# 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 ("DLR", "NVDA", "GOOG", "MSFT", "AMZN")

prices <- tq_get(x = symbols,
                 get = "stockprices",
                 from = "2012-12-31",
                 to = "2026-11-02")

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] "AMZN" "DLR"  "GOOG" "MSFT" "NVDA"
# 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 AMZN        0.2
## 2 DLR         0.2
## 3 GOOG        0.2
## 4 MSFT        0.2
## 5 NVDA        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 = "quarters",
               col_rename = "returns")

portfolio_returns_tbl
## # A tibble: 166 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.0301 
##  2 2013-02-28  0.0201 
##  3 2013-03-28  0.0101 
##  4 2013-04-30  0.0516 
##  5 2013-05-31  0.0164 
##  6 2013-06-28  0.00167
##  7 2013-07-31 -0.0124 
##  8 2013-08-30 -0.00816
##  9 2013-09-30  0.0336 
## 10 2013-10-31  0.0489 
## # ℹ 156 more rows

5 Calculate CAPM Beta

5.1 Get market returns

market_returns_tbl <- tq_get(x = "SPY",
                 get = "stockprices",
                 from = "2012-12-31",
                 to = "2017-12-31") %>%

  # Convert prices to returns
  tq_transmute(select = adjusted, 
               mutate_fun = periodReturn, 
               period = "monthly", 
               type = "log", 
               col_name = "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       0.861

6 Plot: Scatter with regression line

Scatterplot of returns 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")

Line plot of fitted vs actual 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 less sensitive to market movements, with a beta of 0.861. This means that my portfolio generally moves in the same direction as the market, but its returns are smaller on average. For example, if the market increases by 1%, my portfolio is expected to increase by approximately 0.861%. The scatterplot confirms this because the regression line has a positive slope, showing that the portfolio and market move in the same direction. Each dot represents one month’s returns, while the regression line shows the average relationship between market returns and portfolio returns. Since the dots are not all directly on the line, the portfolio does not move exactly according to the beta every month, but the overall relationship supports the calculated beta.