# 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("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

#?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  0.0226 
##  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 Calculate CAPM Beta

5.1 Get market returns

market_returns_tbl <- tq_get(x    = "^IXIC", 
                 get. = "stock.prices",
                 from = "2012-12-31", 
                 to   = Sys.Date()) %>%
    
    # Convert prices to returns
    tq_transmute(select     = adjusted, 
                 mutate_fun = periodReturn, 
                 period     = "monthly", 
                 type       = "log", 
                 col_rename = "returns") %>%
    
    slice(-1)

5.2 Join returns

portfolio_market_returns_tbl <- left_join(market_returns_tbl,
                                  portfolio_returns_tbl, 
                                  by = "date") %>%
    
    set_names("date", "market_returns", "portfolio_returns")

5.3 CAPM Beta

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        1.08

6 Plot: Scatter with regression line

portfolio_market_returns_tbl %>%
    
    ggplot(aes(x = market_returns, 
               y = portfolio_returns)) +
    geom_point(color = "cornflowerblue") +
    geom_smooth(method = "lm", se = FALSE, 
                size = 1.5, color = tidyquant::palette_light()[3]) +
    
    labs(y = "Portfolio Returns",
         x = "Market Returns") +
    
    # To set the limits (zoom window) for both the X and Y axes, 
    # forcing the plot to display only the range from 0 to 0.1 (or 0% to 10%) on both axes
    coord_cartesian(xlim = c(0,0.1), ylim = c(0,0.1))

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

The beta coefficient of 1.08 indicates that the portfolio is slightly more volatile than the overall market. In other words, for every 1% change in the market’s return, the portfolio’s return is expected to change by approximately 1.08%. This means the portfolio tends to amplify market movements, performing a bit better than the market in up periods and slightly worse in down periods.

The scatter plot supports this result. The positively sloped regression line shows a strong linear relationship between portfolio and market returns, with the points generally clustered around the line. The slope being greater than 1 visually confirms that the portfolio moves more aggressively than the market, consistent with the calculated beta of 1.08.