# Load packages

# Core
library(tidyverse)
library(tidyquant)
library(PerformanceAnalytics)
library(ggrepel)

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("NDAQ", "TSLA", "AAPL", "MSFT", "JPM")

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" "JPM"  "MSFT" "NDAQ" "TSLA"
# weights
weights <- c(0.25, 0.25, 0.2, 0.2, 0.1)
weights
## [1] 0.25 0.25 0.20 0.20 0.10
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 5 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AAPL       0.25
## 2 JPM        0.25
## 3 MSFT       0.2 
## 4 NDAQ       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  0.0204
##  2 2013-02-28  0.0224
##  3 2013-03-28  0.0121
##  4 2013-04-30  0.0560
##  5 2013-05-31  0.117 
##  6 2013-06-28 -0.0235
##  7 2013-07-31  0.0521
##  8 2013-08-30  0.0133
##  9 2013-09-30  0.0284
## 10 2013-10-31  0.0372
## # ℹ 50 more rows

5 Calculate CAPM Beta

5.1 Get market returns

market_returns_tbl <- tq_get(x    = "NDAQ",
       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)

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       0.260

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, 
                linewidth = 1.5, color = tidyquant::palette_light()[3]) +
    
    labs(y = "Portfolio Returns",
         x = "Market Returns") +
    
    coord_cartesian(xlim = c(0,0.12), ylim = c(0,0.12))

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 on the graph is positive which is confirmed in the calculation. The actual beta is 0.260. This is a small beta meaning the portfolio is much less volatile than the market. This makes the portfolio much less risky, but with a lot less reward as well. There is also not a strong linear relationship between the market and the portfolio which is represented by the dots on the scatter plot being far away from the line.