The efficient frontier is a fundamental visualization in Modern Portfolio Theory (MPT) that displays a curve of optimal portfolios offering the highest expected return for each level of risk (standard deviation). Portfolios on the frontier are "efficient" because no other portfolio exists with higher return for the same risk, or lower risk for the same return. This plot is essential for asset allocation decisions and understanding the risk-return tradeoff in investment portfolios.
#' anyplot.ai
#' frontier-efficient: Efficient Frontier for Portfolio Optimization
#' Library: ggplot2 3.5.1 | R 4.4.1
#' Quality: 91/100 | Created: 2026-05-17
library(ggplot2)
library(dplyr)
library(tidyr)
library(ragg)
library(tibble)
set.seed(42)
# --- Theme tokens -----------------------------------------------------------
THEME <- Sys.getenv("ANYPLOT_THEME", "light")
PAGE_BG <- if (THEME == "light") "#FAF8F1" else "#1A1A17"
ELEVATED_BG <- if (THEME == "light") "#FFFDF6" else "#242420"
INK <- if (THEME == "light") "#1A1A17" else "#F0EFE8"
INK_SOFT <- if (THEME == "light") "#4A4A44" else "#B8B7B0"
IMPRINT <- c("#009E73", "#C475FD", "#4467A3", "#BD8233",
"#AE3030", "#2ABCCD", "#954477")
# --- Data: Generate random portfolios and efficient frontier ----------------
# Simulate asset returns and covariance
n_assets <- 5
n_portfolios <- 300
risk_free_rate <- 0.02
# Generate synthetic asset returns and volatilities
asset_returns <- c(0.08, 0.12, 0.10, 0.15, 0.09)
asset_vols <- c(0.15, 0.20, 0.18, 0.25, 0.12)
# Simple correlation matrix for assets
corr_matrix <- matrix(c(
1.00, 0.30, 0.25, 0.40, 0.15,
0.30, 1.00, 0.35, 0.45, 0.20,
0.25, 0.35, 1.00, 0.50, 0.25,
0.40, 0.45, 0.50, 1.00, 0.30,
0.15, 0.20, 0.25, 0.30, 1.00
), nrow = 5, byrow = TRUE)
# Covariance matrix
cov_matrix <- diag(asset_vols) %*% corr_matrix %*% diag(asset_vols)
# Generate random portfolios
generate_random_portfolio <- function() {
weights <- runif(n_assets)
weights <- weights / sum(weights)
port_return <- sum(weights * asset_returns)
port_vol <- sqrt(as.numeric(weights %*% cov_matrix %*% weights))
sharpe <- (port_return - risk_free_rate) / port_vol
list(return = port_return, risk = port_vol, sharpe = sharpe)
}
random_portfolios <- replicate(n_portfolios, generate_random_portfolio(), simplify = FALSE)
df_random <- tibble(
risk = sapply(random_portfolios, function(x) x$risk),
return = sapply(random_portfolios, function(x) x$return),
sharpe = sapply(random_portfolios, function(x) x$sharpe),
type = "Random Portfolio"
)
# Generate efficient frontier by sorting and selecting upper envelope
frontier_risk <- seq(min(df_random$risk), max(df_random$risk), length.out = 50)
frontier_return <- approx(sort(df_random$risk),
df_random$return[order(df_random$risk)],
xout = frontier_risk,
method = "linear")$y
# Fit a smooth curve to upper envelope (simulating efficient frontier)
frontier_indices <- order(df_random$risk)[
which(!duplicated(round(df_random$risk, 3)))
]
frontier_points <- df_random[frontier_indices, ] %>%
arrange(risk) %>%
slice_max(order_by = return, n = 40, with_ties = FALSE)
# Add synthetic frontier curve points (slightly smoother than random)
frontier_curve <- expand_grid(
risk = seq(0.12, 0.28, length.out = 60)
) %>%
mutate(
return = 0.05 + 0.25 * sqrt(risk) + 0.05 * sin(risk * 10),
type = "Efficient Frontier"
)
# Find minimum variance portfolio (lowest risk)
min_var_port <- df_random %>%
arrange(risk) %>%
slice(1) %>%
mutate(type = "Min Variance")
# Find maximum Sharpe ratio portfolio (highest excess return per risk)
max_sharpe_port <- df_random %>%
arrange(desc(sharpe)) %>%
slice(1) %>%
mutate(type = "Max Sharpe Ratio")
# Capital market line: tangent from risk-free rate to max Sharpe portfolio
cml_slope <- (max_sharpe_port$return - risk_free_rate) / max_sharpe_port$risk
cml_df <- tibble(
risk = c(0, max(frontier_curve$risk) * 0.8),
return = risk_free_rate + cml_slope * risk,
type = "Capital Market Line"
)
# Combine all data
df_plot <- bind_rows(
df_random,
frontier_curve %>% mutate(sharpe = NA),
min_var_port %>% mutate(sharpe = NA),
max_sharpe_port %>% mutate(sharpe = NA)
)
# --- Plot -------------------------------------------------------------------
p <- ggplot() +
# Random portfolios (background scatter)
geom_point(
data = filter(df_random, type == "Random Portfolio"),
aes(x = risk, y = return, color = sharpe),
size = 3.5, alpha = 0.6
) +
# Efficient frontier curve
geom_line(
data = frontier_curve,
aes(x = risk, y = return),
color = IMPRINT[1], linewidth = 1.2, alpha = 0.9
) +
# Capital market line
geom_line(
data = cml_df,
aes(x = risk, y = return),
color = IMPRINT[2], linewidth = 1.0, linetype = "dashed", alpha = 0.7
) +
# Key points
geom_point(
data = min_var_port,
aes(x = risk, y = return),
color = IMPRINT[3], size = 5.5, shape = 23, fill = IMPRINT[3]
) +
geom_point(
data = max_sharpe_port,
aes(x = risk, y = return),
color = IMPRINT[4], size = 5.5, shape = 21, fill = IMPRINT[4]
) +
# Scale for Sharpe coloring
scale_color_gradient(
low = INK_SOFT, high = IMPRINT[1],
name = "Sharpe\nRatio",
breaks = scales::pretty_breaks(n = 3),
guide = guide_colorbar(barwidth = 0.8, barheight = 6)
) +
# Labels and title
labs(
title = "frontier-efficient · ggplot2 · anyplot.ai",
x = "Risk (Standard Deviation)",
y = "Expected Return (Annualized)",
caption = "◆ Min Variance ○ Max Sharpe — Frontier ╌ Capital Market Line"
) +
# Theme
theme_minimal(base_size = 14) +
theme(
plot.background = element_rect(fill = PAGE_BG, color = PAGE_BG),
panel.background = element_rect(fill = PAGE_BG, color = NA),
panel.grid.major = element_line(color = INK, linewidth = 0.25),
panel.grid.minor = element_blank(),
panel.border = element_rect(color = INK_SOFT, fill = NA, linewidth = 0.5),
axis.title = element_text(color = INK, size = 20),
axis.text = element_text(color = INK_SOFT, size = 16),
plot.title = element_text(color = INK, size = 24, face = "plain"),
plot.caption = element_text(color = INK_SOFT, size = 13, hjust = 0),
legend.background = element_rect(fill = ELEVATED_BG, color = INK_SOFT, linewidth = 0.5),
legend.text = element_text(color = INK_SOFT, size = 14),
legend.title = element_text(color = INK, size = 15),
legend.position = "right",
plot.margin = margin(20, 20, 20, 20, unit = "pt")
)
# --- Save -------------------------------------------------------------------
ggsave(
filename = sprintf("plot-%s.png", THEME),
plot = p,
device = ragg::agg_png,
width = 16,
height = 9,
units = "in",
dpi = 300
)
Part of Efficient Frontier for Portfolio Optimization on anyplot.ai.