# Load packages

# Core
library(tidyverse)
library(tidyquant)

Goal

Visualize and compare skewness of your portfolio and its assets.

1 Import stock prices

symbols <- c("UNH", "LLY", "JNJ", "PFE", "MRK")

prices <- tq_get(x = symbols, 
                 get = "stock.prices", 
                 from = "2010-01-01", 
                 to = "2025-01-01")

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] "JNJ" "LLY" "MRK" "PFE" "UNH"
# weights
weights <- c(0.3, 0.25, 0.20, 0.13, 0.12)
weights
## [1] 0.30 0.25 0.20 0.13 0.12
w_tbl <-tibble(symbols, weights)
w_tbl
## # A tibble: 5 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 JNJ        0.3 
## 2 LLY        0.25
## 3 MRK        0.2 
## 4 PFE        0.13
## 5 UNH        0.12

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: 179 × 2
##    date        returns
##    <date>        <dbl>
##  1 2010-02-26 -0.0103 
##  2 2010-03-31  0.0209 
##  3 2010-04-30 -0.0379 
##  4 2010-05-28 -0.0629 
##  5 2010-06-30  0.00805
##  6 2010-07-30  0.0222 
##  7 2010-08-31  0.00400
##  8 2010-09-30  0.0797 
##  9 2010-10-29  0.00154
## 10 2010-11-30 -0.0318 
## # ℹ 169 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  -0.0675

6 Plot: Skewness Comparison

# 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 - sd_portfolio * 2, "ext_neg", "not_ex_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")

Distribution of Quarterly Returns

asset_returns_tbl %>%
    ggplot(aes(x = returns)) +
    geom_density(aes(color = asset), show.legend = FALSE,  alpha =  1) +
    geom_histogram(aes(fill = asset), show.legend = FALSE, alpha = 0.3, binwidth = 0.01) +
    facet_wrap(~asset, ncol = 1) +
    
    # Labeling
    labs(title = "Distribution of Monthly Returns, 2010-2025",
         y = "Frequency",
         x= "Rate of 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 JNJ       -0.142 
## 2 LLY        0.210 
## 3 MRK       -0.213 
## 4 PFE        0.265 
## 5 UNH       -0.157 
## 6 Portfolio -0.0675
# 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.

Yes, there are assets in the portfolio that appear more likely to deliver extreme positive returns than the portfolio as a whole, based on the skewness of their return distributions. I first looked at the skewness of the assets and noticed that LLY has skewness of about 0.21 and PFE has skewness of about 0.26. When comparing that skewness to the average monthly returns in code along 4 I learned that PFE has a negative average monthly return indicating that it may not more likely to deliver extreme positive returns than the portfolio as a whole. When looking at average monthly returns for LLY they are positive which along with a skewness of 0.21 indicates that it may be more likely to deliver extreme positive returns than the portfolio as a whole. The overall portfolio appears to have a more symmetric and less skewed distribution, as it’s composed of multiple assets whose individual risks and skewness tendencies are diversified away. The portfolio smooths out individual extremes and thus reduces an investors exposure to volatility.