Week 14: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Anthony Giansanti
2025-11-17
# Load packages
# Core
library(tidyverse)
library(tidyquant)
library(readr)
# Time series
library(lubridate)
library(tibbletime)
# modeling
library(broom)Goal
Examine how each asset contributes to portfolio standard deviation. This is to ensure that our risk is not concentrated in any one asset.
five stocks: “SPY”, “EFA”, “IJS”, “EEM”, “AGG” from 2012-12-31 to 2017-12-31
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
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 Component Contribution Step-by-Step
Refresh your memory on covariance with this video. Click this link Refresh your memory on matrix multiplication. Click this link
# Transform data into wide form
asset_returns_wide_tbl <- asset_returns_tbl %>%
pivot_wider(names_from = asset, values_from = returns) %>%
column_to_rownames(var = "date")
asset_returns_wide_tbl## AGG EEM EFA IJS SPY
## 2013-01-31 -0.0062309050 -0.0029352585 0.0366064135 0.052133107 4.992283e-02
## 2013-02-28 0.0058916389 -0.0231055723 -0.0129693806 0.016175669 1.267792e-02
## 2013-03-28 0.0009846233 -0.0102351142 0.0129693806 0.040257987 3.726825e-02
## 2013-04-30 0.0096401513 0.0120847780 0.0489676260 0.001222744 1.902993e-02
## 2013-05-31 -0.0202143618 -0.0494835903 -0.0306556875 0.041976287 2.333549e-02
## 2013-06-28 -0.0157787181 -0.0547281647 -0.0271442523 -0.001403198 -1.343467e-02
## 2013-07-31 0.0026878024 0.0131598622 0.0518603956 0.063541619 5.038606e-02
## 2013-08-30 -0.0082986738 -0.0257057056 -0.0197465144 -0.034743667 -3.045076e-02
## 2013-09-30 0.0111444323 0.0695887157 0.0753387023 0.063873628 3.115546e-02
## 2013-10-31 0.0082923872 0.0408614187 0.0320817394 0.034234344 4.526609e-02
## 2013-11-29 -0.0025104984 -0.0025941931 0.0054495994 0.041660822 2.920816e-02
## 2013-12-31 -0.0055823556 -0.0040740045 0.0215278476 0.012892133 2.559574e-02
## 2014-01-31 0.0152913917 -0.0903230931 -0.0534131927 -0.035775487 -3.588486e-02
## 2014-02-28 0.0037567458 0.0332207412 0.0595048489 0.045258096 4.451116e-02
## 2014-03-31 -0.0014819419 0.0380214613 -0.0046022549 0.013314985 8.260698e-03
## 2014-04-30 0.0081836469 0.0077726757 0.0165291855 -0.023184271 6.927654e-03
## 2014-05-30 0.0117217418 0.0290914332 0.0158286006 0.006205040 2.294087e-02
## 2014-06-30 -0.0005760295 0.0237339449 0.0091652625 0.037719056 2.043464e-02
## 2014-07-31 -0.0025118708 0.0135556888 -0.0263798940 -0.052009743 -1.352860e-02
## 2014-08-29 0.0114304332 0.0279044995 0.0018004770 0.043658191 3.870496e-02
## 2014-09-30 -0.0061672594 -0.0808565541 -0.0395982195 -0.061260558 -1.389246e-02
## 2014-10-31 0.0105839906 0.0140964557 -0.0026547696 0.068874805 2.327798e-02
## 2014-11-28 0.0065494564 -0.0155413256 0.0006251657 0.004773809 2.710131e-02
## 2014-12-31 0.0014749717 -0.0404421179 -0.0407468145 0.025295829 -2.540003e-03
## 2015-01-30 0.0203152655 -0.0068958811 0.0062263668 -0.054628200 -3.007673e-02
## 2015-02-27 -0.0089883924 0.0431362088 0.0614508370 0.056914690 5.468151e-02
## 2015-03-31 0.0037405333 -0.0150861232 -0.0143888736 0.010156390 -1.583006e-02
## 2015-04-30 -0.0032334177 0.0662812921 0.0358166599 -0.018417572 9.785785e-03
## 2015-05-29 -0.0043834442 -0.0419111554 0.0019527114 0.007509784 1.277399e-02
## 2015-06-30 -0.0108254163 -0.0297464684 -0.0316789202 0.004171360 -2.052089e-02
## 2015-07-31 0.0085850533 -0.0651782708 0.0201144168 -0.027375504 2.233776e-02
## 2015-08-31 -0.0033639680 -0.0925121278 -0.0771523411 -0.047268359 -6.288672e-02
## 2015-09-30 0.0080811610 -0.0318252450 -0.0451950235 -0.038464931 -2.584697e-02
## 2015-10-30 0.0006853614 0.0618084243 0.0640261675 0.063590106 8.163472e-02
## 2015-11-30 -0.0038980756 -0.0255604049 -0.0075558110 0.024414959 3.648768e-03
## 2015-12-31 -0.0019190851 -0.0389470640 -0.0235952201 -0.052156689 -1.743350e-02
## 2016-01-29 0.0123302035 -0.0516366963 -0.0567577006 -0.060306980 -5.106877e-02
## 2016-02-29 0.0088311349 -0.0082116146 -0.0339139220 0.020605386 -8.263362e-04
## 2016-03-31 0.0087097651 0.1218791652 0.0637457506 0.089910057 6.510025e-02
## 2016-04-29 0.0025457589 0.0040789675 0.0219750143 0.021044323 3.933256e-03
## 2016-05-31 0.0001354204 -0.0376283957 -0.0008559984 0.004397028 1.686851e-02
## 2016-06-30 0.0191665388 0.0445822210 -0.0244916117 0.008292550 3.469846e-03
## 2016-07-29 0.0054299440 0.0524422375 0.0390002385 0.049348276 3.582200e-02
## 2016-08-31 -0.0021560036 0.0087984716 0.0053266748 0.011260917 1.196974e-03
## 2016-09-30 0.0005156931 0.0248731704 0.0132794159 0.008614877 5.778028e-05
## 2016-10-31 -0.0082055419 -0.0083123261 -0.0224038336 -0.038134810 -1.748906e-02
## 2016-11-30 -0.0259894459 -0.0451616897 -0.0179744875 0.125246255 3.617608e-02
## 2016-12-30 0.0025384174 -0.0025299829 0.0267029875 0.031491867 2.006906e-02
## 2017-01-31 0.0021262162 0.0644314710 0.0323818267 -0.012144020 1.773641e-02
## 2017-02-28 0.0064370642 0.0172575302 0.0118363502 0.013429085 3.853941e-02
## 2017-03-31 -0.0005522345 0.0361892719 0.0318056735 -0.006533498 1.249270e-03
## 2017-04-28 0.0090294318 0.0168661758 0.0239524080 0.005108330 9.877007e-03
## 2017-05-31 0.0068470028 0.0280600145 0.0348100674 -0.022863051 1.401428e-02
## 2017-06-30 -0.0001822131 0.0092236606 0.0029561481 0.029151581 6.354939e-03
## 2017-07-31 0.0033341403 0.0565945349 0.0261877320 0.007481962 2.034551e-02
## 2017-08-31 0.0093690679 0.0232439210 -0.0004482871 -0.027564707 2.913569e-03
## 2017-09-29 -0.0057321766 -0.0004462596 0.0233428816 0.082321780 1.994921e-02
## 2017-10-31 0.0009780019 0.0322785967 0.0166535112 0.005915865 2.329061e-02
## 2017-11-30 -0.0014843218 -0.0038970180 0.0068699622 0.036913148 3.010821e-02
## 2017-12-29 0.0047404246 0.0369253201 0.0133982764 -0.003731416 1.205488e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398479e-05 0.0001042117 4.178628e-05 -7.811829e-05 -9.029894e-06
## EEM 1.042117e-04 0.0017547126 1.039018e-03 6.437760e-04 6.795426e-04
## EFA 4.178628e-05 0.0010390184 1.064238e-03 6.490325e-04 6.975402e-04
## IJS -7.811829e-05 0.0006437760 6.490325e-04 1.565453e-03 8.290270e-04
## SPY -9.029894e-06 0.0006795426 6.975402e-04 8.290270e-04 7.408278e-04# Standard deviation of portfolio
# Summarizes how much each asset's returns vary with those of other assets within the portfolio into a single number
w <- c(0.25, 0.25, 0.2, 0.2, 0.1)
sd_portfolio <- sqrt(t(w) %*% covariance_matrix %*% w)
sd_portfolio## [,1]
## [1,] 0.02347495# Component contribution
# Similar to the formula for sd_portfolio
# Mathematical trick to summarize the same, sd_portfolio, by asset instead of a single number
component_contribution <- (t(w) %*% covariance_matrix * w) / sd_portfolio[1,1]
component_contribution## AGG EEM EFA IJS SPY
## [1,] 0.0003874314 0.009257148 0.005815641 0.005684479 0.002330248rowSums(component_contribution)## [1] 0.02347495# Component contribution in percentage
component_percentages <- (component_contribution / sd_portfolio[1,1]) %>%
round(3) %>%
as_tibble()
component_percentages## # A tibble: 1 × 5
## AGG EEM EFA IJS SPY
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.017 0.394 0.248 0.242 0.099component_percentages %>%
as_tibble() %>%
gather(key = "asset", value = "contribution")## # A tibble: 5 × 2
## asset contribution
## <chr> <dbl>
## 1 AGG 0.017
## 2 EEM 0.394
## 3 EFA 0.248
## 4 IJS 0.242
## 5 SPY 0.0994 Component Contribution with a Custom Function
# Transform data into wide form
asset_returns_wide_tbl <- asset_returns_tbl %>%
pivot_wider(names_from = asset, values_from = returns) %>%
column_to_rownames(var = "date")
# Custom function
calculate_component_contribution <- function(asset_returns_wide_tbl, w) {
# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
# Standard deviation of portfolio
sd_portfolio <- sqrt(t(w) %*% covariance_matrix %*% w)
# Component contribution
component_contribution <- (t(w) %*% covariance_matrix * w) / sd_portfolio[1,1]
# Component contribution in percentage
component_percentages <- (component_contribution / sd_portfolio[1,1]) %>%
round(3) %>%
as_tibble()
return(component_percentages)
}
asset_returns_wide_tbl %>% calculate_component_contribution(w = c(0.25,0.25,0.2,0.2,0.1))## # A tibble: 1 × 5
## AGG EEM EFA IJS SPY
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.017 0.394 0.248 0.242 0.0995 Visualizing Component Contribution
# Figure 10.1 Contribution to Standard Deviation ----
asset_returns_wide_tbl %>%
calculate_component_contribution(w = c(0.25,0.25,0.2,0.2,0.1)) %>%
gather(key = "asset", value = "contribution") %>%
ggplot(aes(asset, contribution)) +
geom_col(fill = "cornflowerblue") +
theme(plot.title = element_text(hjust = 0.5)) +
scale_y_continuous(labels = scales::percent_format(accuracy = 1)) +
labs(title = "Percent Contribution to Portfolio Standard Deviation",
y = "Percent Contribution to Risk",
x = NULL)
# Figure 10.2 Weight versus Contribution ----
asset_returns_wide_tbl %>%
calculate_component_contribution(w = c(0.25,0.25,0.2,0.2,0.1)) %>%
gather(key = "asset", value = "contribution") %>%
add_column(weights = c(0.25,0.25,0.2,0.2,0.1)) %>%
pivot_longer(cols = c(contribution, weights), names_to = "type", values_to = "value") %>%
ggplot(aes(asset, value, fill = type)) +
geom_col(position = "dodge") +
theme(plot.title = element_text(hjust = 0.5)) +
scale_y_continuous(labels = scales::percent_format(accuracy = 1)) +
theme_tq() +
scale_fill_tq() +
labs(title = "Percent Contribution to Volatility",
y = "percent",
x = "asset") 
6 Rolling Component Contribution
calculate_comp_contrib_by_window <- function(asset_returns_wide_tbl,
start = 1,
window = 24,
weights) {
# 1 Define start date
start_date <- rownames(asset_returns_wide_tbl)[start]
# 2 Define end date
end_date <- rownames(asset_returns_wide_tbl)[start + window]
# 3 Subset df
df_subset <- asset_returns_wide_tbl %>%
rownames_to_column(var = "date") %>%
filter(date >= start_date & date < end_date) %>%
column_to_rownames(var = "date")
# 4 Calculate component contribution
component_percentages <-df_subset %>%
calculate_component_contribution(w = weights)
# 5 Add end date to df
component_percentages %>%
mutate(date = ymd(end_date)) %>%
select(date, everything())
}
# Check the custom function
asset_returns_wide_tbl %>% calculate_comp_contrib_by_window(start = 1, window = 24,
w = c(0.25,0.25,0.2,0.2,0.1))## # A tibble: 1 × 6
## date AGG EEM EFA IJS SPY
## <date> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2015-01-30 0.039 0.372 0.256 0.245 0.088asset_returns_wide_tbl %>% calculate_comp_contrib_by_window(start = 2, window = 24,
w = c(0.25,0.25,0.2,0.2,0.1))## # A tibble: 1 × 6
## date AGG EEM EFA IJS SPY
## <date> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2015-02-27 0.036 0.374 0.249 0.252 0.089dump(list = c("calculate_component_contribution",
"calculate_comp_contrib_by_window"),
file = "../00_scripts/calculate_comp_contrib_to_portfolio_volatility.R")# Iterate the custom function
w <- c(0.25,0.25,0.2,0.2,0.1)
window <- 24
rolling_comp_contrib_tbl <- 1:(nrow(asset_returns_wide_tbl) - window) %>%
map_df(.x = ., .f = ~calculate_comp_contrib_by_window(asset_returns_wide_tbl,
start = .x,
weights = w,
window = window))
rolling_comp_contrib_tbl## # A tibble: 36 × 6
## date AGG EEM EFA IJS SPY
## <date> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2015-01-30 0.039 0.372 0.256 0.245 0.088
## 2 2015-02-27 0.036 0.374 0.249 0.252 0.089
## 3 2015-03-31 0.027 0.37 0.255 0.255 0.092
## 4 2015-04-30 0.027 0.372 0.256 0.252 0.093
## 5 2015-05-29 0.024 0.385 0.254 0.246 0.092
## 6 2015-06-30 0.018 0.383 0.248 0.257 0.094
## 7 2015-07-31 0.014 0.375 0.253 0.261 0.096
## 8 2015-08-31 0.013 0.404 0.237 0.257 0.09
## 9 2015-09-30 0.012 0.407 0.248 0.238 0.094
## 10 2015-10-30 0.003 0.405 0.244 0.243 0.105
## # ℹ 26 more rows# Figure 10.3 Component Contribution ggplot ----
rolling_comp_contrib_tbl %>%
# Transform data to long form
pivot_longer(cols = -date, names_to = "asset", values_to = "contribution") %>%
# Plot
ggplot(aes(date, contribution, color = asset)) +
geom_line() +
scale_x_date(breaks = scales::pretty_breaks(n = 7)) +
scale_y_continuous(labels = scales::percent_format()) +
annotate(geom = "text",
x = as.Date("2016-07-01"),
y = 0.03,
color = "red", size = 5,
label = str_glue("AGG dips below zero sometimes, indicating
it reduces the portfolio volatility."))
# Figure 10.4 Stacked Component Contribution ggplot ----
rolling_comp_contrib_tbl %>%
# Transform data to long form
pivot_longer(cols = -date, names_to = "asset", values_to = "contribution") %>%
# Plot
ggplot(aes(date, contribution, fill = asset)) +
geom_area() +
scale_x_date(breaks = scales::pretty_breaks(n = 7)) +
scale_y_continuous(labels = scales::percent_format()) +
annotate(geom = "text",
x = as.Date("2016-07-01"),
y = 0.08,
color = "red", size = 5,
label = str_glue("AGG dips below zero sometimes, indicating
it reduces the portfolio volatility."))