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

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] "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 Calculate Skewness

portfolio_returns_tbl %>%

    tq_performance(Ra = returns,
                   Rb = NULL,
                   performance_fun = table.Stats) %>%
    select(Skewness)
## # A tibble: 1 × 1
##   Skewness
##      <dbl>
## 1    0.172

6 Plot

Expected Returns vs Risk

# Figure 5.2 Shaded histogram returns ----

portfolio_returns_tbl %>%

    # Create a new variable for shade
    mutate(returns_extreme_neg = if_else(returns < mean(returns) - 2*sd(returns),
                                   "yes",
                                   "no")) %>%

    # Plot
    ggplot(aes(returns, fill = returns_extreme_neg)) +
    geom_histogram(alpha = .7,
                   binwidth = .003) +

    scale_x_continuous(breaks = scales::pretty_breaks(n = 8)) +
    scale_fill_tq() +

    labs(x = "monthly returns")

# Figure 5.6 Asset and portfolio skewness comparison ----

asset_returns_skew_tbl <- asset_returns_tbl %>%

    # skewness for each asset
    group_by(asset) %>%
    summarise(skew = skewness(returns)) %>%
    ungroup() %>%

    # skewness of portfolio
    add_row(tibble(asset = "Portfolio",
                  skew = skewness(portfolio_returns_tbl$returns)))


asset_returns_skew_tbl %>%

    ggplot(aes(asset, skew, color = asset)) +
    geom_point() +

    # Add label for portfolio
    ggrepel::geom_text_repel(aes(label = asset),
                             data = asset_returns_skew_tbl %>%
                                 filter(asset == "Portfolio"),
                             size = 5,
                             show.legend = FALSE) +
    labs(y = "skewness")

24 Months Rolling Volatility

# 3 Rolling skewness ----
# Why rolling skewness?
# To check anything unusual in the portfolio's historical risk

# Assign a value to winder
window <- 24

port_rolling_sd_tbl <- portfolio_returns_tbl %>%

    tq_mutate(select = returns,
              mutate_fun = rollapply,
              width      = window,
              FUN        = skewness,
              col_rename = "rolling_skew") %>%
    select(date, rolling_skew) %>%
    na.omit()

Figure 4.8 Rolling skewness ggplot —-

port_rolling_sd_tbl %>%

    ggplot(aes(date, rolling_skew)) +
    geom_line(color = "cornflowerblue") +
    geom_hline(yintercept = 0, linetype = "dotted", size = 2) +

    scale_y_continuous(limits = c(-1,1),
                       breaks = scales::pretty_breaks(n = 10)) +
    scale_x_date(breaks = scales::breaks_pretty(n = 7))+

    labs(title = paste0("Rolling ", window, "-Month Skew"),
         x = NULL,
         y = "skewness") +
    theme(plot.title = element_text(hjust = 0.5)) +

    annotate(geom = "text",
             x = as.Date("2016-09-01"), y = 0.7,
             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, some of the individual stocks in the portfolio, like AAPL and NVDA, are more likely to have very high positive returns compared to the portfolio overall. This is shown by their positive skewness, which means they have a higher chance of big gains. On the other hand, the portfolio has negative skewness, meaning it’s more likely to have large losses than big gains. This happens because combining many stocks in a portfolio reduces both risk and the chance of very high returns from any one stock.