# Load packages

# Core
library(tidyverse)
library(tidyquant)

Goal

Visualize and compare skewness of your portfolio and its assets.

Choose your stocks.

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

1 Import stock prices

symbols <- c("TSLA", "GM", "F", "VWAGY", "HMC")
prices <- tq_get(x = symbols, 
                    from = "2012-12-31",
                    to = "2017-12-31")

2 Convert prices to returns (monthly)

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 (change the weigting scheme)

# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "F"     "GM"    "HMC"   "TSLA"  "VWAGY"
# weights
weight <- c(0.15, 0.25, 0.2, 0.3, 0.1)
weight
## [1] 0.15 0.25 0.20 0.30 0.10
w_tbl <- tibble(symbols, weight)
w_tbl
## # A tibble: 5 × 2
##   symbols weight
##   <chr>    <dbl>
## 1 F         0.15
## 2 GM        0.25
## 3 HMC       0.2 
## 4 TSLA      0.3 
## 5 VWAGY     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  0.0357
##  2 2013-02-28 -0.0476
##  3 2013-03-28  0.0340
##  4 2013-04-30  0.150 
##  5 2013-05-31  0.220 
##  6 2013-06-28  0.0120
##  7 2013-07-31  0.115 
##  8 2013-08-30  0.0404
##  9 2013-09-30  0.0750
## 10 2013-10-31 -0.0302
## # … with 50 more rows

5 Compute 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    0.362

6 Plot: Skewness Comparison

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 F         -0.224  
## 2 GM        -0.00490
## 3 HMC       -0.256  
## 4 TSLA       0.944  
## 5 VWAGY     -1.65   
## 6 Portfolio  0.362
# 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 = "cadetblue") + 
    
    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 = str_glue("The 24 month rolling skewness is positive for about half of the lifetime, 
             even though the overall skewness is negative"))
## mapping: x = ~x, y = ~y 
## geom_text: na.rm = FALSE
## stat_identity: na.rm = FALSE
## position_identity

Is any asset in your portfolio more likely to return extreme positive returns than your portfolio collectively? Discuss in terms of skewness. You may also refer to the distribution of returns you plotted in Code along 4.

TSLA is the only asset with positive skewness as it is above zero and the only asset above the portfolio. Although it is easy to assume that if there is positive skewness as is seen with TSLA, that it is more likely to return large gains. That is not always the case as we have to look at a distribution chart to see where the center of the graph is, as it could be a positive skew but to the left of 0, which does not necessarily mean that its likely going to return a large positive gain. When looking at the distribution chart of TSLA, the only asset with a positive skew above the portfolio, the highest bar is to the left of zero, with an occurance of twice. The rolling 24 month skewness had a positive skew until 2016, where it has remained in the negative. Positive skewness shows a likely large positive return, but with the rolling 24 month skewness being in the negative majority of the time, this portfolio may demonstrate the opposite.