# 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("AAPL", "GOOG", "NVDA", "TGT", "WMT")

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" "GOOG" "NVDA" "TGT"  "WMT"
#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 GOOG       0.25
## 3 NVDA       0.2 
## 4 TGT        0.2 
## 5 WMT        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 -0.0157
##  2 2013-02-28  0.0265
##  3 2013-03-28  0.0241
##  4 2013-04-30  0.0335
##  5 2013-05-31  0.0251
##  6 2013-06-28 -0.0372
##  7 2013-07-31  0.0521
##  8 2013-08-30 -0.0148
##  9 2013-09-30  0.0171
## 10 2013-10-31  0.0651
## # ℹ 50 more rows

5 Compute Skewness

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

portfolio_skew_tidyquant_builtin_percent
## # A tibble: 1 × 1
##   Skewness
##      <dbl>
## 1    0.172
# Calculate sd of portfolio returns
sd_portfolio <- sd(portfolio_returns_tbl$returns)
mean_portfolio <- mean(portfolio_returns_tbl$returns)

portfolio_returns_tbl %>%
    
    # 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 = "monthly returns")

Scatterplot of skewness comparison

# 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      -0.555 
## 2 GOOG       0.784 
## 3 NVDA       0.899 
## 4 TGT        0.148 
## 5 WMT        0.0723
## 6 Portfolio  0.171
# Plot skewness
asset_skewness_tbl %>%
    
    ggplot(aes(x = asset, y = skew)) +
    geom_point() +
    
    ggrepel::geom_text_repel(aes(label = asset),
                             data = asset_skewness_tbl %>%
                                 filter(asset == "Portfolio")) +
    
    labs(y = "skewness")

Rolling Skewness

# Transform data: calculate rolling skewness
rolling_skew_tbl <- portfolio_returns_tbl %>%
    
    tq_mutate(select = returns,
              mutate_fun = rollapply, 
              width = 24,
              FUN = skewness,
              col_rename = "Skew")  %>%
    
    select(-returns) %>%
    na.omit()

# Plot
rolling_skew_tbl %>%
    
    ggplot(aes(x = date, y = Skew)) +
    geom_line(color = "cornflowerblue") +
    
    geom_hline(yintercept = 0, linetype = "dotted", size = 2) +
    
    #Formatting
    scale_y_continuous(limits = c(-1,1), breaks = seq(-1,1,0.2)) +
    theme(plot.title = element_text(hjust = 0.5))+
    
    # Labeling
    labs(y = "Skewness", 
         x = NULL,
         title = "Rolling 24-Month Skewness") +
    
    annotate(geom = "text",
             x = as.Date("2016-07-01"), y = 0.8,
             color = "red", size = 5,
             label = "The 24 month rolling skewness is positive for about half of the lifetime, 
             even though the overall skewness is negative")

6 Plot: Skewness Comparison

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.

The portfolio shows a slightly positive skewness, meaning it has some potential for extreme positive returns, but less than certain individual stocks. For example, NVDA and AAPL have higher positive skewness values, indicating they are more likely to experience large positive returns compared to the portfolio as a whole. Overall, diversification reduces the impact of extreme outcomes, making the portfolio’s return distribution more balanced.