# Load packages

# Core
library(tidyverse)
library(tidyquant)
library(scales)
library(ggrepel)
library(broom)

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("AMGN", "T", "BA", "CAT", "IBM")
prices <- tq_get(x    = symbols, 
                 get = "stock.prices",
                 from = "2012-12-31",
                 to   = "2022-11-03")

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 <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "AMGN" "BA"   "CAT"  "IBM"  "T"
#Weights
weights <- c(0.21, 0.24, 0.15, 0.30, 0.1)
weights
## [1] 0.21 0.24 0.15 0.30 0.10
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 5 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AMGN       0.21
## 2 BA         0.24
## 3 CAT        0.15
## 4 IBM        0.3 
## 5 T          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: 119 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.0298 
##  2 2013-02-28  0.0184 
##  3 2013-03-28  0.0614 
##  4 2013-04-30  0.00358
##  5 2013-05-31  0.0184 
##  6 2013-06-28 -0.0260 
##  7 2013-07-31  0.0349 
##  8 2013-08-30 -0.0231 
##  9 2013-09-30  0.0414 
## 10 2013-10-31  0.0327 
## # … with 109 more rows

5 Calculate CAPM Beta

5.1 Get Market Returns

market_returns_tbl <- tq_get(x    = "DIA", 
                 get = "stock.prices",
                 from = "2012-12-31",
                 to   = "2017-12-31") %>%
    # Convert Prices to monthly returns
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  0.0593
##  2 2013-02-28  0.0160
##  3 2013-03-28  0.0374
##  4 2013-04-30  0.0194
##  5 2013-05-31  0.0234
##  6 2013-06-28 -0.0150
##  7 2013-07-31  0.0428
##  8 2013-08-30 -0.0437
##  9 2013-09-30  0.0230
## 10 2013-10-31  0.0291
## # … with 50 more rows

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")

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        1.01

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 is about in line with the variability of the market. It experiences almost the exact same volatility as the market. It tends to trend with the market. Having a beta of almost exactly one means that the portfolio is really close to being in line with the market risk.

Yes the plot confirms that there is a high correlation, and strong linear relationship between market volatility and the portfolio’s volatility. This supports the calculation ob beta being 1.01