# 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("AAPL", "NFLX", "GOOG", "TSLA", "NVDA")

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" "GOOG" "NFLX" "NVDA" "TSLA"
#weights
weights <- c(0.25, 0.25, 0.2, 0.2, 0.1)
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 GOOG       0.25
## 3 NFLX       0.2 
## 4 NVDA       0.2 
## 5 TSLA       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: 60 × 2
##    date       returns
##    <date>       <dbl>
##  1 2013-01-31  0.104 
##  2 2013-02-28  0.0343
##  3 2013-03-28  0.0109
##  4 2013-04-30  0.0855
##  5 2013-05-31  0.0988
##  6 2013-06-28 -0.0394
##  7 2013-07-31  0.0925
##  8 2013-08-30  0.0665
##  9 2013-09-30  0.0442
## 10 2013-10-31  0.0483
## # 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   -0.380

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"))

# Plot
mean_kurt_tbl %>%
    
    ggplot(aes(x = kurt, y = mean)) +
    geom_point() +
    ggrepel::geom_label_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")

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("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 increased over time, as shown by the rising kurtosis toward the end of the period. This indicates that returns became more volatile, with a higher chance of extreme losses. The negative skewness from the previous analysis also supports this, showing that the portfolio experienced larger downside movements in later years.