Week 14: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Kevin Scott
2024-06-26
# 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 -0.0062311656 -0.0029355736 0.0366061192 0.052133211 4.992323e-02
## 2013-02-28 0.0058908080 -0.0231052330 -0.0129693872 0.016175722 1.267796e-02
## 2013-03-28 0.0009853505 -0.0102353537 0.0129693872 0.040258125 3.726847e-02
## 2013-04-30 0.0096395686 0.0120850211 0.0489678953 0.001222481 1.903005e-02
## 2013-05-31 -0.0202145256 -0.0494832642 -0.0306555943 0.041976139 2.333527e-02
## 2013-06-28 -0.0157778200 -0.0547283223 -0.0271444699 -0.001402810 -1.343470e-02
## 2013-07-31 0.0026876429 0.0131593267 0.0518602560 0.063541572 5.038636e-02
## 2013-08-30 -0.0082980793 -0.0257051122 -0.0197462881 -0.034743607 -3.045120e-02
## 2013-09-30 0.0111440501 0.0695886503 0.0753384162 0.063873497 3.115588e-02
## 2013-10-31 0.0082915285 0.0408614106 0.0320817183 0.034234151 4.526635e-02
## 2013-11-29 -0.0025099208 -0.0025942551 0.0054497013 0.041661368 2.920691e-02
## 2013-12-31 -0.0055829683 -0.0040743618 0.0215282094 0.012891972 2.559600e-02
## 2014-01-31 0.0152919827 -0.0903224971 -0.0534132939 -0.035775468 -3.588444e-02
## 2014-02-28 0.0037564634 0.0332204154 0.0595050757 0.045257183 4.451081e-02
## 2014-03-31 -0.0014812664 0.0380215286 -0.0046029525 0.013315670 8.261035e-03
## 2014-04-30 0.0081826725 0.0077729759 0.0165294491 -0.023184118 6.927565e-03
## 2014-05-30 0.0117222318 0.0290911914 0.0158285760 0.006205059 2.294113e-02
## 2014-06-30 -0.0005761722 0.0237338338 0.0091653334 0.037718571 2.043459e-02
## 2014-07-31 -0.0025122201 0.0135556828 -0.0263797056 -0.052009271 -1.352872e-02
## 2014-08-29 0.0114310023 0.0279044730 0.0018002703 0.043657703 3.870481e-02
## 2014-09-30 -0.0061672707 -0.0808565855 -0.0395984966 -0.061260437 -1.389242e-02
## 2014-10-31 0.0105844841 0.0140964533 -0.0026547321 0.068874903 2.327797e-02
## 2014-11-28 0.0065487360 -0.0155411837 0.0006252305 0.004773801 2.710134e-02
## 2014-12-31 0.0014751869 -0.0404422264 -0.0407466515 0.025295591 -2.539611e-03
## 2015-01-30 0.0203153061 -0.0068954369 0.0062266693 -0.054627717 -3.007716e-02
## 2015-02-27 -0.0089884433 0.0431359538 0.0614504530 0.056914483 5.468184e-02
## 2015-03-31 0.0037405709 -0.0150864834 -0.0143887845 0.010156527 -1.583031e-02
## 2015-04-30 -0.0032335969 0.0662814223 0.0358166578 -0.018417750 9.786164e-03
## 2015-05-29 -0.0043836861 -0.0419107925 0.0019527233 0.007510029 1.277369e-02
## 2015-06-30 -0.0108249832 -0.0297468417 -0.0316790564 0.004171308 -2.052076e-02
## 2015-07-31 0.0085844222 -0.0651778834 0.0201146380 -0.027375425 2.233760e-02
## 2015-08-31 -0.0033636653 -0.0925124547 -0.0771525685 -0.047268502 -6.288692e-02
## 2015-09-30 0.0080812383 -0.0318250603 -0.0451946417 -0.038464548 -2.584699e-02
## 2015-10-30 0.0006855427 0.0618084371 0.0640258005 0.063589562 8.163502e-02
## 2015-11-30 -0.0038979773 -0.0255606045 -0.0075558800 0.024415388 3.648562e-03
## 2015-12-31 -0.0019192654 -0.0389470337 -0.0235949460 -0.052157193 -1.743373e-02
## 2016-01-29 0.0123302160 -0.0516366758 -0.0567577266 -0.060306697 -5.106853e-02
## 2016-02-29 0.0088310462 -0.0082115296 -0.0339141694 0.020605228 -8.263321e-04
## 2016-03-31 0.0087089597 0.1218789765 0.0637456938 0.089910422 6.510043e-02
## 2016-04-29 0.0025467174 0.0040792159 0.0219751003 0.021044144 3.932897e-03
## 2016-05-31 0.0001352651 -0.0376285078 -0.0008560461 0.004397174 1.686912e-02
## 2016-06-30 0.0191668870 0.0445822035 -0.0244915383 0.008292116 3.469733e-03
## 2016-07-29 0.0054291030 0.0524424134 0.0390002829 0.049348536 3.582173e-02
## 2016-08-31 -0.0021557650 0.0087984749 0.0053267805 0.011261145 1.196782e-03
## 2016-09-30 0.0005158996 0.0248729338 0.0132792408 0.008614374 5.803866e-05
## 2016-10-31 -0.0082051511 -0.0083123122 -0.0224037499 -0.038134756 -1.748916e-02
## 2016-11-30 -0.0259897217 -0.0451618992 -0.0179744835 0.125246426 3.617637e-02
## 2016-12-30 0.0025379425 -0.0025298823 0.0267029452 0.031491849 2.006904e-02
## 2017-01-31 0.0021265613 0.0644313953 0.0323820361 -0.012144093 1.773618e-02
## 2017-02-28 0.0064378794 0.0172578390 0.0118362329 0.013429101 3.853939e-02
## 2017-03-31 -0.0005530944 0.0361887584 0.0318057133 -0.006533260 1.249144e-03
## 2017-04-28 0.0090292053 0.0168665151 0.0239522160 0.005107603 9.877223e-03
## 2017-05-31 0.0068472158 0.0280602073 0.0348102595 -0.022862262 1.401429e-02
## 2017-06-30 -0.0001824719 0.0092235481 0.0029559265 0.029151394 6.354541e-03
## 2017-07-31 0.0033342260 0.0565944456 0.0261878679 0.007481745 2.034599e-02
## 2017-08-31 0.0093691094 0.0232439755 -0.0004482935 -0.027564842 2.913491e-03
## 2017-09-29 -0.0057320465 -0.0004460965 0.0233429117 0.082321928 1.994900e-02
## 2017-10-31 0.0009778658 0.0322784686 0.0166535938 0.005915814 2.329090e-02
## 2017-11-30 -0.0014840882 -0.0038971454 0.0068699046 0.036913020 3.010791e-02
## 2017-12-29 0.0047400482 0.0369253964 0.0133984028 -0.003731088 1.205519e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398400e-05 0.0001042085 4.178121e-05 -7.812025e-05 -9.033085e-06
## EEM 1.042085e-04 0.0017547085 1.039016e-03 6.437707e-04 6.795430e-04
## EFA 4.178121e-05 0.0010390164 1.064238e-03 6.490282e-04 6.975407e-04
## IJS -7.812025e-05 0.0006437707 6.490282e-04 1.565449e-03 8.290264e-04
## SPY -9.033085e-06 0.0006795430 6.975407e-04 8.290264e-04 7.408310e-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,] 0.02347489# 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,] 0.0003874035 0.009257137 0.005815633 0.005684463 0.002330252rowSums(component_contribution)## [1] 0.02347489# 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
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 -0.0062311656 -0.0029355736 0.0366061192 0.052133211 4.992323e-02
## 2013-02-28 0.0058908080 -0.0231052330 -0.0129693872 0.016175722 1.267796e-02
## 2013-03-28 0.0009853505 -0.0102353537 0.0129693872 0.040258125 3.726847e-02
## 2013-04-30 0.0096395686 0.0120850211 0.0489678953 0.001222481 1.903005e-02
## 2013-05-31 -0.0202145256 -0.0494832642 -0.0306555943 0.041976139 2.333527e-02
## 2013-06-28 -0.0157778200 -0.0547283223 -0.0271444699 -0.001402810 -1.343470e-02
## 2013-07-31 0.0026876429 0.0131593267 0.0518602560 0.063541572 5.038636e-02
## 2013-08-30 -0.0082980793 -0.0257051122 -0.0197462881 -0.034743607 -3.045120e-02
## 2013-09-30 0.0111440501 0.0695886503 0.0753384162 0.063873497 3.115588e-02
## 2013-10-31 0.0082915285 0.0408614106 0.0320817183 0.034234151 4.526635e-02
## 2013-11-29 -0.0025099208 -0.0025942551 0.0054497013 0.041661368 2.920691e-02
## 2013-12-31 -0.0055829683 -0.0040743618 0.0215282094 0.012891972 2.559600e-02
## 2014-01-31 0.0152919827 -0.0903224971 -0.0534132939 -0.035775468 -3.588444e-02
## 2014-02-28 0.0037564634 0.0332204154 0.0595050757 0.045257183 4.451081e-02
## 2014-03-31 -0.0014812664 0.0380215286 -0.0046029525 0.013315670 8.261035e-03
## 2014-04-30 0.0081826725 0.0077729759 0.0165294491 -0.023184118 6.927565e-03
## 2014-05-30 0.0117222318 0.0290911914 0.0158285760 0.006205059 2.294113e-02
## 2014-06-30 -0.0005761722 0.0237338338 0.0091653334 0.037718571 2.043459e-02
## 2014-07-31 -0.0025122201 0.0135556828 -0.0263797056 -0.052009271 -1.352872e-02
## 2014-08-29 0.0114310023 0.0279044730 0.0018002703 0.043657703 3.870481e-02
## 2014-09-30 -0.0061672707 -0.0808565855 -0.0395984966 -0.061260437 -1.389242e-02
## 2014-10-31 0.0105844841 0.0140964533 -0.0026547321 0.068874903 2.327797e-02
## 2014-11-28 0.0065487360 -0.0155411837 0.0006252305 0.004773801 2.710134e-02
## 2014-12-31 0.0014751869 -0.0404422264 -0.0407466515 0.025295591 -2.539611e-03
## 2015-01-30 0.0203153061 -0.0068954369 0.0062266693 -0.054627717 -3.007716e-02
## 2015-02-27 -0.0089884433 0.0431359538 0.0614504530 0.056914483 5.468184e-02
## 2015-03-31 0.0037405709 -0.0150864834 -0.0143887845 0.010156527 -1.583031e-02
## 2015-04-30 -0.0032335969 0.0662814223 0.0358166578 -0.018417750 9.786164e-03
## 2015-05-29 -0.0043836861 -0.0419107925 0.0019527233 0.007510029 1.277369e-02
## 2015-06-30 -0.0108249832 -0.0297468417 -0.0316790564 0.004171308 -2.052076e-02
## 2015-07-31 0.0085844222 -0.0651778834 0.0201146380 -0.027375425 2.233760e-02
## 2015-08-31 -0.0033636653 -0.0925124547 -0.0771525685 -0.047268502 -6.288692e-02
## 2015-09-30 0.0080812383 -0.0318250603 -0.0451946417 -0.038464548 -2.584699e-02
## 2015-10-30 0.0006855427 0.0618084371 0.0640258005 0.063589562 8.163502e-02
## 2015-11-30 -0.0038979773 -0.0255606045 -0.0075558800 0.024415388 3.648562e-03
## 2015-12-31 -0.0019192654 -0.0389470337 -0.0235949460 -0.052157193 -1.743373e-02
## 2016-01-29 0.0123302160 -0.0516366758 -0.0567577266 -0.060306697 -5.106853e-02
## 2016-02-29 0.0088310462 -0.0082115296 -0.0339141694 0.020605228 -8.263321e-04
## 2016-03-31 0.0087089597 0.1218789765 0.0637456938 0.089910422 6.510043e-02
## 2016-04-29 0.0025467174 0.0040792159 0.0219751003 0.021044144 3.932897e-03
## 2016-05-31 0.0001352651 -0.0376285078 -0.0008560461 0.004397174 1.686912e-02
## 2016-06-30 0.0191668870 0.0445822035 -0.0244915383 0.008292116 3.469733e-03
## 2016-07-29 0.0054291030 0.0524424134 0.0390002829 0.049348536 3.582173e-02
## 2016-08-31 -0.0021557650 0.0087984749 0.0053267805 0.011261145 1.196782e-03
## 2016-09-30 0.0005158996 0.0248729338 0.0132792408 0.008614374 5.803866e-05
## 2016-10-31 -0.0082051511 -0.0083123122 -0.0224037499 -0.038134756 -1.748916e-02
## 2016-11-30 -0.0259897217 -0.0451618992 -0.0179744835 0.125246426 3.617637e-02
## 2016-12-30 0.0025379425 -0.0025298823 0.0267029452 0.031491849 2.006904e-02
## 2017-01-31 0.0021265613 0.0644313953 0.0323820361 -0.012144093 1.773618e-02
## 2017-02-28 0.0064378794 0.0172578390 0.0118362329 0.013429101 3.853939e-02
## 2017-03-31 -0.0005530944 0.0361887584 0.0318057133 -0.006533260 1.249144e-03
## 2017-04-28 0.0090292053 0.0168665151 0.0239522160 0.005107603 9.877223e-03
## 2017-05-31 0.0068472158 0.0280602073 0.0348102595 -0.022862262 1.401429e-02
## 2017-06-30 -0.0001824719 0.0092235481 0.0029559265 0.029151394 6.354541e-03
## 2017-07-31 0.0033342260 0.0565944456 0.0261878679 0.007481745 2.034599e-02
## 2017-08-31 0.0093691094 0.0232439755 -0.0004482935 -0.027564842 2.913491e-03
## 2017-09-29 -0.0057320465 -0.0004460965 0.0233429117 0.082321928 1.994900e-02
## 2017-10-31 0.0009778658 0.0322784686 0.0166535938 0.005915814 2.329090e-02
## 2017-11-30 -0.0014840882 -0.0038971454 0.0068699046 0.036913020 3.010791e-02
## 2017-12-29 0.0047400482 0.0369253964 0.0133984028 -0.003731088 1.205519e-02calculate_component_contribution <- function(.data, w) {
# Covariance of asset returns
covariance_matrix <- cov(.data)
# Standard deviation of portfolio
# Summarizes how much each asset's returns vary with those of other assets within the portfolio into a single number
sd_portfolio <- sqrt(t(w) %*% covariance_matrix %*% w)
# 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 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(.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 = 0.5)) +
labs(title = "Percent Contribution to Portfolio Volatility")
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 Weight
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 = 0.5)) +
theme_tq() +
labs(title = "Percent Contribution to Portfolio Volatility and Weight",
y = "Percent",
x = NULL)