# 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("JPM", "NVDA", "LLY", "AMZN")

prices <- tq_get(x    = symbols,
                 get  = "stock.prices",    
                 from = "2012-12-31",
                 to   = "2017-12-31")

2 Convert prices to returns

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 <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "AMZN" "JPM"  "LLY"  "NVDA"
#weights 
weights <- c(0.25, 0.25, 0.25, 0.25)
weights
## [1] 0.25 0.25 0.25 0.25
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 4 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AMZN       0.25
## 2 JPM        0.25
## 3 LLY        0.25
## 4 NVDA       0.25

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: 60 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.0540 
##  2 2013-02-28  0.0249 
##  3 2013-03-28  0.00741
##  4 2013-04-30  0.00880
##  5 2013-05-31  0.0473 
##  6 2013-06-28 -0.0279 
##  7 2013-07-31  0.0622 
##  8 2013-08-30 -0.0412 
##  9 2013-09-30  0.0405 
## 10 2013-10-31  0.0306 
## # ℹ 50 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 = "2017-12-31") %>%

    # 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        1.03

6 Plot

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")

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 beta coefficient measures the sensitivity of a portfolio’s returns relative to market returns. A beta of 1 suggests that the portfolio moves in tandem with the market. A beta greater than 1 indicates higher sensitivity, meaning the portfolio is more volatile than the market, while a beta less than 1 suggests lower sensitivity or volatility compared to the market.

The portfolio’s risk and returns are likely to experience slightly more volatility than the market. A beta of 1.03 indicates a near-market level of risk with just a slight increase in volatility.

The scatter plot with the regression line, showing a slope close to the benchmark, visually supports this calculated beta of 1.03. The plot confirms that your portfolio’s returns track the market closely, with a slight amplification in reaction to market changes.