max_ret, type = "box", min = 0, max = 1) # Optimize the portfolio to minimize risk optimal_portfolio_2 <- optimize.portfolio(R = returns_date_droped_dividened2, portfolio = port_2_max_ret, optimize_method = "ROI") optimal_weights <- extractWeights(optimal_portfolio_2) asset_names <- names(optimal_weights) weights_df <- data.frame(Asset = asset_names, Weight = optimal_weights) plot_ly(data = weights_df, x = ~Asset, y = ~Weight, type = 'bar') %>% layout(title = "Interactive Portfolio Weights", xaxis = list(title = "Asset"), yaxis = list(title = "Weight"))

port_2_max_ret <- portfolio.spec(assets = colnames(returns_date_droped_dividened2)) # Add objectives - here we minimize risk (VAR) port_2_max_ret <- add.objective(portfolio = port_2_max_ret, type = "risk", name = "StdDev")#added port_2_max_ret <- add.objective(portfolio = port_2_max_ret, type = "return", name = "mean") # Add constraints - fully invested portfolio with no short sales port_2_max_ret <- add.constraint(portfolio = port_2_max_ret, type = "long_only") port_2_max_ret <- add.constraint(portfolio = port_2_max_ret, type = "full_investment") port_2_max_ret <- add.constraint(portfolio = port_2_max_ret, type = "box", min = 0, max = 1) # Optimize the portfolio to minimize risk optimal_portfolio_2 <- optimize.portfolio(R = returns_date_droped_dividened2, portfolio = port_2_max_ret, optimize_method = "DEoptim") # expected_return_optimal_portfolio_2 <- sum(optimal_portfolio_2$weights * colMeans(returns_date_droped_dividened2)) # expected_risk_optimal_portfolio_2 <- sqrt(t(weights) %*% cov(returns_df) %*% weights) # # annualized_return_optimal_portfolio_2 <- Return.annualized(expected_return_optimal_portfolio_2, scale = 252) # # # Step 2: Annualize the risk # trading_days <- 252 # Number of trading days in a year # annualized_risk_tan <- tanRisk * sqrt(trading_days) optimal_weights <- extractWeights(optimal_portfolio_2) asset_names <- names(optimal_weights) weights_df <- data.frame(Asset = asset_names, Weight = optimal_weights) plot_ly(data = weights_df, x = ~Asset, y = ~Weight, type = 'bar') %>% layout(title = "Interactive Portfolio Weights", xaxis = list(title = "Asset"), yaxis = list(title = "Weight"))

# Calculate mean returns mean_returns <- colMeans(returns_date_droped_dividened2) # Function to calculate VaR (assuming normal distribution) VaR <- function(x, alpha = 0.05) { mean(x) - qnorm(1 - alpha) * sd(x) } # Calculate VaR for each stock VaR_values <- apply(returns_date_droped_dividened2, 2, VaR) # Create a dataframe for plotting plot_data <- data.frame(Stock = names(mean_returns), Mean_Return = mean_returns, VaR = VaR_values) # Create the ggplot p <- ggplot(plot_data, aes(x = Mean_Return, y = VaR, text = paste("Stock:", Stock, "<br>Return:", round(Mean_Return, 4), "<br>VaR:", round(VaR, 4)))) + geom_point(color = 'blue', size = 3) + labs(title = "Mean Return vs VaR for Each Stock", x = "Mean Return", y = "Value at Risk (VaR)") + theme_minimal() # Convert ggplot to plotly for interactivity interactive_plot <- ggplotly(p, tooltip = "text") # Display the interactive plot interactive_plot

initial_portfolio <- portfolio.spec(assets = colnames(returns_date_droped_dividened2)) # Add objectives - here we minimize risk (VAR) initial_portfolio <- add.objective(portfolio = initial_portfolio, type = "risk", name = "VaR") initial_portfolio <- add.objective(portfolio = initial_portfolio, type = "risk-adjusted", name = "SortinoRatio") # Add constraints - fully invested portfolio with no short sales initial_portfolio <- add.constraint(portfolio = initial_portfolio, type = "long_only") initial_portfolio <- add.constraint(portfolio = initial_portfolio, type = "full_investment") initial_portfolio <- add.constraint(portfolio = initial_portfolio, type = "box", min = 0, max = 1) # Optimize the portfolio to minimize risk optimal_portfolio <- optimize.portfolio(R = returns_date_droped_dividened2, portfolio = initial_portfolio, optimize_method = "DEoptim") # View the optimal weights optimal_weights <- extractWeights(optimal_portfolio) asset_names <- names(optimal_weights) weights_df <- data.frame(Asset = asset_names, Weight = optimal_weights) plot_ly(data = weights_df, x = ~Asset, y = ~Weight, type = 'bar') %>% layout(title = "Interactive Portfolio Weights", xaxis = list(title = "Asset"), yaxis = list(title = "Weight"))

portfolio <- add.constraint(portfolio, type = "full_investment") portfolio <- add.constraint(portfolio, type = "box", min = 0, max = 1) # Add objective to maximize the Sharpe Ratio portfolio <- add.objective(portfolio, type = "risk", name = "StdDev") portfolio <- add.objective(portfolio, type = "return", name = "mean", target = 0.35/109) portfolio <- add.objective(portfolio, type = "risk_adjusted_return", name = "SharpeRatio", risk_free_rate = risk_free_rate) opt_portfolio_deoptim <- optimize.portfolio(R = returns_xts, portfolio = portfolio, optimize_method = "DEoptim", trace = TRUE)

portfolio <- add.constraint(portfolio, type = "full_investment") portfolio <- add.constraint(portfolio, type = "box", min = 0, max = 1) # Add objective to maximize the Sharpe Ratio portfolio <- add.objective(portfolio, type = "risk", name = "StdDev") portfolio <- add.objective(portfolio, type = "return", name = "mean", target = risk_free_rate) portfolio <- add.objective(portfolio, type = "risk_adjusted_return", name = "SharpeRatio", risk_free_rate = risk_free_rate) opt_portfolio_deoptim <- optimize.portfolio(R = returns_xts, portfolio = portfolio, optimize_method = "DEoptim", trace = TRUE)

portfolio <- add.constraint(portfolio, type = "full_investment") portfolio <- add.constraint(portfolio, type = "box", min = 0, max = 1) # Add objective to maximize the Sharpe Ratio portfolio <- add.objective(portfolio, type = "risk", name = "StdDev") portfolio <- add.objective(portfolio, type = "return", name = "mean", target = 0.35/109) portfolio <- add.objective(portfolio, type = "risk_adjusted_return", name = "SharpeRatio", risk_free_rate = risk_free_rate) opt_portfolio_deoptim <- optimize.portfolio(R = returns_xts, portfolio = portfolio, optimize_method = "DEoptim", trace = TRUE)

7:10

lina

235% return

latest

50% geom mean

using roi

optimal wight # Add constraints portfolio <- add.constraint(portfolio, type = "full_investment") portfolio <- add.constraint(portfolio, type = "box", min = 0, max = 1) # Add objective to maximize the Sharpe Ratio portfolio <- add.objective(portfolio, type = "risk", name = "StdDev") portfolio <- add.objective(portfolio, type = "return", name = "mean", target = 0.35/109) portfolio <- add.objective(portfolio, type = "risk_adjusted_return", name = "SharpeRatio", risk_free_rate = risk_free_rate) opt_portfolio_deoptim <- optimize.portfolio(R = returns_xts, portfolio = portfolio, optimize_method = "DEoptim", trace = TRUE) #

lina

lina 4.9% return port

max return, min risk

portfolio, type = "return", name = "mean"

123

according expected shortfall

Low Risk Portfolio last 6 month

interactive stocks 2

interactive chart 1