# 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("TM", "SBUX", "AEO", "BBW")
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 = "quarterly", 
                 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] "AEO"  "BBW"  "SBUX" "TM"
# weights
weights <- c(0.25, 0.25, 0.2, 0.1)
weights
## [1] 0.25 0.25 0.20 0.10
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 4 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AEO        0.25
## 2 BBW        0.25
## 3 SBUX       0.2 
## 4 TM         0.1

4 Build a portfolio

portfolio_returns_tbl <- asset_returns_tbl %>%
    tq_portfolio(assets_col = asset, 
                 returns_col = returns,
                 weights = w_tbl, 
                 rebalance_on = "months")

portfolio_returns_tbl
## # A tibble: 20 × 2
##    date       portfolio.returns
##    <date>                 <dbl>
##  1 2013-03-28           0.0866 
##  2 2013-06-28           0.0703 
##  3 2013-09-30           0.0102 
##  4 2013-12-31           0.0285 
##  5 2014-03-31           0.00443
##  6 2014-06-30           0.0800 
##  7 2014-09-30           0.0562 
##  8 2014-12-31           0.123  
##  9 2015-03-31           0.0879 
## 10 2015-06-30          -0.0266 
## 11 2015-09-30           0.0197 
## 12 2015-12-31          -0.0902 
## 13 2016-03-31           0.0199 
## 14 2016-06-30          -0.0155 
## 15 2016-09-30          -0.0277 
## 16 2016-12-30           0.0406 
## 17 2017-03-31          -0.126  
## 18 2017-06-30           0.00307
## 19 2017-09-29           0.00925
## 20 2017-12-29           0.0948

5 Compute Standard Deviation

portfolio_sd_tidyquant_builtin_percent <- portfolio_returns_tbl %>%
    
    tq_performance(Ra = portfolio.returns, performance_fun = table.Stats) %>%
    
    select(Stdev) %>%
    mutate(tq_sd = round(Stdev, 4))

portfolio_sd_tidyquant_builtin_percent
## # A tibble: 1 × 2
##   Stdev tq_sd
##   <dbl> <dbl>
## 1 0.062 0.062
# Mean of portfolio returns
portfolio_mean_tidyquant_builtin_percent <- mean(portfolio_returns_tbl$portfolio.returns)

portfolio_mean_tidyquant_builtin_percent
## [1] 0.0223788

6 Plot: Expected Returns versus Risk

Expected Returns vs Risk

sd_mean_tbl <- asset_returns_tbl %>%
    
    group_by(asset) %>%
    
    tq_performance(Ra = returns, 
               performance_fun = table.Stats) %>%
    
    select(Mean = ArithmeticMean, Stdev) %>%
    ungroup() %>%
    
    # Add portfolio sd
    add_row(tibble(asset = "Portfolio", 
                   Mean = portfolio_mean_tidyquant_builtin_percent, 
                   Stdev = portfolio_sd_tidyquant_builtin_percent$tq_sd))

sd_mean_tbl
## # A tibble: 5 × 3
##   asset       Mean  Stdev
##   <chr>      <dbl>  <dbl>
## 1 AEO       0.0037 0.148 
## 2 BBW       0.0439 0.243 
## 3 SBUX      0.0418 0.0713
## 4 TM        0.0211 0.0902
## 5 Portfolio 0.0224 0.062
sd_mean_tbl %>%
    
    ggplot(aes(x = Stdev, y = Mean, color = asset)) +
    geom_point() +
    ggrepel::geom_text_repel(aes(label = asset))

12 Months Rolling Volatility

rolling_sd_tbl <- portfolio_returns_tbl %>%
    
    tq_mutate(select = portfolio.returns, 
              mutate_fun = rollapply,
              width = 12,
              FUN = sd, 
              col_rename = "rolling_sd") %>%
    
    na.omit() %>% 
    select(date, rolling_sd)

rolling_sd_tbl
## # A tibble: 9 × 2
##   date       rolling_sd
##   <date>          <dbl>
## 1 2015-12-31     0.0588
## 2 2016-03-31     0.0569
## 3 2016-06-30     0.0570
## 4 2016-09-30     0.0589
## 5 2016-12-30     0.0592
## 6 2017-03-31     0.0732
## 7 2017-06-30     0.0700
## 8 2017-09-29     0.0681
## 9 2017-12-29     0.0640
rolling_sd_tbl %>%
    
    ggplot(aes(x = date, y = rolling_sd)) +
    geom_line(color = "cornflowerblue") +
    
    # Formatting 
    scale_y_continuous(labels = scales::percent_format()) +
    
    # Labeling 
    labs(x = NULL, 
         y = NULL, 
         title = "12-Months Rolling Volatility") +
    theme(plot.title = element_text(hjust = 0.5))

How should you expect your portfolio to perform relative to its assets in the portfolio? Would you invest all your money in any of the individual stocks instead of the portfolio? Discuss both in terms of expected return and risk.

My portfolio has a much lower risk than all of its assets, and it is in the middle in terms of returns. TM and AEO have lower returns than portfolio and SBUX and BBW have higher returns. I would invest in SBUX instead of the portfolio because it has similar risk but a much higher return.