# Load packages

# Core
library(tidyverse)
library(tidyquant)

Goal

Measure portfolio risk using skewness. Skewness is the extent to which returns are asymmetric around the mean. It is important because a positively skewed distribution means large positive returns are more likely while a negatively skewed distribution implies large negative returns are more likely.

five stocks: “SPY”, “EFA”, “IJS”, “EEM”, “AGG”

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

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] "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 Calculate Skewness

portfolio_returns_tbl %>%

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

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"))