# 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("WMT", "TGT", "COST")

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"))

asset_returns_tbl
## # A tibble: 180 × 3
##    asset date        returns
##    <chr> <date>        <dbl>
##  1 COST  2013-01-31  0.0359 
##  2 COST  2013-02-28 -0.00765
##  3 COST  2013-03-28  0.0465 
##  4 COST  2013-04-30  0.0216 
##  5 COST  2013-05-31  0.0138 
##  6 COST  2013-06-28  0.00854
##  7 COST  2013-07-31  0.0601 
##  8 COST  2013-08-30 -0.0458 
##  9 COST  2013-09-30  0.0291 
## 10 COST  2013-10-31  0.0243 
## # ℹ 170 more rows

3 Assign a weight to each asset (change the weigting scheme)

symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "COST" "TGT"  "WMT"
weights <- c(0.35, 0.3, 0.25)
weights
## [1] 0.35 0.30 0.25
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 3 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 COST       0.35
## 2 TGT        0.3 
## 3 WMT        0.25

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  0.0250  
##  2 2013-02-28  0.0144  
##  3 2013-03-28  0.0569  
##  4 2013-04-30  0.0262  
##  5 2013-05-31 -0.00611 
##  6 2013-06-28 -0.000959
##  7 2013-07-31  0.0426  
##  8 2013-08-30 -0.0645  
##  9 2013-09-30  0.0167  
## 10 2013-10-31  0.0215  
## # ℹ 50 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") %>%
    
     tq_transmute(select     = adjusted, 
                 mutate_fun = periodReturn, 
                 period     = "monthly",
                 type       = "log") %>%
    
    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")

portfolio_market_returns_tbl
## # A tibble: 60 × 3
##    date       market_returns portfolio_returns
##    <date>              <dbl>             <dbl>
##  1 2013-01-31         0.0499          0.0250  
##  2 2013-02-28         0.0127          0.0144  
##  3 2013-03-28         0.0373          0.0569  
##  4 2013-04-30         0.0190          0.0262  
##  5 2013-05-31         0.0233         -0.00611 
##  6 2013-06-28        -0.0134         -0.000959
##  7 2013-07-31         0.0504          0.0426  
##  8 2013-08-30        -0.0305         -0.0645  
##  9 2013-09-30         0.0312          0.0167  
## 10 2013-10-31         0.0453          0.0215  
## # ℹ 50 more rows

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       0.626

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?

For my portfolio, the beta coefficient is .626. Since the coefficient is less than one, it means that it is not as volatile as the market. This means that if the market drops, this porfolio will drop at a 63% rate while if it rose, it would rise at a 63% rate. This also means that it is more prodictible within the market than one would be if it had a coefficient of more than 1. 
The plot does confirm the coffient that was calculated because although it is not directly on the line, it would be expected to be semi distance due to the 63% rate. For the outliers within this profolio, it still makes sense because its only an outlier by around 0.05. As for the linear relationship, it is not exetremely strong but it is also not weak by any means. There definitely is a relationship it just isn't extremely strong. The plot is also moving in a postive, increased direction which makes sense as the coefficent is positive.