# 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("NKE", "LLY", "CELH", "NVDA", "TSLA")

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 weighting scheme)

# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "CELH" "LLY"  "NKE"  "NVDA" "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)

4 Build a portfolio

# ?tq_portfolio

portfolio_returns_tbl <- asset_returns_tbl %>%
    
    tq_portfolio(assets_col = asset,
                 returns_col = returns,
                 weights     = w_tbl,
                 rebalace_on = "months",
                 col_rename = "returns")

portfolio_returns_tbl
## # A tibble: 60 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.0407 
##  2 2013-02-28  0.0624 
##  3 2013-03-28  0.0240 
##  4 2013-04-30  0.0670 
##  5 2013-05-31  0.0604 
##  6 2013-06-28  0.0668 
##  7 2013-07-31  0.121  
##  8 2013-08-30  0.170  
##  9 2013-09-30  0.00172
## 10 2013-10-31 -0.127  
## # ℹ 50 more rows

Calculate Standard Deviation

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    0.375

5 Compute Skewness

Histogram of Expected Returns and Risk

# 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")

6 Plot: Skewness Comparison

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 CELH       0.947 
## 2 LLY       -0.220 
## 3 NKE        0.0783
## 4 NVDA       0.899 
## 5 TSLA       0.944 
## 6 portfolio  0.375
# 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")

### 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 = 4,
             label = str_glue("The 24 Month rolling skewness has been postive the whole time,
                              but at the end it goes into the negatives"))

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.

To answer the question, yes, CELH, NVDA, and TSLA have higher positive skewness than my overall portfolio. This means they have a greater potential for unusually large positive returns. My portfolio has lower positive skewness because diversification helps balance out the extreme movements of individual stocks. Overall, this shows that individual assets can have more potential for extreme gains than a diversified portfolio.