# 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("UNH", "AAPL", "UPS", "WMT", "LME")

prices <- tq_get(x    = symbols, 
                 get  = "stock.prices",
                 from = "2012-12-31",
                 to   = "2017-12-31")

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" "LME"  "UNH"  "UPS"  "WMT"
# weights
weights <- c(0.20, 0.25, 0.2, 0.25, 0.1)
weights
## [1] 0.20 0.25 0.20 0.25 0.10
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 5 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AAPL       0.2 
## 2 LME        0.25
## 3 UNH        0.2 
## 4 UPS        0.25
## 5 WMT        0.1

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: 63 × 2
##    date       returns
##    <date>       <dbl>
##  1 2013-01-31  0.0772
##  2 2013-02-28 -0.0367
##  3 2013-03-28 -0.0148
##  4 2013-04-30  0.0585
##  5 2013-05-31 -0.0894
##  6 2013-06-28  0.0416
##  7 2013-07-31  0.200 
##  8 2013-08-30 -0.0575
##  9 2013-09-30 -0.0248
## 10 2013-10-31 -0.0707
## # ℹ 53 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     8.72

6 Plot: Rolling 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 = "steelblue") +
    
    # Formatting
    scale_y_continuous(breaks = seq(-1, 11, 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("2016-07-01"), y = 3,
             size = 5, color = "orangered3",
             label = str_glue("Downside risk skyrocketed
                              in 2015 slowly falling then
                              rising again 2 years later with a
                              sharp decline with another sharp
                              incline afterwards"))

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 think the sharp Increases in kurtosis due to a large mix of extreme returns skewing the market and the data, with that fully leveling back out where I believe a similar situation happen with it finally at its settling point coming down when the ranges of returns are more moderate and extreme returns lowering in probability