# Load packages

# Core
library(tidyverse)
library(tidyquant)

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,
                  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
symbol <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "SPY" "EFA" "IJS" "EEM" "AGG"
# 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 SPY        0.25
## 2 EFA        0.25
## 3 IJS        0.2 
## 4 EEM        0.2 
## 5 AGG        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  0.0308  
##  2 2013-02-28 -0.000870
##  3 2013-03-28  0.0187  
##  4 2013-04-30  0.0206  
##  5 2013-05-31 -0.00535 
##  6 2013-06-28 -0.0229  
##  7 2013-07-31  0.0412  
##  8 2013-08-30 -0.0255  
##  9 2013-09-30  0.0544  
## 10 2013-10-31  0.0352  
## # … with 50 more rows

5 Calculate Standard Deviation

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   -0.230

6 Plot

Histogram of Expected Returns and 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 of 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 -0.230
# 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"), 
             color = "red", 
             size = 4,
             y = 0.8, 
             label = str_glue("The 24-Month Skewness is positive for about half of the lifetime, 
                              even though the overall skewness is negative."))