# 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 2017-12-31

1 Import stock prices

symbols <- c("TM", "SBUX", "AEO", "BBW")
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] "AEO"  "BBW"  "SBUX" "TM"
# weights
weights <- c(0.25, 0.25, 0.2, 0.3)
weights
## [1] 0.25 0.25 0.20 0.30
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 4 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AEO        0.25
## 2 BBW        0.25
## 3 SBUX       0.2 
## 4 TM         0.3

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  0.0298 
##  2 2013-02-28  0.0725 
##  3 2013-03-28  0.00594
##  4 2013-04-30  0.0452 
##  5 2013-05-31  0.0785 
##  6 2013-06-28 -0.0211 
##  7 2013-07-31  0.0777 
##  8 2013-08-30 -0.0772 
##  9 2013-09-30  0.0233 
## 10 2013-10-31  0.0687 
## # 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") %>%
    
    # 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       0.587

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")

How sensitive is your portfolio to the market? Discuss in terms of the beta coefficient. Does the plot confirm the beta coefficient you calculated?

This portfolio slightly sensitive to the market. The beta coefficient value of 0.587 means that the portfolio is expected to move only half as much as the overall market. The positive value means that portfolio returns increase as market returns increase. This also means that the portfolio is significantly less volatile than the market average.The slope of the plot is about 0.5 which is similar to the calculated beta coefficient value, the upward-slopping line confirms a positive beta coefficient.

The portfolio returns are very scattered far from the line, which suggest a weak correlation between the market and the portfolio. Therefore, there will be variation in portfolio returns and inconsistency in the relationship