# Load packages

# Core
library(tidyverse)
library(tidyquant)

Goal

Visualize and examine changes in the underlying trend in the downside risk of your portfolio in terms of kurtosis.

Choose your stocks.

from 2012-12-31 to present

1 Import stock prices

symbols <- c("MSFT", "DPZ", "AAPL")

prices <- tq_get(x = symbols,
                 get = "stock.prices",
                 from = "2020-12-31",
                 to = "2025-12-31")

2 Convert prices to returns (monthly)

asset_returns_tbl <- prices %>%
    
    group_by(symbol) %>%
    
    tq_transmute(select = adjusted,
                 mutate_fun = periodReturn,
                 period = "monthly",
                 type = "log") %>%
    
    slice(-1) %>%
    
    ungroup() %>%
    
    set_names(c("asset", "date", "returns"))

3 Assign a weight to each asset (change the weigting scheme)

# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "AAPL" "DPZ"  "MSFT"
#weights
weights <- c(0.34, 0.33, 0.33)
weights
## [1] 0.34 0.33 0.33
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 3 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AAPL       0.34
## 2 DPZ        0.33
## 3 MSFT       0.33

4 Build a portfolio

# ?tq_portfolio

portfolio_returns_tbl <- asset_returns_tbl %>%
    
    tq_portfolio(assets_col = asset,
                 returns_col = returns,
                 weights = w_tbl,
                 rebalance_on = "months",
                 col_rename = "returns")

portfolio_returns_tbl
## # A tibble: 54 × 2
##    date         returns
##    <date>         <dbl>
##  1 2021-01-29  0.000869
##  2 2021-02-26 -0.0492  
##  3 2021-03-31  0.0278  
##  4 2021-04-30  0.0928  
##  5 2021-05-28 -0.0166  
##  6 2021-06-30  0.0890  
##  7 2021-07-30  0.0773  
##  8 2021-08-31  0.0284  
##  9 2021-09-30 -0.0725  
## 10 2021-10-29  0.0812  
## # ℹ 44 more rows

5 Compute kurtosis

portfolio_kurt_tidyquant_builtin_percent <- portfolio_returns_tbl %>%
    
    tq_performance(Ra = returns,
                   performance_fun = table.Stats) %>%
    
    select(Kurtosis) 

portfolio_kurt_tidyquant_builtin_percent
## # A tibble: 1 × 1
##   Kurtosis
##      <dbl>
## 1   -0.260

6 Plot: Rolling kurtosis

Distribution of Portfolio Returns

portfolio_returns_tbl %>%
    ggplot(aes(x = returns)) +
    geom_histogram()

Expected Return vs Downside Risk

# Transform data
mean_kurt_tbl <- asset_returns_tbl %>%
    
    # Calculate mean return and kurtosis for assets
    group_by(asset) %>%
    summarise(mean = mean(returns),
              kurt = kurtosis(returns)) %>%
    ungroup()

portfolio_returns_tbl %>%
    summarise(mean = mean(returns),
              kurt = kurtosis(returns)) %>%
    mutate(asset = "Portfolio")
## # A tibble: 1 × 3
##      mean   kurt asset    
##     <dbl>  <dbl> <chr>    
## 1 0.00895 -0.260 Portfolio
# Plot
mean_kurt_tbl %>%
    
    ggplot(aes(x = kurt, y = mean)) +
    geom_point() +
    ggrepel::geom_text_repel(aes(label = asset, color = asset)) +
    
    # Formatting
    theme(legend.position = "none") +
    scale_y_continuous(labels = scales::percent_format(accuracy = 0.1)) +
    
    # Labeling
    labs(x = "Kurtosis",
         y = "Exprected Returns")

Rolling 24 Month Kurtosis

#Assign a value for window

window = 24

# Transform data: calculate 24 month rolling kurtosis
rolling_kurt_tbl <- portfolio_returns_tbl %>%
    
    tq_mutate(select = returns,
              mutate_fun = rollapply,
              width = window,
              FUN = kurtosis,
              col_rename = "kurt") %>%
    
    na.omit() %>%
    select(-returns)

# Plot
rolling_kurt_tbl %>%
    
    ggplot(aes(x = date, y = kurt)) +
    geom_line(color = "cornflowerblue") +
    
    # Formatting
    scale_y_continuous(breaks = seq(-1, 4, 0.5)) +
    scale_x_date(breaks = scales::pretty_breaks(n = 7)) +
    theme(plot.title = element_text(hjust = 0.5)) +
    
    # Labeling
    labs(x = NULL,
         y = "Kurtosis",
         title = paste0("Rolling ", window, " Month Kurtosis")) +
    
    annotate(geom = "text", 
             x = as.Date("2024-01-31"), y = 2,
             size = 3, color = "red",
             label = str_glue("Downside risk increased
                              toward the mid point of 2024 and 2025"))

Has the downside risk of your portfolio increased or decreased over time? Explain using the plot you created. You may also refer to the skewness of the returns distribution you plotted in the previous assignment.

I would say that gradually the downside increased over time but dipped in the beginning of 2025 but is beginning to rise once more. We can see in about 2023 it was -1 using Kurtosis but is now sitting within a 0.4 range, likely soon to hit 0.5