# 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("MSFT", "GOOGL", "AAPL", "NVDA", "META")
prices <- tq_get(x    = symbols,
                 get  = "stock.prices", 
                 from = "2012-12-31")

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"  "GOOGL" "META"  "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 AAPL        0.2
## 2 GOOGL       0.2
## 3 META        0.2
## 4 MSFT        0.2
## 5 NVDA        0.2

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: 155 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.0179 
##  2 2013-02-28 -0.00726
##  3 2013-03-28 -0.00542
##  4 2013-04-30  0.0673 
##  5 2013-05-31  0.0121 
##  6 2013-06-28 -0.0269 
##  7 2013-07-31  0.0957 
##  8 2013-08-30  0.0459 
##  9 2013-09-30  0.0516 
## 10 2013-10-31  0.0584 
## # ℹ 145 more rows

5 Calculate CAPM Beta

5.1 Get market returns

market_returns_tbl <- tq_get(x    = "SPY",
                 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       0.939

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") +
    # 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?

Answer: With a CAPM beta coefficient of 0.939, my portfolio is positively correlated with the market base-line and moves near perfectly in-sync with the S&P 500. For every 10% increase in the market, my portfolio responds with a 9.39% move in that same direction. Concerning the plotted regression line on the chart, it depicts a positive slope showing how my portfolio responds to the market base-line. Because all stocks in my portfolio exist in the S&P 500 as well, this correlation makes perfect sense. If the slope were negative, my portfolio would move against the market (negative correlation) given the CAPM beta coefficient was -0.939.