# 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 
## # … with 50 more rows

5 Calculate Kurtosis

portfolio_kurt_tidyquant_builtin_percent <- portfolio_returns_tbl %>%

    tq_performance(Ra = returns,
                   performance_fun = table.Stats) %>%
    
    select(Kurtosis)

portfolio_kurt_tidyquant_builtin_percent
## # A tibble: 1 × 1
##   Kurtosis
##      <dbl>
## 1    0.488

6 Plot

Distribution of portfolio returns

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

Expected return vs Downside risk

mean_kurt_table <- asset_returns_tbl %>%
    
    group_by(asset) %>%
    summarise(mean = mean(returns), 
              kurt = kurtosis(returns)) %>%
    ungroup() %>%
    
    add_row(portfolio_returns_tbl %>%
            summarise(mean = mean(returns),
                      kurt = kurtosis(returns)) %>%
            mutate(asset = "Portfolio"))


mean_kurt_table %>%
    
    ggplot(aes(x = kurt, y = mean)) +
    geom_point() +
    ggrepel::geom_text_repel(aes(label = asset, color = asset)) +
    
    theme(legend.position = "none") +
    scale_y_continuous(labels = scales::percent_format(accuracy = 0.1))+
    
    labs(x = "Kurtosis",
         y = "Expected Returns")

24-month rolling Kurtosis

window = 24

rolling_kurt_table <- portfolio_returns_tbl %>%
    
    tq_mutate(select = returns, 
              mutate_fun = rollapply, 
              width = window, 
              FUN = kurtosis,
              col_rename = "Kurt") %>%
    na.omit() %>%
    select(-returns)

rolling_kurt_table%>%
    ggplot(aes(x = date, y = Kurt)) +
    geom_line(color = "cornflowerblue") +
    
    scale_y_continuous(breaks = seq(-1, 4, 0.5)) +
    
    scale_x_date(breaks = scales::pretty_breaks(n = 7))+
    theme(plot.title = element_text(hjust = 0.5))+
    
    labs(x = NULL, y = "Kurtosis",
         title = paste0("Rolling ", window, " month kurtosis")) +
    
    annotate(geom = "text", 
             x = as.Date("2016-07-01"), 
             y = 3,
             size = 5,
             color = "red",
             label = str_glue("The downside risk skyrocketed 
                              towards the end of 2017"))