# 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", "MSFT", "META", "TSLA", "NFLX")

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" "META" "MSFT" "NFLX" "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 META       0.25
## 3 MSFT       0.2 
## 4 NFLX       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  0.131   
##  2 2013-02-28 -0.0158  
##  3 2013-03-28  0.000339
##  4 2013-04-30  0.112   
##  5 2013-05-31  0.0533  
##  6 2013-06-28 -0.0327  
##  7 2013-07-31  0.166   
##  8 2013-08-30  0.113   
##  9 2013-09-30  0.0734  
## 10 2013-10-31  0.0247  
## # … with 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   -0.505

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     = 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 level decreasing in 
                              2015-07 and forward"))

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.

Throughout 2012-12-31 & 2017-12-31 looking at the rolling 24-month kurtosis chart, I can identify a low kurtosis level with a peak of 0 and a low by approximately -1.3 over this period of time. generally speaking, a kurtosis level under 3, means that it has a much thinner tail than the normal distribution and more returns will fall within the center. (less risky and more predictable) My portfolio skewness is 0.0436 which falls under the category of being fairly symmetrical and slightly positively skewed.

To conclude, the downside risk of my portfolio over time has decreased since a lower kurtosis proves less risk and more predictable gains. Also, with a fairly symmetrical positive skewness, it proves that my portfolio is low risk and has more predictable gains towards the normal distribution over time.