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R/plot_risk_adjusted_returns.R
Defines functions plot_risk_adjusted_returns
Documented in plot_risk_adjusted_returns
#' Plotting risk adjusted returns
#'
#' Plots the risk adjusted returns for portfolios
#' of various allocations to the risky asset.
#'
#' @seealso
#' * [How to Determine Our Optimal Asset Allocation?](https://www.r4good.academy/en/blog/optimal-asset-allocation/index.en.html#how-much-risk-is-enough)
#' * Haghani V., White J. (2023) "The Missing Billionaires: A Guide to Better Financial Decisions." ISBN:978-1-119-74791-8.
#'
#' @inheritParams calc_risk_adjusted_return
#' @inheritParams calc_optimal_risky_asset_allocation
#'
#' @param current_risky_asset_allocation A numeric.
#' The current allocation to the risky asset.
#' For comparison with the optimal allocation.
#'
#' @returns A [ggplot2::ggplot()] object.
#'
#' @examples
#' plot_risk_adjusted_returns(
#' safe_asset_return = 0.02,
#' risky_asset_return_mean = 0.04,
#' risky_asset_return_sd = 0.15,
#' risk_aversion = 2,
#' current_risky_asset_allocation = 0.8
#' )
#' @export
#'
plot_risk_adjusted_returns <- function(
safe_asset_return,
risky_asset_return_mean,
risky_asset_return_sd,
risk_aversion = 2,
current_risky_asset_allocation = NULL
) {
risky_asset_allocations <- seq(from = 0.00, to = 1.00, by = 0.001)
risk_adjusted_returns <-
calc_risk_adjusted_return(
safe_asset_return = safe_asset_return,
risky_asset_return_mean = risky_asset_return_mean,
risky_asset_return_sd = risky_asset_return_sd,
risky_asset_allocation = risky_asset_allocations,
risk_aversion = risk_aversion
)
optimal_risky_asset_allocation <-
calc_optimal_risky_asset_allocation(
safe_asset_return = safe_asset_return,
risky_asset_return_mean = risky_asset_return_mean,
risky_asset_return_sd = risky_asset_return_sd,
risk_aversion = risk_aversion
)
optimal_risk_adjusted_return <-
calc_risk_adjusted_return(
safe_asset_return = safe_asset_return,
risky_asset_return_mean = risky_asset_return_mean,
risky_asset_return_sd = risky_asset_return_sd,
risky_asset_allocation = optimal_risky_asset_allocation,
risk_aversion = risk_aversion
)
colours <- PrettyCols::prettycols("Bold")
current_risky_asset_allocation_colour <- colours[5]
optimal_allocation_colour <- colours[4]
risky_asset_allocation_colour <- colours[1]
arrow_colour <- colours[2]
safe_asset_return_color <- "grey50"
y_limit_min <- min(risk_adjusted_returns)
y_limit_min <- ifelse(y_limit_min > 0, 0, y_limit_min)
add_labels <- function(to_plot) {
to_plot +
ggplot2::geom_label(
ggplot2::aes(
x = 0,
y = safe_asset_return,
label = print_percent(safe_asset_return)
),
color = safe_asset_return_color
) +
ggplot2::geom_label(
ggplot2::aes(
x = optimal_risky_asset_allocation,
y = y_limit_min,
label = print_percent(optimal_risky_asset_allocation)
),
color = optimal_allocation_colour
) +
ggplot2::geom_label(
ggplot2::aes(
x = 0,
y = max(risk_adjusted_returns),
label = print_percent(max(risk_adjusted_returns))
),
color = optimal_allocation_colour
)
}
value_colour <- "grey40"
to_plot <-
ggplot2::ggplot() +
ggplot2::geom_vline(
xintercept = optimal_risky_asset_allocation,
color = optimal_allocation_colour,
linetype = "dashed"
) +
ggplot2::geom_hline(
yintercept = max(risk_adjusted_returns),
color = optimal_allocation_colour,
linetype = "dashed"
) +
ggplot2::geom_hline(
yintercept = safe_asset_return,
color = safe_asset_return_color,
linetype = "dashed"
) +
ggplot2::geom_hline(
yintercept = 0,
color = safe_asset_return_color,
linetype = "dotted"
) +
ggplot2::geom_line(
ggplot2::aes(
x = risky_asset_allocations,
y = risk_adjusted_returns
),
color = risky_asset_allocation_colour,
linewidth = 1
) +
ggplot2::labs(
title = "Optimal Risky Asset Allocation",
subtitle = glue::glue(paste0(
"<span style='color: {optimal_allocation_colour};'>**Optimal**</span> ",
ifelse(
is.null(current_risky_asset_allocation),
"",
"vs <span style='color: {current_risky_asset_allocation_colour};'>**current**</span> "
),
"risky asset allocations and corresponding ",
"<span style='color: {risky_asset_allocation_colour};'>**risk adjusted returns**</span>"
)),
x = "Risky Asset Allocation",
y = "Risk Adjusted Returns",
caption = glue::glue(paste(
"*Safe asset return*: <span style='color: {value_colour};'>**{print_percent(safe_asset_return)}**</span>;",
"*Risky asset return*: <span style='color: {value_colour};'>**{print_percent(risky_asset_return_mean)}**</span>;",
"*Risky asset sd*: <span style='color: {value_colour};'>**{print_percent(risky_asset_return_sd)}**</span>;",
"*Risk aversion*: <span style='color: {value_colour};'>**{risk_aversion}**</span>."
))
) +
ggplot2::scale_x_continuous(
breaks = seq(0, 1, by = 0.1),
labels = scales::percent
) +
ggplot2::scale_y_continuous(
breaks = seq(
y_limit_min,
max(risk_adjusted_returns),
by = 0.005
),
limits = c(y_limit_min, NA),
labels = scales::percent
) +
ggplot2::theme_minimal() +
ggplot2::theme(
panel.grid.minor = ggplot2::element_blank(),
plot.caption =
ggtext::element_markdown(
color = "grey60",
size = 10
),
plot.subtitle = ggtext::element_markdown(color = "grey60")
) +
ggplot2::geom_point(
ggplot2::aes(
x = optimal_risky_asset_allocation,
y = optimal_risk_adjusted_return
),
color = optimal_allocation_colour,
size = 4)
if (is.null(current_risky_asset_allocation)) {
to_plot <- add_labels(to_plot)
return(to_plot)
}
current_risk_adjusted_return <-
calc_risk_adjusted_return(
safe_asset_return = safe_asset_return,
risky_asset_return_mean = risky_asset_return_mean,
risky_asset_return_sd = risky_asset_return_sd,
risky_asset_allocation = current_risky_asset_allocation,
risk_aversion = risk_aversion
)
arrow_length <- 9/10
to_plot <-
to_plot +
ggplot2::geom_hline(
yintercept = current_risk_adjusted_return,
color = current_risky_asset_allocation_colour
) +
ggplot2::geom_vline(
xintercept = current_risky_asset_allocation,
color = current_risky_asset_allocation_colour
) +
ggplot2::geom_label(
ggplot2::aes(
x = 1,
y = current_risk_adjusted_return,
label = print_percent(current_risk_adjusted_return)
),
color = current_risky_asset_allocation_colour
) +
ggplot2::geom_label(
ggplot2::aes(
x = current_risky_asset_allocation,
y = y_limit_min + 0.002,
label = print_percent(current_risky_asset_allocation)
),
color = current_risky_asset_allocation_colour
) +
ggplot2::geom_segment(
ggplot2::aes(
x = current_risky_asset_allocation,
y = current_risk_adjusted_return,
xend =
current_risky_asset_allocation - (
current_risky_asset_allocation - optimal_risky_asset_allocation
) * arrow_length,
yend =
current_risk_adjusted_return + (
optimal_risk_adjusted_return - current_risk_adjusted_return
) * arrow_length
),
arrow = ggplot2::arrow(type = "closed",
length = ggplot2::unit(0.12, "inches")),
color = arrow_colour
) +
ggplot2::geom_point(
ggplot2::aes(
x = current_risky_asset_allocation,
y = current_risk_adjusted_return
),
color = current_risky_asset_allocation_colour,
size = 4
)
add_labels(to_plot)
}
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