# 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("MSFT", "NFLX", "META", "AMZN", "AAPL")
prices <- tq_get(x    = symbols,
                 get  = "stock.prices", 
                 from = "2012-12-31")

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 weighting scheme)

# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "AAPL" "AMZN" "META" "MSFT" "NFLX"
# weights
weights <- c(0.15, 0.25, 0.2, 0.3, 0.1)
weights
## [1] 0.15 0.25 0.20 0.30 0.10
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 5 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AAPL       0.15
## 2 AMZN       0.25
## 3 META       0.2 
## 4 MSFT       0.3 
## 5 NFLX       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: 154 × 2
##    date         returns
##    <date>         <dbl>
##  1 2013-01-31  0.0873  
##  2 2013-02-28 -0.0114  
##  3 2013-03-28 -0.000877
##  4 2013-04-30  0.0613  
##  5 2013-05-31  0.0143  
##  6 2013-06-28 -0.0169  
##  7 2013-07-31  0.109   
##  8 2013-08-30  0.0491  
##  9 2013-09-30  0.0701  
## 10 2013-10-31  0.0746  
## # ℹ 144 more rows

5 Compute kurtosis + Skewness

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    0.381
# 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: 6 × 2
##   asset        skew
##   <chr>       <dbl>
## 1 AAPL      -0.292 
## 2 AMZN      -0.0902
## 3 META      -0.401 
## 4 MSFT       0.0146
## 5 NFLX      -0.628 
## 6 Portfolio -0.383

6 Plot: Rolling kurtosis

# Plot skewness

asset_skewness_tbl %>%
    
    ggplot(aes(x = asset, y = skew, color = asset)) +
    geom_point() +

    geom_text(aes(label = asset),
              vjust = 1.5,   # Nudges labels down
              hjust = 0.5,   # Centers labels horizontally
              size = 4)      # Sets text size

# Assign a value for window

window = 24
# Transform data: calculate 24 months 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"))

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.

Answer: The skewness of my portfolio is at around -0.39, telling me that it has a slightly negatively skewed distribution. Since 2012-12-31, the portfolio’s kurtosis has fluctuated from -1.0 to 0.75 indicating the the portfolio has been susceptible to occasional, albeit infrequent, large losses within this timeframe. From what I’ve read, a mostly negative kurtosis is called “Platykurtic” and is representative of significantly fewer gains/losses depending on the portfolio’s overall skewness.