# 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 ("GS", "NVDA", "MS", "JPM", "BAC")

prices <- tq_get(x = symbols,
                 get = "stockprices",
                 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] "BAC"  "GS"   "JPM"  "MS"   "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 BAC         0.2
## 2 GS          0.2
## 3 JPM         0.2
## 4 MS          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: 60 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.0750 
##  2 2013-02-28  0.0147 
##  3 2013-03-28  0.00152
##  4 2013-04-30  0.0245 
##  5 2013-05-31  0.105  
##  6 2013-06-28 -0.0500 
##  7 2013-07-31  0.0814 
##  8 2013-08-30 -0.0468 
##  9 2013-09-30  0.0273 
## 10 2013-10-31  0.0150 
## # ℹ 50 more rows

5 Calculate CAPM Beta

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)

5.1 Get market returns

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

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        1.37

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")

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 has a beta of 1.37, which means it is 37% more sensitive to market movements than the overall market (S&P 500). If the market increases by 1%, my portfolio would be expected to increase by approximately 1.37%. However, if the market decreases by 1%, my portfolio would also be expected to decrease by approximately 1.37%.

The scatter plot confirms this result because it shows a positive relationship between market returns and portfolio returns. The upward-sloping regression line indicates that my portfolio generally moves in the same direction as the market. Overall, my portfolio has higher systematic risk than the market because its beta is greater than 1.