# Load packages

# Core
library(tidyverse)
library(tidyquant)

Goal

Calculate and visualize your portfolio’s beta.

Choose your stocks and the baseline market.

from 2012-12-31 to present

1 Import stock prices

symbols <- c("AMZN", "AAPL", "TSLA", "NFLX", "GOOGL")

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 %>%

    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 <- asset_returns_tbl %>% distinct(asset) %>% pull
symbols
## [1] "AAPL"  "AMZN"  "GOOGL" "NFLX"  "TSLA"
weight <- c(0.25, 0.25, 0.2, 0.2, 0.1)
weight
## [1] 0.25 0.25 0.20 0.20 0.10
w_tbl <- tibble(symbols, weight)
w_tbl
## # A tibble: 5 × 2
##   symbols weight
##   <chr>    <dbl>
## 1 AAPL      0.25
## 2 AMZN      0.25
## 3 GOOGL     0.2 
## 4 NFLX      0.2 
## 5 TSLA      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",
                 col_rename = "returns")

portfolio_returns_tbl
## # A tibble: 60 × 2
##    date       returns
##    <date>       <dbl>
##  1 2013-01-31  0.115 
##  2 2013-02-28  0.0226
##  3 2013-03-28  0.0107
##  4 2013-04-30  0.0573
##  5 2013-05-31  0.0998
##  6 2013-06-28 -0.0261
##  7 2013-07-31  0.107 
##  8 2013-08-30  0.0462
##  9 2013-09-30  0.0585
## 10 2013-10-31  0.0830
## # ℹ 50 more rows

5 Calculate

market_returns_tbl <- tq_get(x = "SPY",
                 get = "stock.prices",
                 from = "2012-12-31",
                 to = "2017-12-31") %>%
    tq_transmute(select = adjusted,
                 mutate_fun = periodReturn,
                 period = "monthly",
                 type = "log", 
                 col_rename = "returns") %>%
    slice(-1)
market_returns_tbl
## # A tibble: 60 × 2
##    date       returns
##    <date>       <dbl>
##  1 2013-01-31  0.0499
##  2 2013-02-28  0.0127
##  3 2013-03-28  0.0373
##  4 2013-04-30  0.0190
##  5 2013-05-31  0.0233
##  6 2013-06-28 -0.0134
##  7 2013-07-31  0.0504
##  8 2013-08-30 -0.0305
##  9 2013-09-30  0.0312
## 10 2013-10-31  0.0453
## # ℹ 50 more rows
portfolio_market_returns_tbl <- left_join(market_returns_tbl, 
          portfolio_returns_tbl, 
          by = "date") %>%
    set_names("date",
              "market_returns",
              "portfolio_returns")
portfolio_market_returns_tbl
## # A tibble: 60 × 3
##    date       market_returns portfolio_returns
##    <date>              <dbl>             <dbl>
##  1 2013-01-31         0.0499            0.115 
##  2 2013-02-28         0.0127            0.0226
##  3 2013-03-28         0.0373            0.0107
##  4 2013-04-30         0.0190            0.0573
##  5 2013-05-31         0.0233            0.0998
##  6 2013-06-28        -0.0134           -0.0261
##  7 2013-07-31         0.0504            0.107 
##  8 2013-08-30        -0.0305            0.0462
##  9 2013-09-30         0.0312            0.0585
## 10 2013-10-31         0.0453            0.0830
## # ℹ 50 more rows
portfolio_market_returns_tbl %>%
    tq_performance(Ra = portfolio_returns,
                   Rb = market_returns, 
                   performance_fun = CAPM.beta)
## # A tibble: 1 × 1
##   CAPM.beta.1
##         <dbl>
## 1        1.16

6 Plot

portfolio_market_returns_tbl %>%
    ggplot(aes(x = market_returns, 
               y = portfolio_returns)) +
    geom_point(color = "cornflowerblue") + 
    geom_smooth(method = "lm", 
                se = FALSE, 
                linewidth = 1.5, 
                color = tidyquant::palette_light()[3]) +
labs(y = "Portfolio Returns", 
     x = "Market Returns")

actual_fitted_long_tbl <- portfolio_market_returns_tbl %>%
    
    #linear regression model
    lm(portfolio_returns ~ market_returns, data = .) %>%
    
    # get fitted and actual returns
    broom::augment() %>%
   
     # add date 
    mutate(date = portfolio_market_returns_tbl$date) %>%
    select(date, 
           portfolio_returns,
           .fitted) %>%
    
    # Transform data to long
    pivot_longer(cols = c(portfolio_returns, .fitted),
                 names_to = "type", 
                 values_to = "returns")

actual_fitted_long_tbl %>%
    ggplot(aes(x = date, y = returns, color = type)) +
    geom_line()

How sensitive is your portfolio to the market? Discuss in terms of the beta coefficient. Does the plot confirm the beta coefficient you calculated?

My portfolio is just as sensitive to market movements as the overall market. Its beta of 1.00 shows that it’s expected to move in the same direction and with the same volatility as the market. This is confirmed by the line’s 45-degree angle, which represents a slope (beta) of 1.0. Also all of the points on the graph seem to be pretty close to the line which shows us that the dots and the line have some correlation. The closer the dots are to the line the stronger the linear relationship.