# 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("SPY", "EFA", "IJS", "EEM", "AGG")

prices <- tq_get(x    = symbols,
                 get  = "stock.prices",    
                 from = "2012-12-31",
                 to   = "2014-12-31")

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] "AGG" "EEM" "EFA" "IJS" "SPY"
# 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 AGG        0.25
## 2 EEM        0.25
## 3 EFA        0.2 
## 4 IJS        0.2 
## 5 SPY        0.1

4 Build a portfolio

# ?tq_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: 24 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.0204 
##  2 2013-02-28 -0.00239
##  3 2013-03-28  0.0121 
##  4 2013-04-30  0.0174 
##  5 2013-05-31 -0.0128 
##  6 2013-06-28 -0.0247 
##  7 2013-07-31  0.0321 
##  8 2013-08-30 -0.0224 
##  9 2013-09-30  0.0511 
## 10 2013-10-31  0.0301 
## # ℹ 14 more rows

5 Calculate CAPM Beta

5.1 Get market returns

# Get market returns
market_returns_tbl <- tq_get("SPY",
                             get = "stock.prices",
                             from = "2012-12-31",
                             to = "2014-12-31") %>%

    # Convert prices to returns
    tq_transmute(select     = adjusted, 
                 mutate_fun = periodReturn, 
                 period     = "monthly",
                 type       = "log", 
                 col_rename = "returns") %>%
    
    slice(-1)

5.2 Join returns

# Combine market returns with portfolio returns
portfolio_market_returns_tbl <- portfolio_returns_tbl %>%

    # Add market returns
    mutate(market_returns = market_returns_tbl %>% pull(returns))

5.3 CAPM Beta

# 3 Calculating CAPM Beta ----

# A complete list of functions for performance_fun()
# tq_performance_fun_options()

portfolio_market_returns_tbl %>%

    tq_performance(Ra = returns,
                   Rb = market_returns,
                   performance_fun = CAPM.beta)
## # A tibble: 1 × 1
##   CAPM.beta.1
##         <dbl>
## 1       0.827

6 Plot: Scatter with regression line

Scatter with regression line

# Figure 8.2 Scatter with regression line from ggplot ----

portfolio_market_returns_tbl %>%

    ggplot(aes(market_returns, returns)) +
    geom_point(color = "cornflowerblue") +

    geom_smooth(method = "lm", se = FALSE,
                size = 1.5, color = tidyquant::palette_light()[3]) +

    labs(x = "market returns",
         y = "portfolio returns")

Actual versus fitted returns

# Figure 8.5 Actual versus fitted returns ----

portfolio_market_returns_tbl %>%

    # Run regression
    lm(returns ~ market_returns, data = .) %>%

    # Get fitted
    broom::augment() %>%

    # Add date %>%
    mutate(date = portfolio_market_returns_tbl$date) %>%

    # Transform data to long format
    pivot_longer(cols = c(returns, .fitted),
                 names_to = "type",
                 values_to = "returns") %>%

    # Plot
    ggplot(aes(date, returns, color = type)) +
    geom_line()

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 data visualization supports the beta coefficient I calculated. First, the sign of beta (positive) is clearly confirmed by the upward-sloping regression line in the scatter plot. This means that when the market goes up, the portfolio tends to go up as well—and when the market goes down, the portfolio usually drops too. Second, the magnitude of beta (0.827) is also reflected in the visualization, as the slope is upward, but not extremely steep, which matches a beta below 1. This means the portfolio moves with the market, but with smaller swings than the market itself. Finally, the spread of the points around the line helps us see how strong the relationship is. Because the points are somewhat scattered—not tightly clustered—it shows that the portfolio doesn’t follow the market perfectly. In other words, while the market helps explain some of the portfolio’s movement, other factors also affect returns.