# Load packages

# Core
library(tidyverse)
library(tidyquant)

Goal

Measure the portfolio’s beta coefficient, which can be thought of as the portfolio’s sensitivity to the market or its riskiness relative to the market.

five stocks: “SPY”, “EFA”, “IJS”, “EEM”, “AGG”

market: “SPY”

from 2012-12-31 to 2017-12-31

1 Import stock prices

symbols <- c("AMZN", "NVDA", "MCD", "GME", "TSLA")

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

# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "AMZN" "GME"  "MCD"  "NVDA" "TSLA"
# weights
weights <- c(0.20, 0.20, 0.30, 0.15, 0.15)
weights
## [1] 0.20 0.20 0.30 0.15 0.15
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 5 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AMZN       0.2 
## 2 GME        0.2 
## 3 MCD        0.3 
## 4 NVDA       0.15
## 5 TSLA       0.15

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  0.0341
##  2 2013-02-28  0.0134
##  3 2013-03-28  0.0521
##  4 2013-04-30  0.106 
##  5 2013-05-31  0.0860
##  6 2013-06-28  0.0706
##  7 2013-07-31  0.0822
##  8 2013-08-30  0.0211
##  9 2013-09-30  0.0532
## 10 2013-10-31  0.0191
## # 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        1.05

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 plot ends up showing a positive relationship between market and portfolio returns which means the portfolio moves with the market. Upwards slope would mean a positive beta, so the portfolio is a little sensitive to the market changes.