# Load packages

# Core
library(tidyverse)
library(tidyquant)

Goal

Visualize expected returns and risk to make it easier to compare the performance of multiple assets and portfolios.

Choose your stocks.

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

1 Import stock prices

symbols <- c("SPY", "EFA", "IJS", "EEM", "AGG")

prices <- tq_get(x    =symbols,
                 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] "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")
portfolio_returns_tbl
## # A tibble: 60 × 2
##    date       portfolio.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 
## # … with 50 more rows

5 Calculate Standard Deviation

portfolio_sd_tidyquant_builtin_percent <- portfolio_returns_tbl %>%
    
    tq_performance(Ra =  portfolio.returns,
                   performance_fun = table.Stats) %>%
    
    select(Stdev) %>%
    mutate(tq_sd = round(Stdev, 4)*100)

portfolio_sd_tidyquant_builtin_percent
## # A tibble: 1 × 2
##    Stdev tq_sd
##    <dbl> <dbl>
## 1 0.0235  2.35
# Mean of portfolio returns
portfolio_mean_tidyquant_builtin_percent <-
mean(portfolio_returns_tbl$portfolio.returns)

portfolio_mean_tidyquant_builtin_percent
## [1] 0.005899129

6 Plot

# Excepted Returns vs Risk
sd_mean_tbl <- asset_returns_tbl %>%
    
    group_by(asset) %>%
    tq_performance(Ra= returns,
                   performance_fun = table.Stats) %>%
    select(Mean = ArithmeticMean, Stdev) %>%
    ungroup() %>%
    mutate(Stdev = Stdev * 100,
           Mean = Mean * 100) %>% 
    
    # Add portfolio sd
    add_row(tibble(asset = "Portfolio",
                  Mean  = portfolio_mean_tidyquant_builtin_percent * 100,
                  Stdev = portfolio_sd_tidyquant_builtin_percent$tq_sd))
sd_mean_tbl
## # A tibble: 6 × 3
##   asset      Mean Stdev
##   <chr>     <dbl> <dbl>
## 1 AGG       0.17   0.86
## 2 EEM       0.28   4.19
## 3 EFA       0.6    3.26
## 4 IJS       1.19   3.96
## 5 SPY       1.21   2.72
## 6 Portfolio 0.590  2.35

Expected Returns

sd_mean_tbl %>%
    
    ggplot(aes(x = Stdev, y= Mean, color = asset)) +
    geom_point() +
    ggrepel::geom_label_repel(aes(label = asset))

## 24 Months Rolling

rolling_sd_tbl <- portfolio_returns_tbl %>%
    
    tq_mutate(select     = portfolio.returns,
              mutate_fun = rollapply,
              width      = 24,
              FUN        = sd,
              col_rename = "rolling sd") %>%
    
    na.omit() %>%
    select(date, "rolling sd")

rolling_sd_tbl
## # A tibble: 37 × 2
##    date       `rolling sd`
##    <date>            <dbl>
##  1 2014-12-31       0.0237
##  2 2015-01-30       0.0236
##  3 2015-02-27       0.0245
##  4 2015-03-31       0.0246
##  5 2015-04-30       0.0247
##  6 2015-05-29       0.0245
##  7 2015-06-30       0.0242
##  8 2015-07-31       0.0238
##  9 2015-08-31       0.0262
## 10 2015-09-30       0.0247
## # … with 27 more rows
rolling_sd_tbl %>%
    
    ggplot(aes(x = date, y= "rolling sd")) +
    geom_line(color = "cornflowerblue")

    # Formatting
    scale_y_continuous(labels = scales::percent_format())
## <ScaleContinuousPosition>
##  Range:  
##  Limits:    0 --    1
    #Labeling
    labs(x = NULL,
         y = NULL,
         title = "24 Month Rolling Volatility")+
    theme(plot.title = element_text(hjust = 0.5))    
## NULL

How should you expect your portfolio to perform relative to its assets in the portfolio? Would you invest all your money in any of the individual stocks instead of the portfolio? Discuss both in terms of expected return and risk.

The portfolio returns are very neutral in terms of the fact that it falls almost in the center of the graph. So I wouldn’t necessarily get a high rate of return, rather it a safer rate of return with some profit. I would probably invest my money in a stock like SPY or IJS because the profit rate is much higher, yet their is a lot more risk involved. SPY has basically the same rate of return as IJS but there is less risk involved. Thus,I would invest in SPY.