# 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("HMC", "WMT", "TGT")

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"))

    asset_returns_tbl
## # A tibble: 180 × 3
##    asset date        returns
##    <chr> <date>        <dbl>
##  1 HMC   2013-01-31  0.0201 
##  2 HMC   2013-02-28 -0.00666
##  3 HMC   2013-03-28  0.0263 
##  4 HMC   2013-04-30  0.0440 
##  5 HMC   2013-05-31 -0.0622 
##  6 HMC   2013-06-28 -0.00318
##  7 HMC   2013-07-31 -0.00296
##  8 HMC   2013-08-30 -0.0328 
##  9 HMC   2013-09-30  0.0640 
## 10 HMC   2013-10-31  0.0466 
## # … with 170 more rows

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

# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "HMC" "TGT" "WMT"
# weights 
weight <- c(0.20, 0.20, 0.60)
weight
## [1] 0.2 0.2 0.6
w_tbl <- tibble(symbols, weight)
w_tbl
## # A tibble: 3 × 2
##   symbols weight
##   <chr>    <dbl>
## 1 HMC        0.2
## 2 TGT        0.2
## 3 WMT        0.6

4 Build a portfolio

# ?tq_portfolio

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

portfolio_returns_tbl
## # A tibble: 60 × 2
##    date       portfolio.returns
##    <date>                 <dbl>
##  1 2013-01-31           0.0231 
##  2 2013-02-28           0.0152 
##  3 2013-03-28           0.0595 
##  4 2013-04-30           0.0375 
##  5 2013-05-31          -0.0330 
##  6 2013-06-28          -0.00539
##  7 2013-07-31           0.0340 
##  8 2013-08-30          -0.0660 
##  9 2013-09-30           0.0221 
## 10 2013-10-31           0.0340 
## # … with 50 more rows

5 Compute kurtosis

portfolio_kurt_tidyquant_builtin_percent <- portfolio_returns_tbl %>%

    tq_performance(Ra = portfolio.returns, 
                   performance_fun = table.Stats) %>%
    
    select(Kurtosis)

portfolio_kurt_tidyquant_builtin_percent
## # A tibble: 1 × 1
##   Kurtosis
##      <dbl>
## 1    0.834

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     = portfolio.returns, 
              mutate_fun = rollapply, 
              width      = window, 
              FUN        = kurtosis, 
              col_rename = "kurt") %>%
    
    na.omit() %>%
    select(-portfolio.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("2016-01-01"), 
             y     = 0.4, 
             size  = 4, 
             color = "red",
             label = str_glue ("Starting second half of 2016, 
                               returns become more wildly variable"))

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.

In the graph, from the beginning of 2015 to the middle of 2016, kurtosis had a peaked positive value around the center. This means it had very few outliers during this time. Towards the right side of the graph, from the middle of 2016 to 2018, the kurtosis was more flat with negative values. This means that through the middle of 2016 and the end of 2018, their were more outliers in the data. If I assumed that skewness was also negative during this time, kurtosis would be more left tail and flat with negative results. Hence, greater downside risk.