Week 14: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Anton Jellvik
2023-04-23
# 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 -0.0062309888 -0.0029353167 0.0366061698 0.052133582 4.992272e-02
## 2013-02-28 0.0058912518 -0.0231055150 -0.0129693901 0.016175505 1.267880e-02
## 2013-03-28 0.0009846966 -0.0102348834 0.0129693901 0.040257950 3.726776e-02
## 2013-04-30 0.0096392318 0.0120848841 0.0489677741 0.001222579 1.902962e-02
## 2013-05-31 -0.0202140245 -0.0494836345 -0.0306556320 0.041976613 2.333576e-02
## 2013-06-28 -0.0157778815 -0.0547281099 -0.0271445692 -0.001403289 -1.343466e-02
## 2013-07-31 0.0026869950 0.0131596226 0.0518602840 0.063541488 5.038593e-02
## 2013-08-30 -0.0082979604 -0.0257057495 -0.0197462111 -0.034743648 -3.045100e-02
## 2013-09-30 0.0111441858 0.0695888320 0.0753385007 0.063873713 3.115583e-02
## 2013-10-31 0.0082920122 0.0408614901 0.0320818466 0.034234070 4.526657e-02
## 2013-11-29 -0.0025098782 -0.0025938709 0.0054493211 0.041661127 2.920706e-02
## 2013-12-31 -0.0055828075 -0.0040748507 0.0215282292 0.012892372 2.559601e-02
## 2014-01-31 0.0152910845 -0.0903227048 -0.0534134224 -0.035775628 -3.588423e-02
## 2014-02-28 0.0037572819 0.0332208430 0.0595051175 0.045257428 4.450991e-02
## 2014-03-31 -0.0014818485 0.0380216248 -0.0046024868 0.013315541 8.261408e-03
## 2014-04-30 0.0081829402 0.0077729142 0.0165293619 -0.023184275 6.927557e-03
## 2014-05-30 0.0117225161 0.0290911879 0.0158285764 0.006205137 2.294118e-02
## 2014-06-30 -0.0005763326 0.0237339251 0.0091652100 0.037718806 2.043455e-02
## 2014-07-31 -0.0025119014 0.0135554632 -0.0263797279 -0.052009395 -1.352850e-02
## 2014-08-29 0.0114308477 0.0279046023 0.0018003989 0.043657823 3.870481e-02
## 2014-09-30 -0.0061675911 -0.0808565822 -0.0395984775 -0.061260465 -1.389262e-02
## 2014-10-31 0.0105847771 0.0140964530 -0.0026547927 0.068874767 2.327815e-02
## 2014-11-28 0.0065490048 -0.0155413204 0.0006252355 0.004773781 2.710130e-02
## 2014-12-31 0.0014746139 -0.0404420932 -0.0407466701 0.025295975 -2.540027e-03
## 2015-01-30 0.0203149434 -0.0068957476 0.0062264210 -0.054628293 -3.007686e-02
## 2015-02-27 -0.0089879255 0.0431362506 0.0614507429 0.056914681 5.468177e-02
## 2015-03-31 0.0037401556 -0.0150863546 -0.0143888272 0.010156550 -1.583021e-02
## 2015-04-30 -0.0032328079 0.0662813686 0.0358164986 -0.018417828 9.786066e-03
## 2015-05-29 -0.0043839202 -0.0419110105 0.0019526917 0.007509932 1.277383e-02
## 2015-06-30 -0.0108253798 -0.0297467767 -0.0316787464 0.004171261 -2.052100e-02
## 2015-07-31 0.0085850554 -0.0651780201 0.0201143002 -0.027375259 2.233789e-02
## 2015-08-31 -0.0033642783 -0.0925125610 -0.0771523012 -0.047268453 -6.288686e-02
## 2015-09-30 0.0080815023 -0.0318246508 -0.0451948664 -0.038464762 -2.584684e-02
## 2015-10-30 0.0006853394 0.0618081961 0.0640259447 0.063589675 8.163503e-02
## 2015-11-30 -0.0038984543 -0.0255603250 -0.0075559415 0.024415567 3.648425e-03
## 2015-12-31 -0.0019186686 -0.0389472195 -0.0235950350 -0.052157414 -1.743371e-02
## 2016-01-29 0.0123300638 -0.0516367575 -0.0567576593 -0.060306538 -5.106862e-02
## 2016-02-29 0.0088315122 -0.0082115386 -0.0339139774 0.020605107 -8.262749e-04
## 2016-03-31 0.0087088881 0.1218790767 0.0637455859 0.089910154 6.509992e-02
## 2016-04-29 0.0025465250 0.0040791550 0.0219751218 0.021044350 3.933700e-03
## 2016-05-31 0.0001354420 -0.0376283922 -0.0008562057 0.004397116 1.686839e-02
## 2016-06-30 0.0191664950 0.0445821604 -0.0244913251 0.008292306 3.470131e-03
## 2016-07-29 0.0054298579 0.0524422525 0.0390001135 0.049348247 3.582171e-02
## 2016-08-31 -0.0021564410 0.0087986314 0.0053269244 0.011261141 1.196801e-03
## 2016-09-30 0.0005159386 0.0248727224 0.0132791048 0.008614677 5.805468e-05
## 2016-10-31 -0.0082050216 -0.0083120145 -0.0224035594 -0.038134764 -1.748902e-02
## 2016-11-30 -0.0259899782 -0.0451617810 -0.0179747621 0.125246607 3.617588e-02
## 2016-12-30 0.0025379523 -0.0025300915 0.0267031820 0.031491486 2.006908e-02
## 2017-01-31 0.0021266209 0.0644314144 0.0323818541 -0.012143782 1.773651e-02
## 2017-02-28 0.0064375887 0.0172578913 0.0118363213 0.013428578 3.853932e-02
## 2017-03-31 -0.0005525514 0.0361891103 0.0318056750 -0.006532835 1.249205e-03
## 2017-04-28 0.0090290430 0.0168663664 0.0239523104 0.005107819 9.877394e-03
## 2017-05-31 0.0068473195 0.0280597646 0.0348100711 -0.022862671 1.401412e-02
## 2017-06-30 -0.0001824934 0.0092239409 0.0029561916 0.029151703 6.354571e-03
## 2017-07-31 0.0033343053 0.0565943781 0.0261877724 0.007481729 2.034592e-02
## 2017-08-31 0.0093689881 0.0232437060 -0.0004483141 -0.027564976 2.913399e-03
## 2017-09-29 -0.0057319725 -0.0004461787 0.0233425840 0.082321631 1.994912e-02
## 2017-10-31 0.0009781270 0.0322784865 0.0166538437 0.005916090 2.329072e-02
## 2017-11-30 -0.0014844552 -0.0038969510 0.0068698864 0.036913200 3.010804e-02
## 2017-12-29 0.0047402246 0.0369253399 0.0133984842 -0.003731107 1.205509e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398369e-05 0.0001042129 4.178513e-05 -7.812064e-05 -9.030157e-06
## EEM 1.042129e-04 0.0017547108 1.039018e-03 6.437743e-04 6.795433e-04
## EFA 4.178513e-05 0.0010390182 1.064237e-03 6.490288e-04 6.975379e-04
## IJS -7.812064e-05 0.0006437743 6.490288e-04 1.565452e-03 8.290240e-04
## SPY -9.030157e-06 0.0006795433 6.975379e-04 8.290240e-04 7.408259e-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,] 0.02347492# 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,] 0.0003874243 0.009257153 0.005815633 0.005684466 0.002330245rowSums(component_contribution)## [1] 0.02347492# 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
## # … with 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."))