# 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", "EFA", "IJS", "EEM", "AGG")

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 weigting scheme)

# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "AGG" "EEM" "EFA" "IJS" "SPY"
# 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 AGG        0.25
## 2 EEM        0.25
## 3 EFA        0.2 
## 4 IJS        0.2 
## 5 SPY        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  0.0204 
##  2 2013-02-28 -0.00239
##  3 2013-03-28  0.0121 
##  4 2013-04-30  0.0174 
##  5 2013-05-31 -0.0128 
##  6 2013-06-28 -0.0247 
##  7 2013-07-31  0.0321 
##  8 2013-08-30 -0.0224 
##  9 2013-09-30  0.0511 
## 10 2013-10-31  0.0301 
## # ℹ 50 more rows

5 Compute Skewness

portfolio_returns_tbl %>%

    tq_performance(Ra = returns,
                   Rb = NULL,
                   performance_fun = table.Stats) %>%
    select(Skewness)
## # A tibble: 1 × 1
##   Skewness
##      <dbl>
## 1   -0.168

6 Plot: Skewness Comparison

# 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.

SPY and IJS are the most likely to have extremeky positive returns. This is because they have the greatest positive skewness, and a longer right tail.