# 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",
                 fro = "2012-12-31",
                 to  = "2024-12-31")

2 Convert prices to returns (monthly)

asset_returns_tbl1 <- 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_tbl1 %>% distinct(asset) %>% pull()
symbols
## [1] "AGG" "EEM" "EFA" "IJS" "SPY"
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)

4 Build a portfolio

portfolio_returns_tbl1 <- asset_returns_tbl1 %>%
    tq_portfolio(assets_col = asset, 
                 returns_col = returns,
                 weights = w_tbl, 
                 rebalance_on = "months")

5 Calculate CAPM Beta

5.1 Get market returns

market_returns_tbl1 <- tq_get(x   = "SPY", 
                 get = "stock.prices",
                 fro = "2012-12-31",
                 to  = "2024-12-31")  %>%
    
    tq_transmute(select     = adjusted,
                 mutate_fun = periodReturn,
                 period     = "monthly",
                 type       = "log", col_rename = "returns") %>%
    
    slice(-1)

market_returns_tbl1
## # A tibble: 143 × 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 133 more rows

5.2 Join returns

portfolio_market_returns_tbl1 <- left_join(market_returns_tbl1, portfolio_returns_tbl1, by = "date") %>%
    
    set_names("date", "market_returns", "portfolio_returns")

portfolio_market_returns_tbl1
## # A tibble: 143 × 3
##    date       market_returns portfolio_returns
##    <date>              <dbl>             <dbl>
##  1 2013-01-31         0.0499           0.0204 
##  2 2013-02-28         0.0127          -0.00239
##  3 2013-03-28         0.0373           0.0121 
##  4 2013-04-30         0.0190           0.0174 
##  5 2013-05-31         0.0233          -0.0128 
##  6 2013-06-28        -0.0134          -0.0247 
##  7 2013-07-31         0.0504           0.0321 
##  8 2013-08-30        -0.0305          -0.0224 
##  9 2013-09-30         0.0312           0.0511 
## 10 2013-10-31         0.0453           0.0301 
## # ℹ 133 more rows

5.3 CAPM Beta

portfolio_market_returns_tbl1 %>%
    
    tq_performance(Ra = portfolio_returns, Rb = market_returns, performance_fun = CAPM.beta)
## # A tibble: 1 × 1
##   CAPM.beta.1
##         <dbl>
## 1       0.742

6 Plot: Scatter with regression line

portfolio_market_returns_tbl1 %>%
    
    ggplot(aes(x = market_returns, y = portfolio_returns)) +
    geom_point(color = "cornflowerblue") +
    geom_smooth(method = "lm", se = FALSE, size = 1.5, color = tidyquant::palette_light()[3]) +
    
    labs(y = "Portfolio Returns",
         x = "Market 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?

My portfolio is less volatile than the market. The Beta coefficient is .742, meaning the portfolio is around 25% less volatile than the market. For an aggressive investor, a Beta above 1 would be sought after. Since this portfolio is below 1, it would me more suited for conservative investors. This means that if the market moved 10%, the portfolio would move 7.42%. While it may not be the most aggressive returns, in down times, this would help the investor. The plot does confirm the beta coefficient calculated. As we can see, the line trends upwards as market returns increase. This would be the case if the beta were negative. More specifically, we can see that for specific market returns, the portfolio returns are below by a bit, however, still positive.