# Load packages

# Core
library(tidyverse)
library(tidyquant)
library(scales)
library(ggrepel)

Goal

Collect individual returns into a portfolio by assigning a weight to each stock

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 <- 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 Skewness

portfolio_skew_tidyquant_builtin_percent <- portfolio_returns_tbl %>%
    
    tq_performance(Ra = returns, 
                   performance_fun = table.Stats) %>%
    select(Skewness) 

portfolio_skew_tidyquant_builtin_percent
## # A tibble: 1 × 1
##   Skewness
##      <dbl>
## 1   -0.168

6 Plot

Histogram Expected Returns and Risks

# Calculate the standard deviation
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 = .003) + 
    scale_x_continuous(breaks = seq(-.06, .06, .02)) + 
    labs(x = "monthly returns")

Scatterplot of Skewness comparison

# Data Transformation Calculate Skewness
asset_skewness_tbl <- asset_returns_tbl %>%
    
    group_by(asset)%>%
    
    summarise(skew = skewness(returns)) %>%
    ungroup() %>%
    
    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")

Plot 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 = "blue") +
    geom_hline(yintercept = 0, linetype = "dotted", size = 2 ) +
    
    #formatting 
    scale_y_continuous(limits = c(-1, 1), breaks = seq(-1, 1, .2)) +
    theme(plot.title = element_text(hjust = .5)) + 
    
    #Labeling 
    labs(y = "skewness",
         x = NULL,
         title = "Rolling 24-month skewness") +
    annotate(geom  = "text", 
             x     = as.Date("2016-07-01"),
             y     = .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 skewnesss is negative"))