# 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("SPY", "WMT", "COST", "AMZN")
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 %>%
# I added asset_returns_tbl here (wasn't in video) otherwise the code would not run, and mistake code wouldn't be fixable
# In video
    
    group_by(symbol) %>%

    tq_transmute(select     = adjusted, 
                 mutate_fun = periodReturn, 
                 period     = "monthly",
                 type       = "log") %>%
    slice(-1) %>%
    #Remove the first row, but since data is group, it will remove the first line of each group
    
    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] "AMZN" "COST" "SPY"  "WMT"
# weights
weights <- c(0.30, 0.30, 0.20, 0.20)
weights
## [1] 0.3 0.3 0.2 0.2
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 4 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AMZN        0.3
## 2 COST        0.3
## 3 SPY         0.2
## 4 WMT         0.2

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  0.0427 
##  2 2013-02-28  0.00121
##  3 2013-03-28  0.0363 
##  4 2013-04-30  0.00325
##  5 2013-05-31  0.0201 
##  6 2013-06-28  0.00825
##  7 2013-07-31  0.0616 
##  8 2013-08-30 -0.0526 
##  9 2013-09-30  0.0497 
## 10 2013-10-31  0.0694 
## # 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  -0.0778

6 Plot: Skewness Comparison

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)) +
    #order of data: far left value, far right value, intervals
    
    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: 5 × 2
##   asset        skew
##   <chr>       <dbl>
## 1 AMZN       0.187 
## 2 COST      -0.244 
## 3 SPY       -0.264 
## 4 WMT        0.0723
## 5 Portfolio -0.0778
# 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)) +

    # Labelling
    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("The 24-month skewness is positive for about half of the lifetime, 
                              even though the overall skewness is negative"))

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, AMZN is more likely to return extreme positive returns than my portfolio collectively. As seen in this graph,it has however more risks too. In term of skewness, AMNZ has a positive value of ~0.17, compared to ~0.7 for WMT, and ~ -0.09 for my portfolio, thus making it the one with the highest positive skewness by far.

As I did not have the same stocks in Apply 4, I’m putting a picture of what the graph would have been below:

out.width = "20px"
echo = FALSE
fig.cap = "Apply 4 img.png"
knitr::include_graphics("Apply 4 img.png")

Based on this distribution of returns, AMZN tends to have more frequent large gains, as well as large losses, while WMT seems to have more often moderate gains. The larger right tail in the graph for AMZN also indicates larger and more frequent gains, thus more frequently positive outcomes. This is consistent with my earlier response, confirming that AMZN is the most likely to return extreme positive returns than the portfolio or any other assets in the portfolio.