# 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

# Choose stocks

symbols <- c("AAPL", "NKE", "GE", "DIS", "SBUX")

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 %>%

    # Calculate monthly returns
    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" "DIS"  "GE"   "NKE"  "SBUX"
# weight
weights <- c(0.25, 
       0.25, 
       0.20, 
       0.20, 
       0.10)
weights
## [1] 0.25 0.25 0.20 0.20 0.10
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 5 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AAPL       0.25
## 2 DIS        0.25
## 3 GE         0.2 
## 4 NKE        0.2 
## 5 SBUX       0.1

4 Build a 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 2013-01-31  0.00658
##  2 2013-02-28  0.00714
##  3 2013-03-28  0.0296 
##  4 2013-04-30  0.0396 
##  5 2013-05-31  0.0141 
##  6 2013-06-28 -0.0206 
##  7 2013-07-31  0.0549 
##  8 2013-08-30 -0.00593
##  9 2013-09-30  0.0549 
## 10 2013-10-31  0.0700 
## # ℹ 50 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    0.659

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()

    # Add portfolio stats
    add_row(portfolio_returns_tbl %>%
                summarise(mean = mean(returns),
                          kurt = kurtosis(returns)) %>%
                mutate(asset = "Portfolio"))
## # A tibble: 2 × 3
##      mean   kurt asset    
##     <dbl>  <dbl> <chr>    
## 1  0.0117  0.659 Portfolio
## 2 NA      NA     <NA>
# 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 = "Expected Returns")

# 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("2016-07-01"), y = 3,
             size = 5, color = "red", 
             label = str_glue( " Downside risk skyrocketed 
                               toward the end of 2017"))

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.

The downside risk of my portfolio has decreased from 0.25 percent to -0.1 percent during the time period of 2017-2018. This means the risk has decreased since the kurtosis is falling.