# 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("INTL", "NVDA", "MSFT", "AMD")
prices <- tq_get(x    = symbols, 
                 get  = "stock.prices",
                 from = "2018-12-31",
                 to   = "2023-12-31")

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"))

asset_returns_tbl
## # A tibble: 192 × 3
##    asset date        returns
##    <chr> <date>        <dbl>
##  1 AMD   2019-01-31  0.279  
##  2 AMD   2019-02-28 -0.0367 
##  3 AMD   2019-03-29  0.0812 
##  4 AMD   2019-04-30  0.0794 
##  5 AMD   2019-05-31 -0.00799
##  6 AMD   2019-06-28  0.103  
##  7 AMD   2019-07-31  0.00263
##  8 AMD   2019-08-30  0.0323 
##  9 AMD   2019-09-30 -0.0814 
## 10 AMD   2019-10-31  0.157  
## # ℹ 182 more rows

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

symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "AMD"  "INTL" "MSFT" "NVDA"
# weights
weights <- c(0.25, 0.25, 0.25, 0.25)
weights 
## [1] 0.25 0.25 0.25 0.25
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 4 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AMD        0.25
## 2 INTL       0.25
## 3 MSFT       0.25
## 4 NVDA       0.25

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: 60 × 2
##    date        returns
##    <date>        <dbl>
##  1 2019-01-31  0.0953 
##  2 2019-02-28  0.0273 
##  3 2019-03-29  0.0711 
##  4 2019-04-30  0.0473 
##  5 2019-05-31 -0.0869 
##  6 2019-06-28  0.0937 
##  7 2019-07-31  0.0117 
##  8 2019-08-30  0.0103 
##  9 2019-09-30 -0.00865
## 10 2019-10-31  0.0830 
## # ℹ 50 more rows

5 Compute kurtosis

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

6 Plot: Rolling kurtosis

# Assing 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("My Portfolio Risk Has Become More Stable Over Time")) +
    
    annotate(geom = "text", x = as.Date("2018-12-31", "2023-12-01"), y = 1,
             size = 2, color = "red",
             label = str_glue(""))

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.

Answer

The kurtosis graph of my portfolio indicates changes in downside risk over time. Initially, the negative kurtosis suggests lower risk with fewer extreme returns. But around mid-2022, a peak in kurtosis indicates an increased risk in my portfolio due to the potential for more extreme outcomes. After this peak, the kurtosis decreases and remains negative, signaling a reduction in downside risk as the distribution of returns shows lighter tails. Therefore, my portfolio’s downside risk increased briefly in 2022 but has since declined, suggesting a more stable risk profile recently.