# 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")
symbols
## [1] "SPY" "EFA" "IJS" "EEM" "AGG"
prices
## # A tibble: 6,300 × 8
##    symbol date        open  high   low close    volume adjusted
##    <chr>  <date>     <dbl> <dbl> <dbl> <dbl>     <dbl>    <dbl>
##  1 SPY    2012-12-31  140.  143.  140.  142. 243935200     114.
##  2 SPY    2013-01-02  145.  146.  145.  146. 192059000     117.
##  3 SPY    2013-01-03  146.  146.  145.  146. 144761800     117.
##  4 SPY    2013-01-04  146.  147.  146.  146. 116817700     117.
##  5 SPY    2013-01-07  146.  146.  145.  146. 110002500     117.
##  6 SPY    2013-01-08  146.  146.  145.  146. 121265100     117.
##  7 SPY    2013-01-09  146.  146.  146.  146.  90745600     117.
##  8 SPY    2013-01-10  147.  147.  146.  147. 130735400     118.
##  9 SPY    2013-01-11  147.  147.  147.  147. 113917300     118.
## 10 SPY    2013-01-14  147.  147.  146.  147.  89567200     118.
## # ℹ 6,290 more rows

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"))
asset_returns_tbl
## # A tibble: 300 × 3
##    asset date         returns
##    <chr> <date>         <dbl>
##  1 AGG   2013-01-31 -0.00623 
##  2 AGG   2013-02-28  0.00589 
##  3 AGG   2013-03-28  0.000985
##  4 AGG   2013-04-30  0.00964 
##  5 AGG   2013-05-31 -0.0202  
##  6 AGG   2013-06-28 -0.0158  
##  7 AGG   2013-07-31  0.00269 
##  8 AGG   2013-08-30 -0.00830 
##  9 AGG   2013-09-30  0.0111  
## 10 AGG   2013-10-31  0.00829 
## # ℹ 290 more rows

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

# 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 
## # ℹ 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   -0.168

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 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 -0.168
# 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", linewidth = 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 = "The 24 month rolling skewness is positive for about half of the lifetime,
             even theough the overall skewness is negative")