Visualizing Asset Returns in R Using ggplot2 and highcharter

Monthly log returns highcharts

       The highcharter package is a wrapper for the “Highcharts” Library, which has an amazing visualization infrastructure for time series and financial data. The highcharter package houses functions that accept xts objects (R’s time series object class) as arguments, making it seamless to move from time series data to visualizations. The plot below displays the line chart for a subset of the ETF’s. We could have easily plotted all five ETF’s on the same line chart, but it would be harder for our eyes to compare, contrast, and identify patterns.

# Crate Highstock widget
highchart(type = "stock") %>%
  # Add chart main title
  hc_title(text = "Monthly Log Returns for SPY, QQQ, DIA") %>%
  # Add returns series to highchart objects
  # We use "symbols" to reference series since we may need to add/remove ETF's in the future
  # Use matrix sub-setting and character indexing to select returns by column
  hc_add_series(
    data = asset_returns_xts[, symbols[[1]]],
    name = symbols[[1]]
  ) %>%
  hc_add_series(
    data = asset_returns_xts[, symbols[[4]]],
    name = symbols[[4]]
  ) %>%
  hc_add_series(
    data = asset_returns_xts[, symbols[[3]]],
    name = symbols[[3]]
  ) %>%
  # Add theme to highchart object
  # More themes to be found in the vignette
  hc_add_theme(hc_thm = hc_theme_flat()) %>%
  # Navigator
  hc_navigator(enabled = TRUE) %>%
  # Scrollbar
  hc_scrollbar(enabled = TRUE) %>%
  # Exporting
  hc_exporting(enabled = TRUE) %>%
  # Add legend
  hc_legend(enabled = TRUE)

• The navigator is a small series below the main series, displaying a view of the entire data set. It provides tools to zoom in and out on parts of the data as well as panning across the data-set.

• The scroll-bar is a means of panning over the X axis of a stock chart. Scroll-bars can also be applied to other types of axes.

Note: Highcharter plots are highly interactive; that is, an user can hover over the line chart to interact with it. However, due to internal conflicts with blogdown themes, this Highcharter plot cannot be rendered dynamically. Please navigate to this link to view the interactive version of this line chart.

Monthly log returns Histograms

       Create a function that returns a uni-variate histogram given a series of returns. The function will also take several other arguments— an xts object of returns, a vector of ticker symbols, a symbol index, and a color for plotting. Internally, the function creates a list of histogram components: counts, density, bin breaks, etc. Then, the function hchart() is called on the histogram list object to plot the uni-variate histogram; this is the final output of the function.

hc_hist_fun <- function(xts_obj, tickers, symbol_index, color) {

  # Check for invalid input
  if (!is.xts(xts_obj) || !rlang::is_character(color) || !rlang::is_character(tickers)) {
    rlang::abort(
      message = "Invalid input type for xts_object, tickers, and/or color arguments"
    )
  }

  # Create histogram list object with 6 elements
  hc_hist <- graphics::hist(xts_obj[, tickers[[symbol_index]]],
    breaks = "Freedman-Diaconis",
    plot = FALSE
  )

  # Call hchart on the histogram list object
  hchart(object = hc_hist, color = color) %>%
    hc_title(
      text =
        paste(tickers[[symbol_index]], "Log Returns Distribution", sep = " ")
    ) %>%
    hc_add_theme(hc_thm = hc_theme_flat()) %>%
    hc_exporting(enabled = TRUE) %>%
    hc_legend(enabled = FALSE)
}

Now, we utilize the functional programming tool from purrr to apply the function above to each of the five uni-variate returns series.

# Map the histogram function to each of the returns series
list_of_histogram <- purrr::map(
  .x = 1:5,
  .f = ~ hc_hist_fun(
    xts_obj = asset_returns_xts,
    tickers = symbols,
    symbol_index = .x,
    color = "cornflowerblue"
  )
)

Note: Please navigate to this link to view the interactive version of these histograms.

       As can be seen, most of our assets are negatively skewed, indicating that there were a few really bad months. For the iShares Core US Aggregate Bond ETF (AGG), most months have returns that may be statistically indistinguishable from zero. From a sheer numbers perspective, investors who wish to maximize gains may consider such an asset undesirable. However, other performance factors such as risk, diversifier effect, and time horizon are important. The iShares Core US Aggregate Bond ETF seeks to track the investment results of an index composed of the total U.S. investment-grade bond market. And we expect bonds to produce lower returns for investors because they are also considered less volatile than stocks.

The Invesco QQQ Trust Series 1 ETF (QQQ) stands out as a strong performing asset. Out of 103 months, about \(22%\) of its monthly returns fall between \(2\%\) and \(4\%\). Hover over the histograms here to see the counts and break points of the returns distribution.

Histogram

       Here are the histograms. Notice that we can either overlay the histograms on top of each other or show them in separate panels. I recommend using the panel approach for studying the shapes (spread, central tendency, skewness, tailed-ness, etc.) of the uni-variate distributions, and employ the overlaying histograms for making comparisons between these distributions.

# Compute Freedman-Diaconis bin numbers
bins_fd <- function(vec) {
  diff(range(vec)) / (2 * IQR(vec) / length(vec)^(1 / 3))
}
# Histogram
ggplot(data = asset_returns_dplyr, mapping = aes(x = returns)) +
  geom_histogram(
    alpha = 0.5,
    mapping = aes(fill = asset),
    bins = bins_fd(asset_returns_dplyr[["returns"]])
  ) +
  ggtitle("Distributions of Monthly Log Returns") +
  theme(
    panel.background = element_rect(fill = "grey97"),
    panel.grid = element_blank(),
  )

# Histogram with panels
ggplot(data = asset_returns_dplyr, mapping = aes(x = returns)) +
  geom_histogram(
    alpha = 0.5,
    mapping = aes(fill = asset),
    bins = bins_fd(asset_returns_dplyr[["returns"]])
  ) +
  facet_wrap(~asset) +
  ggtitle("Distributions of Monthly Log Returns") +
  theme(
    panel.background = element_rect(fill = "grey97"),
    panel.grid = element_blank(),
  )

Densty

       We could also plot the probability density functions of these historical returns. Take a look at the y-axis of these plots and compare them to those of the histograms. This is an important distinction between these otherwise similar visualizations.

# Density plot
ggplot(data = asset_returns_dplyr, mapping = aes(x = returns)) +
  geom_density(mapping = aes(color = asset)) +
  ggtitle("Distributions of Monthly Log Returns") +
  theme(
    panel.background = element_rect(fill = "grey97"),
    panel.grid = element_blank(),
  )

# Density plot with panels
ggplot(data = asset_returns_dplyr, mapping = aes(x = returns)) +
  geom_density(mapping = aes(color = asset)) +
  geom_histogram(
    alpha = 0.5,
    mapping = aes(fill = asset),
    bins = bins_fd(asset_returns_dplyr[["returns"]])
  ) +
  facet_wrap(~asset) +
  ggtitle("Distributions of Monthly Log Returns") +
  theme(
    panel.background = element_rect(fill = "grey97"),
    panel.grid = element_blank(),
  )

       The smoothed densities can be useful for estimating the probabilities of returns, or an infinitesimal interval of returns, to be mathematically precise. Take caution when interpreting these kernel densities as it is important to understand that the heights of the curve (the y-axis) do not represent probabilities. The y-axis in a density plot is the probability density function for the kernel density estimation. To convert to an actual probability, we need to find the area under the curve for a specific interval of returns. It is generally difficult to estimate probabilities from densities and we will have to tackle this problem in another post.

       For now, we have equipped ourselves with some nice visualization techniques in R. These are not the only ways to visualize financial data by any means. In future posts, I will explore other aspects of financial analytics and portfolio analytics.