# 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

# Choose stocks

symbols <- c("SPY", "EFA", "IJS", "EEM", "AGG")

# Using tq_get() ----
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 %>%
  
  # Calculate monthly returns
  group_by(symbol) %>%
  tq_transmute(select     = adjusted,
               mutate_fun = periodReturn,
               period     = "monthly",
               type       = "log") %>%
  slice (-1) %>%
  ungroup() %>%
  
  # rename
  set_names(c("asset", "date", "returns"))

# period_returns = c("yearly", "quarterly", "monthly", "weekly")

3 Assign a weight to each asset

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

w <- c(0.25,
       0.25,
       0.20,
       0.20,
       0.10)

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: 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 
## # ℹ 50 more rows

5 Calculate Skewness

portfolio_returns_tbl %>%
  
  tq_performance(Ra = returns,
                 Rb = NULL,
                 performance_fun = table.Stats) %>%
  select(Skewness)
## # A tibble: 1 × 1
##   Skewness
##      <dbl>
## 1   -0.168

6 Plot

Histogram of Expected Returns vs Risk

# Calculate sd of portfolio returns
sd_portfolio <- sd(portfolio_returns_tbl$returns)
mean_portfolio <- mean(portfolio_returns_tbl$returns)

portfolio_returns_tbl %>%
  
  # Add a new variable
  mutate(extreme_neg = ifelse(returns < mean_portfolio - 2 * sd_portfolio,
                                       "ext_neg",
                                       "not_ext_neg")) %>%

  ggplot(aes(x = returns, fill = extreme_neg)) +
  geom_histogram(binwidth = 0.003) +
  
  scale_x_continuous(breaks = seq(-0.06, 0.06, 0.02)) +
  
  labs(x = "monthly returns")

Scatterplot for Skewness Comparison

# Data transformation: calculate skewness
asset_skewness_tbl <- asset_returns_tbl %>%
  
  group_by(asset) %>%
  summarise(skew = skewness(returns)) %>%
  ungroup() %>%
  
  # Add portfolio skewness
  add_row(tibble(asset = "Portfolio",
                 skew = skewness(portfolio_returns_tbl$returns)))

asset_skewness_tbl
## # A tibble: 6 × 2
##   asset        skew
##   <chr>       <dbl>
## 1 AGG       -0.599 
## 2 EEM       -0.0512
## 3 EFA       -0.142 
## 4 IJS        0.216 
## 5 SPY       -0.264 
## 6 Portfolio -0.168
# Plot skewness
asset_skewness_tbl %>%
  
  ggplot(aes(x = asset, y = skew, color = asset)) +
  geom_point() +
  
  ggrepel::geom_text_repel(aes(label = asset),
                           data = asset_skewness_tbl %>%
                             filter(asset == "Portfolio")) +
  labs(y = "skewness")

Rolling 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()

# 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 = "Rolling 24-month Skewness") +
  
  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 about half of the lifetime, 
                            even though the overall skewness is negative"))