# Load packages
# Core
library(tidyverse)
library(tidyquant)

1 Import stock prices

symbols <- c("NKE", "AMZN", "GOOG", "MSFT", "TSLA")
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" "GOOG" "MSFT" "NKE"  "TSLA"
# 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 GOOG       0.25
## 3 MSFT       0.2 
## 4 NKE        0.2 
## 5 TSLA       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 0.0556 
##  2 2013-02-28 0.0125 
##  3 2013-03-28 0.0301 
##  4 2013-04-30 0.0767 
##  5 2013-05-31 0.0943 
##  6 2013-06-28 0.0241 
##  7 2013-07-31 0.0261 
##  8 2013-08-30 0.00515
##  9 2013-09-30 0.0769 
## 10 2013-10-31 0.0805 
## # … with 50 more rows

5 Calculate Skewness

portfolio_returns_tbl %>%
    tq_performance(Ra = returns,
                   Rb = NULL,
                   performance_fun = table.Stats) %>%
    select(Kurtosis)
## # A tibble: 1 × 1
##   Kurtosis
##      <dbl>
## 1   -0.295

6 Plot

Distribution of portfolio returns

portfolio_returns_tbl %>% 
    ggplot(aes(returns)) + 
    geom_histogram()

Expected Return vs Risk

# Figure 6.3 Asset and Portfolio Kurtosis Comparison ----
asset_returns_kurtosis_tbl <- asset_returns_tbl %>%
    # kurtosis for each asset
    group_by(asset) %>%
    summarise(kt = kurtosis(returns),
              mean = mean(returns)) %>%
    ungroup() %>%
    # kurtosis of portfolio
    add_row(tibble(asset = "Portfolio",
                   kt = kurtosis(portfolio_returns_tbl$returns),
                   mean = mean(portfolio_returns_tbl$returns)))
asset_returns_kurtosis_tbl %>%
    ggplot(aes(kt, mean)) +
    geom_point() +
    
    # Formatting
    scale_y_continuous(labels = scales::percent_format(accuracy = 0.1)) +
    theme(legend.position = "none") +
    # Add label
    ggrepel::geom_text_repel(aes(label = asset, color = asset), size = 5) +
    labs(y = "Expected Return",
         x = "Kurtosis")

Rolling kurtosis

# 3 Rolling kurtosis ----
# Assign a value to winder
window <- 24
port_rolling_kurtosis_tbl <- portfolio_returns_tbl %>%
    tq_mutate(select = returns,
              mutate_fun = rollapply,
              width      = window,
              FUN        = kurtosis,
              col_rename = "rolling_kurtosis") %>%
    select(date, rolling_kurtosis) %>%
    na.omit()
# Figure 6.5 Rolling kurtosis ggplot ----
port_rolling_kurtosis_tbl %>%
    ggplot(aes(date, rolling_kurtosis)) +
    geom_line(color = "cornflowerblue") +
    scale_y_continuous(breaks = scales::pretty_breaks(n = 10)) +
    scale_x_date(breaks = scales::breaks_pretty(n = 7)) +
    labs(title = paste0("Rolling ", window, "-Month Kurtosis"),
         x = NULL,
         y = "kurtosis") +
    theme(plot.title = element_text(hjust = 0.5)) +
    annotate(geom = "text",
             x = as.Date("2016-12-01"), y = 3,
             color = "red", size = 5,
             label = str_glue("The risk level plumeted at the end of the period
                              with the 24-month kurtosis dropping below -0.5 after being up around 0.5 right before that. The skewness is fairly symmetrical and doesn't have much variance, meaning there aren't extreme outliers leading to kurtosis not mattering too much."))