# Load packages

# Core
library(tidyverse)
library(tidyquant)

Goal

Visualize expected returns and risk to make it easier to compare the performance of multiple assets and portfolios.

Choose your stocks.

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

1 Import stock prices

symbols <- c("LULU", "NKE", "UA") 
prices <- tq_get(x    = symbols, 
                 get = "stock.prices",
                 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] "LULU" "NKE"  "UA"
# weights
weights <- c(0.6, 0.3, 0.6)
weights
## [1] 0.6 0.3 0.6
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 3 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 LULU        0.6
## 2 NKE         0.3
## 3 UA          0.6

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 -0.0459 
##  2 2013-02-28 -0.0138 
##  3 2013-03-28 -0.0195 
##  4 2013-04-30  0.142  
##  5 2013-05-31  0.00481
##  6 2013-06-28 -0.0937 
##  7 2013-07-31  0.0326 
##  8 2013-08-30  0.0114 
##  9 2013-09-30  0.0627 
## 10 2013-10-31 -0.0215 
## # ℹ 50 more rows

5 Compute 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   -0.161

6 Plot

Histogram of Expected Returns vs 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: 4 × 2
##   asset        skew
##   <chr>       <dbl>
## 1 LULU      -0.345 
## 2 NKE        0.0783
## 3 UA        -0.621 
## 4 Portfolio -0.161
#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_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"), y =0.8,
             color = "red", size = 4,
             label = str_glue("The 24 month rolling skewness is positive for about half of the lifetime, 
                              even though the overall skewness is negative"))

Nike is the only stock that has positive skewness and is above the portfolio in this plot. However, the results from code along 4 do not indicate that Nike will have extreme positive returns compared to the overall portfolio.