# 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

# Choose stocks

symbols <- c("AAPL", "DIS", "NKE", "GE", "SBUX")

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 %>%

    # Calculate monthly returns
    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" "DIS"  "GE"   "NKE"  "SBUX"
# weight
weights <- c(0.25, 
             0.25, 
             0.20, 
             0.20, 
             0.10)
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 DIS        0.25
## 3 GE         0.2 
## 4 NKE        0.2 
## 5 SBUX       0.1

4 Build a portfolio

portfolio_returns_rebalanced_monthly_tbl <- asset_returns_tbl %>%

    tq_portfolio(assets_col = asset,
                 returns_col = returns,
                 weigh = w_tbl,
                 rebalance_on = "months",
                 col_rename = "returns")

portfolio_returns_rebalanced_monthly_tbl
## # A tibble: 60 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.00658
##  2 2013-02-28  0.00714
##  3 2013-03-28  0.0296 
##  4 2013-04-30  0.0396 
##  5 2013-05-31  0.0141 
##  6 2013-06-28 -0.0206 
##  7 2013-07-31  0.0549 
##  8 2013-08-30 -0.00593
##  9 2013-09-30  0.0549 
## 10 2013-10-31  0.0700 
## # ℹ 50 more rows

5 Calculate Standard Deviation

portfolio_skew_tidyquant_builtin_percent <- portfolio_returns_rebalanced_monthly_tbl %>%

    tq_performance(Ra = returns,
                   Rb = NULL, 
                   performance_fun = table.Stats) %>%

    select(Skewness)

portfolio_skew_tidyquant_builtin_percent
## # A tibble: 1 × 1
##   Skewness
##      <dbl>
## 1   -0.281

6 Plot

Histogram of Expected Returns and Risk

# calculate sd of porfolio returns
sd_portfolio <- sd(portfolio_returns_rebalanced_monthly_tbl$returns)
mean_portfolio <- mean(portfolio_returns_rebalanced_monthly_tbl$returns)

portfolio_returns_rebalanced_monthly_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_rebalanced_monthly_tbl$returns)))

asset_skewness_tbl
## # A tibble: 6 × 2
##   asset        skew
##   <chr>       <dbl>
## 1 AAPL      -0.555 
## 2 DIS       -0.502 
## 3 GE        -0.333 
## 4 NKE        0.0783
## 5 SBUX      -0.320 
## 6 portfolio -0.281
# 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

rolling_skew_tbl <- portfolio_returns_rebalanced_monthly_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" ))