# 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("TSLA", "AMZN", "AAPL", "NVDA", "PG")

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] "AAPL" "AMZN" "NVDA" "PG"   "TSLA"
# weights
weights <- c(0.2, 0.2, 0.2, 0.2, 0.2)
weights
## [1] 0.2 0.2 0.2 0.2 0.2
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 5 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AAPL        0.2
## 2 AMZN        0.2
## 3 NVDA        0.2
## 4 PG          0.2
## 5 TSLA        0.2

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: 60 × 2
##    date       portfolio.returns
##    <date>                 <dbl>
##  1 2013-01-31           0.0226 
##  2 2013-02-28          -0.0105 
##  3 2013-03-28           0.0240 
##  4 2013-04-30           0.0760 
##  5 2013-05-31           0.146  
##  6 2013-06-28          -0.00567
##  7 2013-07-31           0.103  
##  8 2013-08-30           0.0473 
##  9 2013-09-30           0.0486 
## 10 2013-10-31           0.0208 
## # ℹ 50 more rows

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 0.0477 0.0477
# Mean of portfolio returns
portfolio_mean_tidyquant_builtin_percent <- mean(portfolio_returns_tbl$portfolio.returns)

portfolio_mean_tidyquant_builtin_percent
## [1] 0.02648772

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 Standard Deviation
    add_row(tibble(asset = "Portfolio",
                   Mean  = portfolio_mean_tidyquant_builtin_percent, 
                   Stdev = portfolio_sd_tidyquant_builtin_percent$tq_sd))

sd_mean_tbl
## # A tibble: 6 × 3
##   asset       Mean  Stdev
##   <chr>      <dbl>  <dbl>
## 1 AAPL      0.015  0.0695
## 2 AMZN      0.0257 0.0739
## 3 NVDA      0.0471 0.0881
## 4 PG        0.0077 0.0372
## 5 TSLA      0.037  0.145 
## 6 Portfolio 0.0265 0.0477
sd_mean_tbl %>%
    
    ggplot(aes(x = Stdev, y = Mean, color = asset)) +
    geom_point() + 
    ggrepel::geom_text_repel(aes(label = asset))

24 Months Rolling volatility

rolling_sd_tbl <- portfolio_returns_tbl %>%
    
    tq_mutate(select     = portfolio.returns,
              mutate_fun = rollapply,
              width      = 24, 
              FUN        = sd, 
              col_rename = "rolling_sd") %>%
    
    na.omit() %>%
    select(date, rolling_sd)

rolling_sd_tbl
## # A tibble: 37 × 2
##    date       rolling_sd
##    <date>          <dbl>
##  1 2014-12-31     0.0529
##  2 2015-01-30     0.0532
##  3 2015-02-27     0.0531
##  4 2015-03-31     0.0552
##  5 2015-04-30     0.0550
##  6 2015-05-29     0.0488
##  7 2015-06-30     0.0490
##  8 2015-07-31     0.0459
##  9 2015-08-31     0.0465
## 10 2015-09-30     0.0460
## # ℹ 27 more rows
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 = "24-Month Rolling Volatility") + 
    theme(plot.title = element_text(hjust = 0.5))

Question:

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.

Answer:

The diversified portfolio should deliver steadier returns with lower risk than any single stock because diversification smooths the ride. I wouldn’t put all my money in one stock like TSLA or NVDA since their risk is much higher. The portfolio offers a solid expected return for much less volatility, which is the safer choice.