# 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, 
                 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

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 
## # ℹ 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 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 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(-.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 -0.168
# 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")
## $y
## [1] "Skewness"
## 
## attr(,"class")
## [1] "labels"

Rolling Skewness

# Transforming 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()
    
rolling_skew_tbl
## # A tibble: 37 × 2
##    date         Skew
##    <date>      <dbl>
##  1 2014-12-31 -0.402
##  2 2015-01-30 -0.264
##  3 2015-02-27 -0.335
##  4 2015-03-31 -0.247
##  5 2015-04-30 -0.255
##  6 2015-05-29 -0.271
##  7 2015-06-30 -0.272
##  8 2015-07-31 -0.122
##  9 2015-08-31 -0.398
## 10 2015-09-30 -0.477
## # ℹ 27 more rows
# Plot
rolling_skew_tbl %>% 
    
    ggplot(aes(x = date, y = Skew)) +
    geom_line(color = "steelblue2") +
    
    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)) + 
    
    # Labelling 
    labs(y = "Skewness", 
         title = "Rolling 24-Months Skewness") + 
        
    annotate(geom = "text", 
             x = as.Date("2016-07-01"), y = 0.8, 
             color = "tomato", 
             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"))