#clear the environment 
rm(list=ls()) 
## ------------------------------------------------------------------------
setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
library(data.table)
library(scales)
library(ggplot2)
library(xts)
link <- "https://raw.githubusercontent.com/DavZim/Efficient_Frontier/master/data/fin_data.csv"
dt <- fread(link)
dt[, date := as.Date(date)]

# create indexed values
dt[, idx_price := price/price[1], by = ticker]

# plot the indexed values
ggplot(dt, aes(x = date, y = idx_price, color = ticker)) +
  geom_line() +
  # Miscellaneous Formatting
  theme_bw() + ggtitle("Price Developments") +
  xlab("Date") + ylab("Price\n(Indexed 2000 = 1)") +
  scale_color_discrete(name = "Company")
# calculate the arithmetic returns
dt[, ret := price / shift(price, 1) - 1, by = ticker]

# summary table
# take only non-na values
tab <- dt[!is.na(ret), .(ticker, ret)]

# calculate the expected returns (historical mean of returns) and volatility (standard deviation of returns)
tab <- tab[, .(er = round(mean(ret), 4), 
               sd = round(sd(ret), 4)), 
           by = "ticker"]
ggplot(tab, aes(x = sd, y = er, color = ticker)) +
  geom_point(size = 5) +
  # Miscellaneous Formatting
  theme_bw() + ggtitle("Risk-Return Tradeoff") +
  xlab("Volatility") + ylab("Expected Returns") +
  scale_y_continuous(label = percent, limits = c(0, 0.03)) +
  scale_x_continuous(label = percent, limits = c(0, 0.1))



# load the data
link <- "https://raw.githubusercontent.com/DavZim/Efficient_Frontier/master/data/mult_assets.csv"
df <- data.table(read.csv(link))

df_table <- melt(df)[, .(mean = mean(value), sd = sd(value)), by = variable]

er_x <- mean(df$x)
er_y <- mean(df$y)
er_z <- mean(df$z)
sd_x <- sd(df$x)
sd_y <- sd(df$y)
sd_z <- sd(df$z)
cov_xy <- cov(df$x, df$y)
cov_xz <- cov(df$x, df$z)
cov_yz <- cov(df$y, df$z)

# two assets
two_assets_seq <- seq(from = 0, to = 1, length.out = 1000)

two <- data.table(wx = two_assets_seq,
                  wy = 1 - two_assets_seq)

two[, ':=' (er_p = wx * er_x + wy * er_y,
            sd_p = sqrt(wx^2 * sd_x^2 +
                          wy^2 * sd_y^2 +
                          2 * wx * (1 - wx) * cov_xy))]

# plot_two <- ggplot() +
#   geom_point(data = two, aes(x = sd_p, y = er_p, color = wx)) +
#   geom_point(data = df_table[variable != "z"],
#              aes(x = sd, y = mean), color = "red", size = 3, shape = 18) +
#   theme_bw() + ggtitle("Possible Portfolios with Two Risky Assets") +
#   xlab("Volatility") + ylab("Expected Returns") +
#   scale_y_continuous(label = percent, limits = c(0, max(two$er_p) * 1.2)) +
#   scale_x_continuous(label = percent, limits = c(0, max(two$sd_p) * 1.2)) +
#   scale_color_continuous(name = expression(omega[x]), labels = percent)
# 
# ggsave(plot_two, file = "two_assets.png", scale = 1, dpi = 600)

  ggplot() +
  geom_point(data = two, aes(x = sd_p, y = er_p, color = wx)) +
  geom_point(data = df_table[variable != "z"],
             aes(x = sd, y = mean), color = "red", size = 3, shape = 18) +
  theme_bw() + ggtitle("Possible Portfolios with Two Risky Assets") +
  xlab("Volatility") + ylab("Expected Returns") +
  scale_y_continuous(label = percent, limits = c(0, max(two$er_p) * 1.2)) +
  scale_x_continuous(label = percent, limits = c(0, max(two$sd_p) * 1.2)) +
  scale_color_continuous(name = expression(omega[x]), labels = percent)

# three assets
three_assets_seq <- seq(from = 0, to = 1, length.out = 1000)

three <- data.table(wx = rep(three_assets_seq, each = length(three_assets_seq)),
                    wy = rep(three_assets_seq, length(three_assets_seq)))

three[, wz := 1 - wx - wy]

three[, ':=' (er_p = wx * er_x + wy * er_y + wz * er_z,
              sd_p = sqrt(wx^2 * sd_x^2 +
                            wy^2 * sd_y^2 +
                            wz^2 * sd_z^2 +
                            2 * wx * wy * cov_xy +
                            2 * wx * wz * cov_xz +
                            2 * wy * wz * cov_yz))]

three <- three[wx >= 0 & wy >= 0 & wz >= 0]

plot_three <- ggplot() +
  geom_point(data = three, aes(x = sd_p, y = er_p, color = wx - wz)) +
  geom_point(data = df_table, aes(x = sd, y = mean), color = "red", size = 3, shape = 18) +
  theme_bw() + ggtitle("Possible Portfolios with Three Risky Assets") +
  xlab("Volatility") + ylab("Expected Returns") +
  scale_y_continuous(label = percent, limits = c(0, max(three$er_p) * 1.2)) +
  scale_x_continuous(label = percent, limits = c(0, max(three$sd_p) * 1.2)) +
  scale_color_gradientn(colors = c("red", "blue", "yellow"),
                        name = expression(omega[x] - omega[z]), labels = percent)

ggsave(plot_three, file = "three_assets.png", scale = 1, dpi = 600)