# 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("AAPL", "MSFT", "GOOG")

prices <- tq_get(x = symbols,
                 get = "stock.prices",
                 from = "2012-12-31")

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 <- asset_returns_tbl %>% distinct(asset) %>% pull()

w <- c(0.35,
       0.35,
       0.30)

w_tbl <- tibble(symbols, w)

4 Build a portfolio

portfolio_returns_tbl <- asset_returns_tbl %>%
    
    tq_portfolio(assets_col   = asset,
                 returns_col  = returns,
                 weights      = w_tbl,
                 col_rename   = "returns",
                 rebalance_on = "months")

portfolio_returns_tbl
## # A tibble: 142 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31 -0.0231 
##  2 2013-02-28  0.0178 
##  3 2013-03-28  0.00654
##  4 2013-04-30  0.0570 
##  5 2013-05-31  0.0450 
##  6 2013-06-28 -0.0435 
##  7 2013-07-31  0.0247 
##  8 2013-08-30  0.0281 
##  9 2013-09-30  0.00311
## 10 2013-10-31  0.108  
## # ℹ 132 more rows

5 Compute kurtosis

asset_returns_kurtosis_tbl <- asset_returns_tbl %>%

    group_by(asset) %>%
    summarise(kt = kurtosis(returns),
              mean = mean(returns)) %>%
    ungroup() %>%

    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() +
    
    scale_y_continuous(labels = scales::percent_format(accuracy = 0.1)) +
    theme(legend.position = "none") +

    ggrepel::geom_text_repel(aes(label = asset, color = asset), size = 5) +

    labs(y = "Expected Return",
         x = "Kurtosis")

6 Plot: Rolling kurtosis

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()

port_rolling_kurtosis_tbl %>%

    ggplot(aes(date, rolling_kurtosis)) +
    geom_line(color = "magenta") +

    scale_y_continuous(breaks = scales::pretty_breaks(n = 10)) +
    scale_x_date(breaks = scales::breaks_pretty(n = 7)) +

    labs(title = paste0("Rolling ", "Kurtosis"),
         x = NULL,
         y = "kurtosis") +
    theme(plot.title = element_text(hjust = 0.5))

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 is not something that needs to be worries about. The kurtosis has ranged between -1 and .8 with it currently being at -.05, showing that the tailedness of my distribution is very skinny. The skewness of my portfolio is very close to zero, which calls for a normal appearing distribution. This then means that my portfolio shows no signs of potential downside risk.