# 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 = "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] "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,
                replace_on = "months", 
                col_rename = "returns")

portfolio_returns_tbl
## # A tibble: 60 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.0204 
##  2 2013-02-28 -0.00220
##  3 2013-03-28  0.0127 
##  4 2013-04-30  0.0173 
##  5 2013-05-31 -0.0113 
##  6 2013-06-28 -0.0233 
##  7 2013-07-31  0.0342 
##  8 2013-08-30 -0.0231 
##  9 2013-09-30  0.0513 
## 10 2013-10-31  0.0305 
## # ℹ 50 more rows

5 Calculate CAPM Beta

##5.1
# 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)

5.1 Get market returns

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       0.761

6 Plot: Scatter with regression line

 ###Scatter with regression line from ggplot 

portfolio_market_returns_tbl %>%
    ggplot(aes(market_returns, portfolio_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_fitted_long_tbl <- portfolio_market_returns_tbl %>%
  
  # Linear Regression Model
  lm(portfolio_returns ~ market_returns, data = .) %>%
  
  # Get Fitted and Actual Returns
  broom::augment() %>%
  
  # Add Date
  mutate(date = portfolio_market_returns_tbl$date) %>%
  select(date, portfolio_returns, .fitted) %>%
  
  # Transform Data to Long
  pivot_longer(cols = c(portfolio_returns, .fitted), 
               names_to = "type", values_to = "returns")

actual_fitted_long_tbl %>%
  
  ggplot(aes(x = date, y = 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?

My portfolio’s sensitivity to the market is displayed by the beta coefficient, the slope of the trend line on the first scatter plot of portfolio returns versus market returns. Most of the data points are close to the line, explains that my portfolio’s returns tend to follow the market’s volitility. For example, when the market return is around 0.02, my portfolio return is about 0.015, and when the market drops to -0.03, my portfolio return is around -0.025. This close fit between the data points and the line confirms that my calculated beta is a good measure of how my portfolio responds to the market’s movements.Data points that are typically surrounding the line represent a positive measure and its predictable at least most of the time. Cant predict everything!