Apply to Your Data 6

Comparing Expected Returns and Risk Across Portfolio Assets

Step 1: Import Stock Prices

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

prices <- tq_get(
  x    = symbols,
  get  = "stock.prices",
  from = "2012-01-01",
  to   = "2017-01-01"
)

Step 2: Convert Prices to Quarterly Returns

asset_returns_tbl <- prices %>%
  group_by(symbol) %>%
  tq_transmute(
    select     = adjusted,
    mutate_fun = periodReturn,
    period     = "quarterly",
    type       = "log"
  ) %>%
  slice(-1) %>%
  ungroup() %>%
  set_names(c("asset", "date", "returns"))

Step 3: Assign a Weight to Each Asset

symbols_vec <- asset_returns_tbl %>%
  distinct(asset) %>%
  pull()

weights <- c(0.25, 0.25, 0.20, 0.20, 0.10)

w_tbl <- tibble(symbols_vec, weights) %>%
  set_names(c("asset", "weights"))

w_tbl

## # A tibble: 5 × 2
##   asset weights
##   <chr>   <dbl>
## 1 AGG      0.25
## 2 EEM      0.25
## 3 EFA      0.2 
## 4 IJS      0.2 
## 5 SPY      0.1

Step 4: Build a Portfolio

portfolio_returns_tbl <- asset_returns_tbl %>%
  tq_portfolio(
    assets_col   = asset,
    returns_col  = returns,
    weights      = w_tbl,
    col_rename   = "returns",
    rebalance_on = "quarters"
  )

## Warning in check_weights(weights, assets_col, map, x): Sum of weights does not
## equal 1.

Step 5: Calculate Standard Deviation

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

portfolio_sd_tbl

## # A tibble: 1 × 1
##   tq_sd
##   <dbl>
## 1  3.85

Step 6: Scatter Plot of Expected Return vs. Risk

asset_sd_mean_tbl <- asset_returns_tbl %>%
  group_by(asset) %>%
  tq_performance(Ra = returns, performance_fun = table.Stats) %>%
  ungroup() %>%
  select(asset, Stdev, ArithmeticMean) %>%
  set_names(c("asset", "stdev", "mean"))

portfolio_mean <- mean(portfolio_returns_tbl$returns)

portfolio_row <- tibble(
  asset = "Portfolio",
  stdev = portfolio_sd_tbl$tq_sd / 100,
  mean  = portfolio_mean
)

sd_mean_table <- asset_sd_mean_tbl %>%
  add_row(portfolio_row) %>%
  mutate(
    stdev = stdev * 100,
    mean  = mean * 100
  )

sd_mean_table

## # A tibble: 6 × 3
##   asset     stdev  mean
##   <chr>     <dbl> <dbl>
## 1 AGG        1.67  0.54
## 2 EEM        6.97 -0.53
## 3 EFA        5.56  1.07
## 4 IJS        6.13  3.43
## 5 SPY        4.05  2.95
## 6 Portfolio  3.85  1.20

sd_mean_table %>%
  ggplot(aes(x = stdev, y = mean, color = asset)) +
  geom_point() +
  geom_text_repel(aes(label = asset)) +
  labs(
    title = "Expected Quarterly Return vs. Risk",
    x     = "Standard Deviation (Risk)",
    y     = "Mean Return"
  ) +
  theme_tq() +
  theme(legend.position = "none")

Question: How do expected returns and risk compare across your portfolio and its individual assets?

Based on the plot above, (name the asset(s) with the highest standard deviation) carries the most risk in this portfolio, with an expected quarterly return of (fill in). The portfolio as a whole sits at (describe its position relative to the individual assets), which shows the effect of diversification: combining assets with different risk/return profiles typically produces a portfolio with lower overall risk than its riskiest individual components, without necessarily sacrificing much expected return.