Week 13: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Alex St. Pierre
2025-11-15
# 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 -0.0062314812 -0.0029353724 0.0366061223 0.052133234 4.992252e-02
## 2013-02-28 0.0058912517 -0.0231053453 -0.0129694754 0.016175672 1.267837e-02
## 2013-03-28 0.0009849122 -0.0102348794 0.0129694754 0.040258407 3.726794e-02
## 2013-04-30 0.0096391959 0.0120845432 0.0489677151 0.001222538 1.903017e-02
## 2013-05-31 -0.0202139882 -0.0494829810 -0.0306554090 0.041976188 2.333526e-02
## 2013-06-28 -0.0157775381 -0.0547287740 -0.0271446199 -0.001403198 -1.343396e-02
## 2013-07-31 0.0026871102 0.0131597987 0.0518603956 0.063541532 5.038526e-02
## 2013-08-30 -0.0082982754 -0.0257056421 -0.0197466059 -0.034743386 -3.045089e-02
## 2013-09-30 0.0111442302 0.0695885941 0.0753389633 0.063873802 3.115603e-02
## 2013-10-31 0.0082919948 0.0408614236 0.0320814055 0.034233814 4.526662e-02
## 2013-11-29 -0.0025098145 -0.0025940764 0.0054497637 0.041661250 2.920721e-02
## 2013-12-31 -0.0055833352 -0.0040741220 0.0215280075 0.012892049 2.559595e-02
## 2014-01-31 0.0152921720 -0.0903229756 -0.0534133526 -0.035775570 -3.588445e-02
## 2014-02-28 0.0037566479 0.0332206168 0.0595050079 0.045257770 4.451054e-02
## 2014-03-31 -0.0014816517 0.0380218851 -0.0046025734 0.013315231 8.260700e-03
## 2014-04-30 0.0081827801 0.0077724951 0.0165295022 -0.023184355 6.927952e-03
## 2014-05-30 0.0117218398 0.0290914298 0.0158284436 0.006205450 2.294078e-02
## 2014-06-30 -0.0005758402 0.0237339422 0.0091654156 0.037718653 2.043493e-02
## 2014-07-31 -0.0025117759 0.0135556873 -0.0263798899 -0.052009420 -1.352898e-02
## 2014-08-29 0.0114309015 0.0279047127 0.0018005552 0.043657787 3.870487e-02
## 2014-09-30 -0.0061682005 -0.0808571130 -0.0395985366 -0.061260404 -1.389265e-02
## 2014-10-31 0.0105850227 0.0140963434 -0.0026547698 0.068874811 2.327799e-02
## 2014-11-28 0.0065485235 -0.0155408614 0.0006254112 0.004773887 2.710159e-02
## 2014-12-31 0.0014750648 -0.0404422354 -0.0407468077 0.025295599 -2.539647e-03
## 2015-01-30 0.0203157235 -0.0068955117 0.0062263657 -0.054627728 -3.007710e-02
## 2015-02-27 -0.0089886650 0.0431357216 0.0614507473 0.056914372 5.468161e-02
## 2015-03-31 0.0037403506 -0.0150860651 -0.0143888725 0.010156618 -1.582997e-02
## 2015-04-30 -0.0032331434 0.0662812399 0.0358165791 -0.018418031 9.785698e-03
## 2015-05-29 -0.0043835358 -0.0419110434 0.0019527114 0.007510092 1.277425e-02
## 2015-06-30 -0.0108254163 -0.0297463480 -0.0316790808 0.004171207 -2.052106e-02
## 2015-07-31 0.0085848688 -0.0651783269 0.0201146561 -0.027375117 2.233767e-02
## 2015-08-31 -0.0033640611 -0.0925123329 -0.0771523348 -0.047268594 -6.288636e-02
## 2015-09-30 0.0080817140 -0.0318248859 -0.0451949307 -0.038464334 -2.584725e-02
## 2015-10-30 0.0006855447 0.0618084113 0.0640259062 0.063589590 8.163489e-02
## 2015-11-30 -0.0038985343 -0.0255606100 -0.0075558116 0.024414957 3.648421e-03
## 2015-12-31 -0.0019194542 -0.0389472098 -0.0235951360 -0.052156850 -1.743359e-02
## 2016-01-29 0.0123305727 -0.0516365505 -0.0567578828 -0.060306898 -5.106869e-02
## 2016-02-29 0.0088313156 -0.0082116146 -0.0339138341 0.020605386 -8.261509e-04
## 2016-03-31 0.0087088679 0.1218788225 0.0637455795 0.089910369 6.510033e-02
## 2016-04-29 0.0025466540 0.0040793101 0.0219751066 0.021044011 3.933255e-03
## 2016-05-31 0.0001353311 -0.0376283957 -0.0008559120 0.004397028 1.686851e-02
## 2016-06-30 0.0191667124 0.0445824922 -0.0244917913 0.008292324 3.469761e-03
## 2016-07-29 0.0054299426 0.0524419664 0.0390005046 0.049348359 3.582175e-02
## 2016-08-31 -0.0021564397 0.0087985353 0.0053266748 0.011261345 1.196811e-03
## 2016-09-30 0.0005160423 0.0248731688 0.0132793321 0.008614593 5.843409e-05
## 2016-10-31 -0.0082050124 -0.0083122629 -0.0224037498 -0.038135103 -1.748922e-02
## 2016-11-30 -0.0259899694 -0.0451618807 -0.0179744003 0.125246871 3.617616e-02
## 2016-12-30 0.0025377862 -0.0025301146 0.0267029852 0.031491544 2.006882e-02
## 2017-01-31 0.0021266667 0.0644316066 0.0323816596 -0.012143830 1.773649e-02
## 2017-02-28 0.0064376895 0.0172575919 0.0118363511 0.013428394 3.853956e-02
## 2017-03-31 -0.0005529492 0.0361891550 0.0318059121 -0.006532872 1.249047e-03
## 2017-04-28 0.0090293441 0.0168661777 0.0239522507 0.005107765 9.877155e-03
## 2017-05-31 0.0068470040 0.0280602412 0.0348102158 -0.022862293 1.401427e-02
## 2017-06-30 -0.0001820372 0.0092237704 0.0029557777 0.029151696 6.354506e-03
## 2017-07-31 0.0033338773 0.0565944180 0.0261879539 0.007481465 2.034587e-02
## 2017-08-31 0.0093685491 0.0232438163 -0.0004482871 -0.027564835 2.913569e-03
## 2017-09-29 -0.0057312200 -0.0004463619 0.0233427407 0.082321737 1.994934e-02
## 2017-10-31 0.0009773033 0.0322785008 0.0166535828 0.005915750 2.329054e-02
## 2017-11-30 -0.0014837981 -0.0038971182 0.0068700315 0.036913497 3.010802e-02
## 2017-12-29 0.0047405116 0.0369256184 0.0133983443 -0.003731303 1.205475e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398489e-05 0.0001042096 4.178133e-05 -7.811913e-05 -9.033150e-06
## EEM 1.042096e-04 0.0017547121 1.039017e-03 6.437725e-04 6.795413e-04
## EFA 4.178133e-05 0.0010390169 1.064240e-03 6.490315e-04 6.975398e-04
## IJS -7.811913e-05 0.0006437725 6.490315e-04 1.565451e-03 8.290251e-04
## SPY -9.033150e-06 0.0006795413 6.975398e-04 8.290251e-04 7.408260e-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,] 0.02347491# 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,] 0.0003874109 0.009257144 0.005815637 0.005684472 0.002330244rowSums(component_contribution)## [1] 0.02347491# 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
calculate_component_contribution <- function(.data, w) {
covariance_matrix <- cov(.data)
sd_portfolio <- sqrt(t(w) %*% covariance_matrix %*% w)
component_contribution <- (t(w) %*% covariance_matrix * w) / sd_portfolio[1,1]
component_percentages <- (component_contribution / sd_portfolio[1,1]) %>%
round(3) %>%
as_tibble()
return(component_percentages)
}
asset_returns_wide_tbl %>% calculate_component_contribution(w = c(.25, .25, .2, .2, .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
Column Chart of Component Contribution
plot_data <- asset_returns_wide_tbl %>%
calculate_component_contribution(w = c(.25, .25, .2, .2, .1)) %>%
# Transform to long form
pivot_longer(cols = everything(),names_to = "Asset", values_to = "Contribution")
plot_data %>%
ggplot(aes(x = Asset, y = Contribution)) +
geom_col(fill = "cornflowerblue") +
scale_y_continuous(labels = scales::percent_format(accuracy = 1)) +
theme(plot.title = element_text(hjust = .5)) +
labs(title = "Percent Contribution to Portfolio Volatility")
6 Rolling Component Contribution
Column Chart of Component Contribution and weight
plot_data <- asset_returns_wide_tbl %>%
calculate_component_contribution(w = c(.25, .25, .2, .2, .1)) %>%
# Transform to long form
pivot_longer(cols = everything(),names_to = "Asset", values_to = "Contribution") %>%
# Add weights
add_column(weight = c(.25, .25, .2, .2, .1)) %>%
# Transform to long
pivot_longer(cols = c(Contribution, weight), names_to = "type", values_to = "value")
plot_data %>%
ggplot(aes(x = Asset, y = value, fill = type)) +
geom_col(position = "dodge") +
scale_y_continuous(labels = scales::percent_format(accuracy = 1)) +
scale_fill_tq() +
theme(plot.title = element_text(hjust = .5)) +
theme_tq()+
labs(title = "Percent Contribution to Portfolio Volatility and Weight",
y = "Percent", x = NULL)