# 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("AMZN", "LLY", "KO", "GLD") 

prices <- tq_get(x = symbols,
                 get = "stock.prices",
                 from = "2012-12-31")
symbols
## [1] "AMZN" "LLY"  "KO"   "GLD"
prices
## # A tibble: 12,948 × 8
##    symbol date        open  high   low close   volume adjusted
##    <chr>  <date>     <dbl> <dbl> <dbl> <dbl>    <dbl>    <dbl>
##  1 AMZN   2012-12-31  12.2  12.6  12.1  12.5 68380000     12.5
##  2 AMZN   2013-01-02  12.8  12.9  12.7  12.9 65420000     12.9
##  3 AMZN   2013-01-03  12.9  13.0  12.8  12.9 55018000     12.9
##  4 AMZN   2013-01-04  12.9  13.0  12.8  13.0 37484000     13.0
##  5 AMZN   2013-01-07  13.1  13.5  13.1  13.4 98200000     13.4
##  6 AMZN   2013-01-08  13.4  13.4  13.2  13.3 60214000     13.3
##  7 AMZN   2013-01-09  13.4  13.5  13.3  13.3 45312000     13.3
##  8 AMZN   2013-01-10  13.4  13.4  13.1  13.3 57268000     13.3
##  9 AMZN   2013-01-11  13.3  13.4  13.2  13.4 48266000     13.4
## 10 AMZN   2013-01-14  13.4  13.7  13.4  13.6 85500000     13.6
## # ℹ 12,938 more rows

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: 620 × 3
##    asset date        returns
##    <chr> <date>        <dbl>
##  1 AMZN  2013-01-31  0.0567 
##  2 AMZN  2013-02-28 -0.00464
##  3 AMZN  2013-03-28  0.00837
##  4 AMZN  2013-04-30 -0.0488 
##  5 AMZN  2013-05-31  0.0589 
##  6 AMZN  2013-06-28  0.0311 
##  7 AMZN  2013-07-31  0.0813 
##  8 AMZN  2013-08-30 -0.0696 
##  9 AMZN  2013-09-30  0.107  
## 10 AMZN  2013-10-31  0.152  
## # ℹ 610 more rows

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

# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "AMZN" "GLD"  "KO"   "LLY"
# weights
weights <- c(0.2, 0.25, 0.35, 0.2)
weights
## [1] 0.20 0.25 0.35 0.20
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 4 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AMZN       0.2 
## 2 GLD        0.25
## 3 KO         0.35
## 4 LLY        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  0.0365 
##  2 2013-02-28  0.00507
##  3 2013-03-28  0.0294 
##  4 2013-04-30 -0.0185 
##  5 2013-05-31 -0.0306 
##  6 2013-06-28 -0.0354 
##  7 2013-07-31  0.0495 
##  8 2013-08-30 -0.0229 
##  9 2013-09-30  0.00467
## 10 2013-10-31  0.0428 
## # 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") %>%
    tq_transmute(select = adjusted,
                 mutate_fun = periodReturn,
                 period = "monthly",
                 type = "log", 
                 col_rename = "returns") %>%
    slice(-1)
market_returns_tbl
## # A tibble: 155 × 2
##    date       returns
##    <date>       <dbl>
##  1 2013-01-31  0.0499
##  2 2013-02-28  0.0127
##  3 2013-03-28  0.0373
##  4 2013-04-30  0.0190
##  5 2013-05-31  0.0233
##  6 2013-06-28 -0.0134
##  7 2013-07-31  0.0504
##  8 2013-08-30 -0.0305
##  9 2013-09-30  0.0312
## 10 2013-10-31  0.0453
## # ℹ 145 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")
portfolio_market_returns_tbl
## # A tibble: 155 × 3
##    date       market_returns portfolio_returns
##    <date>              <dbl>             <dbl>
##  1 2013-01-31         0.0499           0.0365 
##  2 2013-02-28         0.0127           0.00507
##  3 2013-03-28         0.0373           0.0294 
##  4 2013-04-30         0.0190          -0.0185 
##  5 2013-05-31         0.0233          -0.0306 
##  6 2013-06-28        -0.0134          -0.0354 
##  7 2013-07-31         0.0504           0.0495 
##  8 2013-08-30        -0.0305          -0.0229 
##  9 2013-09-30         0.0312           0.00467
## 10 2013-10-31         0.0453           0.0428 
## # ℹ 145 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       0.526

6 Plot: Scatter with regression line

portfolio_market_returns_tbl %>%
    ggplot(aes(x = market_returns, 
               y = portfolio_returns)) +
    geom_point(color = "red") + 
    geom_smooth(method = "lm", 
                se = FALSE, 
                linewidth = 1.5, 
                color = "green") +
labs(y = "Portfolio Returns", 
     x = "Market Returns") +
    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? The portfolio beta of 0.5 indicates that the portfolio is half as volatile as the market which in this case is SPY. This means the portfolio is less sensitive to market swings and is less risky compared to the market benchmark. The plot shows slightly more positive returns for the portfolio than the market. The magnitude of the beta coefficient is confirmed by the visualization because it is flatter than a 45 degree angle. The points are fairly spread out from the regression line with outliers meaning that the regression line is mostly inaccurate.