# Load packages

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

Goal

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

five stocks: “AAPL”, “TSLA”, “JPM”, “MSFT”, “NKE”

from 2012-12-31 to 2017-12-31

1 Import stock prices

symbols <- c("AAPL", "TSLA", "JPM", "MSFT", "NKE")

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] "AAPL" "JPM"  "MSFT" "NKE"  "TSLA"
# 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 AAPL       0.25
## 2 JPM        0.25
## 3 MSFT       0.2 
## 4 NKE        0.2 
## 5 TSLA       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  0.00469
##  2 2013-02-28  0.00240
##  3 2013-03-28  0.0234 
##  4 2013-04-30  0.0892 
##  5 2013-05-31  0.0983 
##  6 2013-06-28 -0.0261 
##  7 2013-07-31  0.0521 
##  8 2013-08-30  0.0299 
##  9 2013-09-30  0.0420 
## 10 2013-10-31  0.0260 
## # ℹ 50 more rows

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   -0.274

6 Plot

Histogram of Expected Returns & Risk

# Calculate sd and mean 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 AAPL      -0.555 
## 2 JPM       -0.330 
## 3 MSFT       0.0825
## 4 NKE        0.0783
## 5 TSLA       0.944 
## 6 Portfolio -0.274
# 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", x = "Asset")

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 Skwness")

Distribution of Monthly Returns

asset_returns_tbl %>%
    
    ggplot(aes(x = returns)) +
    geom_density(aes(color = asset), show.legend = FALSE, alpha = 1) +
    geom_histogram(aes(fill = asset), show.legend = FALSE, alpha = 0.4, binwidth = 0.02) +
    facet_wrap(~asset, ncol = 1) +
    
    # labeling
    labs(title = "Distribution of Monthly Returns, 2012-2017",
         y = "Frequency",
         x = "Rate of Returns")

Interpretation

Is any asset in your portfolio more likely to return extreme positive returns than your portfolio collectively?

yes there are three assets that are more likely to return extreme positives. These assets are TSLA, MSFT, and NKE. These three assets have positive skewness compared to the portfolio which has a negative skewness. TSLA is the most likely to return extreme positives because it has data with a 60% return in a month.