R 中的投资组合优化：市场投资组合

Question

我对编码还很陌生，所以如果我的代码中有任何重大错误，我提前道歉。目前，我在处理涉及无风险资产和资本市场线的投资组合优化时遇到了一个问题。问题出在我的代码中，Vanguard Index Fund 变量无意中包含在我的有效投资组合中，尽管我打算让它只代表市场投资组合。我已多次尝试纠正此问题，但我不确定正确的方法。如果有人能指导我度过这一挑战，我将不胜感激。提前谢谢你！

library(rlang)
library(tidyquant)
library(tidyverse)
library(plotly)
library(timetk)

# Define the market ticker symbol (Vanguard Energy Index)
market_ticker <- 'VDE'

tick <- c('XOM', 'CVX', 'BP', 'FCEL', 'DVN', market_ticker)

price_data <- tq_get(tick,
                     from = '2018-01-01',
                     to = '2022-05-31',
                     get = 'stock.prices')

log_ret_tidy <- price_data %>%
  group_by(symbol) %>%
  tq_transmute(select = adjusted,
               mutate_fun = periodReturn,
               period = 'daily',
               col_rename = 'ret',
               type = 'log')

log_ret_xts <- log_ret_tidy %>%
  spread(symbol, value = ret) %>%
  tk_xts()

# Add a risk-free asset
rf_data <- data.frame(date = time(log_ret_xts),
                      rf = rep(0.02/252, length(time(log_ret_xts))))
rf_xts <- tk_xts(rf_data, date_col = date)

# Merge the risk-free asset to the log return data
log_ret_xts <- merge(log_ret_xts, rf_xts)

mean_ret <- colMeans(log_ret_xts)
cov_mat <- cov(log_ret_xts) * 252

print(round(cov_mat, 4))

num_port <- 50000
all_wts <- matrix(nrow = num_port, ncol = length(tick)+1) # add one for the risk-free asset
port_returns <- vector('numeric', length = num_port)
port_risk <- vector('numeric', length = num_port)
sharpe_ratio <- vector('numeric', length = num_port)

# Function to generate random weights with shorting
generate_weights <- function(n_assets) {
  wts <- runif(n_assets, min = -1, max = 1)
  wts <- wts / sum(abs(wts))
  return(wts)
}

for (i in seq_along(port_returns)) {
  wts <- generate_weights(length(tick)+1) # add one for the risk-free asset
  all_wts[i, ] <- wts
  
  port_ret <- sum(wts * mean_ret)
  port_ret <- ((port_ret + 1) ^ 252) - 1
  port_returns[i] <- port_ret
  
  port_sd <- sqrt(t(wts) %*% (cov_mat %*% wts))
  port_risk[i] <- port_sd
  
  sr <- (port_ret - 0.02) / port_sd # subtract risk-free rate from portfolio return
  sharpe_ratio[i] <- sr
}

portfolio_values <- tibble(Return = port_returns,
                           Risk = port_risk,
                           SharpeRatio = sharpe_ratio)

all_wts <- tk_tbl(all_wts)
colnames(all_wts) <- c(colnames(log_ret_xts)[-ncol(log_ret_xts)], "rf") # rename last column as risk-free
portfolio_values <- tk_tbl(cbind(all_wts, portfolio_values))

head(portfolio_values)

min_var <- portfolio_values[which.min(portfolio_values$Risk), ]
max_sr <- portfolio_values[which.max(portfolio_values$SharpeRatio), ]

p <- min_var %>%
  gather(BP:XOM, key = Asset, value = Weights) %>%
  mutate(Asset = as.factor(Asset)) %>%
  ggplot(aes(x = fct_reorder(Asset, Weights), y = Weights, fill = Asset)) +
  geom_bar(stat = 'identity') +
  theme_minimal() +
  labs(x = 'Assets', y = 'Weights', title = "Minimum Variance Portfolio Weights") +
  scale_y_continuous(labels = scales::percent)

ggplotly(p)

p <- max_sr %>%
  gather(BP:XOM, key = Asset, value = Weights) %>%
  mutate(Asset = as.factor(Asset)) %>%
  ggplot(aes(x = fct_reorder(Asset, Weights), y = Weights, fill = Asset)) +
  geom_bar(stat = 'identity') +
  theme_minimal() +
  labs(x = 'Assets', y = 'Weights', title = "Tangency Portfolio Weights") +
  scale_y_continuous(labels = scales::percent)

# Tangency Portfolio Weights
ggplotly(p)

p <- portfolio_values %>%
  ggplot(aes(x = Risk, y = Return, color = SharpeRatio)) +
  geom_point() +
  theme_classic() +
  scale_y_continuous(labels = scales::percent) +
  scale_x_continuous(labels = scales::percent) +
  labs(x = 'Annualized Risk',
       y = 'Annualized Returns',
       title = "Portfolio Optimization & Efficient Frontier") +
  geom_point(aes(x = Risk, y = Return), data = min_var, color = 'red') +
  geom_point(aes(x = Risk, y = Return), data = max_sr, color = 'red')

# Capital Market Line (CML)
# Risk-free rate
risk_free_rate <- 0.02

# Calculating CML
cml_df <- tibble(Risk = seq(0, 0.3, 0.001))
cml_df$Return <- risk_free_rate + cml_df$Risk * (max_sr$Return - risk_free_rate) / max_sr$Risk

# Adding CML to the plot
p <- p +
  geom_line(data = cml_df, aes(x = Risk, y = Return), color = 'blue') +
  annotate(geom = 'text', x = 0.2, y = 0.09, label = 'Capital Market Line', color = 'blue')

ggplotly(p)