# 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("TSLA", "AMZN", "NVDA", "DELL", "WMT")
prices <- tq_get(x    = symbols,
                 get = "stock.prices",
                 from = "2012-12-31",
                 to   = "2017-12-31")

2 Convert prices to returns

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

#Symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "AMZN" "DELL" "NVDA" "TSLA" "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 AMZN       0.25
## 2 DELL       0.25
## 3 NVDA       0.2 
## 4 TSLA       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, 
                 reabalance_on = "months",
                 col_rename = "returns")

portfolio_returns_tbl
## # A tibble: 60 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.0371 
##  2 2013-02-28 -0.00840
##  3 2013-03-28  0.0278 
##  4 2013-04-30  0.0799 
##  5 2013-05-31  0.176  
##  6 2013-06-28  0.0338 
##  7 2013-07-31  0.109  
##  8 2013-08-30  0.0816 
##  9 2013-09-30  0.0901 
## 10 2013-10-31 -0.0687 
## # ℹ 50 more rows

5 Calculate Standard Deviation

portfolio_skew_tidquant_builtin_percent <- portfolio_returns_tbl %>%
    
  tq_performance(Ra = returns, 
                 performance_fun = table.Stats) %>%
    
  select(Skewness) 
portfolio_skew_tidquant_builtin_percent
## # A tibble: 1 × 1
##   Skewness
##      <dbl>
## 1  -0.0689

6 Plot

Histogram of Expected Returns and Risk

# Calculate SD of peortfolio 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 AMZN       0.187 
## 2 DELL      -0.620 
## 3 NVDA       0.899 
## 4 TSLA       0.944 
## 5 WMT        0.0723
## 6 Portfolio -0.0689
# 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 = "coral3") +
    geom_hline(yintercept = 0, linetype = "dotted", size = 2) +

# Formatting
scale_y_continuous(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 = str_glue(""))

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 2012=2015",
     y = "frequency",
     x = "rate of returns",
     caption =
"A typical monthly return is higher for SPV and 135 than for AGG, EEM, and EFA")
## $y
## [1] "frequency"
## 
## $x
## [1] "rate of returns"
## 
## $title
## [1] "Distribution of Monthly Returns 2012=2015"
## 
## $caption
## [1] "A typical monthly return is higher for SPV and 135 than for AGG, EEM, and EFA"
## 
## attr(,"class")
## [1] "labels"

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.

NVDA and TSLA are the most likely to return extreme positives in comparison to the portfolio. Tesla and Nvidia’s skewness are close to 1, and the portfolio is at