# Load packages

# Core
library(tidyverse)
library(tidyquant)

Goal

Visualize and compare skewness of your portfolio and its assets.

Choose your stocks.

from 2012-12-31 to 2017-12-31

1 Import stock prices

symbols <- c("NKE", "ADDYY", "SKX", "UAA")

prices <- tq_get(x    = symbols, 
                 get  = "stock.prices",
                 from = "2012-12-31",
                 to   = "2017-12-31")

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
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "ADDYY" "NKE"   "SKX"   "UAA"
# weights
weights <- c(0.4, 0.2, 0.25, 0.15)
weights
## [1] 0.40 0.20 0.25 0.15
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 4 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 ADDYY      0.4 
## 2 NKE        0.2 
## 3 SKX        0.25
## 4 UAA        0.15

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  0.0150
##  3 2013-03-28  0.0760
##  4 2013-04-30  0.0284
##  5 2013-05-31  0.0519
##  6 2013-06-28  0.0120
##  7 2013-07-31  0.0604
##  8 2013-08-30  0.0204
##  9 2013-09-30  0.0542
## 10 2013-10-31  0.0157
## # ℹ 50 more rows

5 Compute Skewness

# Transform data: calculate rolling skewness
rolling_skew_tbl <- portfolio_returns_tbl %>%
    
    tq_mutate(select     = returns,
              mutate_fun = rollapply,
              width      = 24,
              FUN        = skewness,
              col_rename = "Skew") %>%
    
    select(-returns) %>%
    na.omit()

6 Plot: Skewness Comparison

# Plot
rolling_skew_tbl %>%
    
    ggplot(aes(x = date, y = Skew)) +
    geom_line(color = "cornflowerblue") +
    
    geom_hline(yintercept = 0, linetype = "dotted", size = 2) +
    
    # Formatting
    scale_y_continuous(limits = c(-1,1), breaks = seq(-1,1,0.2)) +
    theme(plot.title = element_text(hjust = 0.5)) +
    
    # Labeling
    labs(y = "Skewness",
         x = NULL,
         title = "Skewness Comparison") +
    
    annotate(geom = "text",
             x = as.Date("2016-07-01"), y = 0.8,
             color = "red", size = 5,
             label = str_glue("The 24 month rolling skewness is positive for some time peaking in 2017, 
                              even though the overall skewness is negative"))

Is any asset in your portfolio more likely to return extreme positive returns than your portfolio collectively? Discuss in terms of skewness. You may also refer to the distribution of returns you plotted in Code along 4.

Yes, UAA is more likely to return extreme positive returns than the portfolio collectively. It has the highest positive skewness at 0.666, indicating a strong right tail — meaning that while most of its returns are modest, there’s a significant chance for unusually large positive returns.

In contrast, the portfolio’s skewness is mostly negative or near zero, based on the plot, meaning it’s less likely to deliver extreme positive outcomes due to diversification smoothing out those spikes.