# Load packages

# Core
library(tidyverse)
library(tidyquant)

Goal

Visualize and examine changes in the underlying trend in the downside risk of your portfolio in terms of kurtosis.

Choose your stocks.

from 2012-12-31 to present

1 Import stock prices

symbols <- c("SPY", "IBM", "QQQ", "TSLA", "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"  "IBM"  "QQQ"  "SPY"  "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 AGG        0.25
## 2 IBM        0.25
## 3 QQQ        0.2 
## 4 SPY        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  0.0385 
##  2 2013-02-28 -0.00444
##  3 2013-03-28  0.0371 
##  4 2013-04-30  0.0337 
##  5 2013-05-31  0.0739 
##  6 2013-06-28 -0.0233 
##  7 2013-07-31  0.0505 
##  8 2013-08-30 -0.00164
##  9 2013-09-30  0.0359 
## 10 2013-10-31 -0.00637
## # ℹ 50 more rows
portfolio_returns_tbl %>%

    tq_performance(Ra = returns,
                   Rb = NULL,
                   performance_fun = table.Stats) %>%
    select(Kurtosis)
## # A tibble: 1 × 1
##   Kurtosis
##      <dbl>
## 1    0.693

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 skyrocketed at the end of the period
                              with the 24-month kurtosis rising above three."))

Has the downside risk of your portfolio increased or decreased over time? Explain using the plot you created. You may also refer to the skewness of the returns distribution you plotted in the previous assignment.

The downside risk of my portfolio increased over time. The 24-month rolling kurtosis rose steadily and exceeded 3 near the end, indicating a higher chance of extreme negative returns and greater overall volatility.