# 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("TSLA", "META", "XOM", "AAPL", "PG", "AMZN")

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" "AMZN" "META" "PG"   "TSLA" "XOM"
# weights
weights <- c(0.2, 0.2, 0.2, 0.1, 0.2, 0.1)
weights
## [1] 0.2 0.2 0.2 0.1 0.2 0.1
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 6 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AAPL        0.2
## 2 AMZN        0.2
## 3 META        0.2
## 4 PG          0.1
## 5 TSLA        0.2
## 6 XOM         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  0.0458 
##  2 2013-02-28 -0.0450 
##  3 2013-03-28  0.00821
##  4 2013-04-30  0.0767 
##  5 2013-05-31  0.111  
##  6 2013-06-28  0.00424
##  7 2013-07-31  0.174  
##  8 2013-08-30  0.0615 
##  9 2013-09-30  0.0789 
## 10 2013-10-31  0.0223 
## # 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    0.637

6 Plot: Rolling kurtosis

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, 1.5, 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("2017-01-01"), 
             y     = 0.5, 
             size  = 5, 
             color = "red",
             label = str_glue("The kurtosis for the portfolio dropped 
                              dramatically halfway through 2015, 
                              and remained relatively stable after that, 
                              increasing slowly."))

Observations from Kurtosis Plot

The kurtosis plot shows a dramatic drop in kurtosis halfway through 2015, followed by relatively stable values. The drop in kurtosis indicates a shift from heavier tails to lighter tails in the distribution. This implies a decrease in the likelihood of extreme returns (both positive and negative) during the period.

Furthermore, the gradual increase in kurtosis suggests a slight normalization in the distribution, but it remains in the range of lighter tails compared to normal distribution.

Skewness Plot from Apply 7

# Data transformation: calculate skewness 
asset_skewness_tbl <- asset_returns_tbl %>%
    
    group_by(asset) %>%
    summarise(skew = skewness(returns)) %>%
    ungroup() %>%
        
    # Add portfolio skewness
    add_row(tibble(asset = "Portfolio",
                   skew  = skewness(portfolio_returns_tbl$returns)))

asset_skewness_tbl
## # A tibble: 7 × 2
##   asset         skew
##   <chr>        <dbl>
## 1 AAPL      -0.555  
## 2 AMZN       0.187  
## 3 META       1.15   
## 4 PG         0.0728 
## 5 TSLA       0.944  
## 6 XOM       -0.00356
## 7 Portfolio  0.405
# Plot skewness
asset_skewness_tbl %>%
    
    ggplot(aes(x = asset, y = skew, color = asset)) +
    geom_point() +
    
    ggrepel::geom_text_repel(aes(label = asset), data = asset_skewness_tbl %>% 
                                 filter(asset == "Portfolio")) + 
    
    labs(y = "skewness")

7 Question

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.

Conclusion based on observations

Based on the skewness and kurtosis information, I was able to conclude the following:

The positive skewness suggests a lower likelihood of extreme negative returns, indicating a potentially decreased downside risk.

The drop in kurtosis halfway through 2015 suggests a decrease in the likelihood of extreme returns, supporting the notion of reduced downside risk during that period.

The stable kurtosis values indicate that the downside risk remained relatively stable after 2015, with lighter tails compared to a normal distribution.

So, it appears that the downside risk of the portfolio may have decreased initially, and then remained relatively stable over time.