# Load packages

# Core
library(tidyverse)
library(tidyquant)

Goal

Visualize and compare skewness of your portfolio and its assets.

Choose your stocks.

from 2012-12-31 to 2017-12-31

1 Import stock prices

symbols <- c("RTX", "GD", "LMT", "BA")
stock_prices <- tq_get(x    = symbols, 
                 get  = "stock.prices", 
                 from = "2012-12-31", 
                 to   = "2017-12-31")

2 Convert prices to returns (monthly)

ar_table <- stock_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 <- ar_table %>% distinct(asset) %>% pull()
symbols
## [1] "BA"  "GD"  "LMT" "RTX"
# weights
weights <- c(0.35, 0.30, 0.20, 0.15)
weights
## [1] 0.35 0.30 0.20 0.15
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 4 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 BA         0.35
## 2 GD         0.3 
## 3 LMT        0.2 
## 4 RTX        0.15

4 Build a portfolio

portfolio_returns_table <- ar_table %>%
    
    tq_portfolio(assets_col   = asset, 
                 returns_col  = returns, 
                 weights      = w_tbl, 
                 rebalance_on = "months", 
                 col_rename   = ("returns"))
portfolio_returns_table
## # A tibble: 60 × 2
##    date       returns
##    <date>       <dbl>
##  1 2013-01-31 -0.0224
##  2 2013-02-28  0.0349
##  3 2013-03-28  0.0727
##  4 2013-04-30  0.0405
##  5 2013-05-31  0.0642
##  6 2013-06-28  0.0184
##  7 2013-07-31  0.0764
##  8 2013-08-30 -0.0114
##  9 2013-09-30  0.0773
## 10 2013-10-31  0.0423
## # … with 50 more rows

5 Compute Skewness

portfolio_skew_tidyquant_builtin_percent <- portfolio_returns_table %>% 
    
    tq_performance(Ra = returns,
                   performance_fun = table.Stats) %>%
    
    select(Skewness) 

portfolio_skew_tidyquant_builtin_percent
## # A tibble: 1 × 1
##   Skewness
##      <dbl>
## 1   -0.355

6 Plot: Skewness Comparison

# Calculate sd of portfolio returns
sd_portfolio <- sd(portfolio_returns_table$returns)
mean_portfolio <- mean(portfolio_returns_table$returns)

portfolio_returns_table %>% 
    
    # Add a new variable 
    mutate(extreme_neg = ifelse(returns < mean_portfolio - 2 * sd_portfolio, "ext_neg", "not_ext_neg")) %>%
    
    ggplot(aes(x = returns, fill = extreme_neg)) + 
    geom_histogram(binwidth = 0.003) + 
    
    scale_x_continuous(breaks = seq(-0.06, 0.06, 0.02)) + 
    
    labs(x = "montly returns")

Scaterplot of skewness comparison

# Data transformation: calculate skewness

asset_skewness_tbl <- ar_table %>% 
    
    group_by(asset) %>% 
    summarise(skew = skewness(returns)) %>% 
    ungroup() %>% 
    
    # Add portfolio skewness
    add_row(tibble(asset = "Portfolio", 
                   skew  = skewness(portfolio_returns_table$returns)))
    
asset_skewness_tbl
## # A tibble: 5 × 2
##   asset       skew
##   <chr>      <dbl>
## 1 BA        -0.310
## 2 GD         0.385
## 3 LMT       -0.240
## 4 RTX       -0.144
## 5 Portfolio -0.355
#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")

Is any asset in your portfolio more likely to return extreme positive returns than your portfolio collectively? Discuss in terms of skewness. You may also refer to the distribution of returns you plotted in Code along 4.

From the plot, you can see that GD is the only stock witha positive skewness out of the 4 stocks. Also, if we look at the plot from section 4, we can see that the peak of GD is to the right of zero and is at about 0.09. From these two graphs, it can be said with a high degree of certainty that GD will produce extreme positive returns more frequently and extreme negative returns less frequently than the other stocks.