# 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("SPY", "EFA", "IJS", "EEM", "AGG")

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] "AGG" "EEM" "EFA" "IJS" "SPY"
#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 AGG        0.25
## 2 EEM        0.25
## 3 EFA        0.2 
## 4 IJS        0.2 
## 5 SPY        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,
                replace_on = "months", 
                col_rename = "returns")

portfolio_returns_tbl
## # A tibble: 60 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.0204 
##  2 2013-02-28 -0.00220
##  3 2013-03-28  0.0127 
##  4 2013-04-30  0.0173 
##  5 2013-05-31 -0.0113 
##  6 2013-06-28 -0.0233 
##  7 2013-07-31  0.0342 
##  8 2013-08-30 -0.0231 
##  9 2013-09-30  0.0513 
## 10 2013-10-31  0.0305 
## # 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    0.337
# Mean of portfolio returns
portfolio_mean_tidyquant_builtin_percent <-
    mean(portfolio_returns_tbl$returns)

portfolio_kurt_tidyquant_builtin_percent
## # A tibble: 1 × 1
##   Kurtosis
##      <dbl>
## 1    0.337

6 Plot: Rolling kurtosis

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_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")

Rolling 24-Month Votality

# 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 = "Kurtois",
         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.

Downside risk of the portfolio has increased alot towards the end of 2017, as shown in graph by the rising kurtosis, which suggests a higher likelihood of extreme, potentially negative returns. A negative skew implies a tendency for more frequent or larger negative returns. This translates to an increased downside risk because there is a higher likelihood of significant losses during periods of negative skew.