Week 14: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Sumaj Billin
2024-11-19
# 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 -0.0062313750 -0.0029354630 0.0366063075 0.052133543 4.992272e-02
## 2013-02-28 0.0058912661 -0.0231051173 -0.0129694791 0.016175455 1.267848e-02
## 2013-03-28 0.0009850712 -0.0102351227 0.0129694791 0.040258194 3.726772e-02
## 2013-04-30 0.0096393383 0.0120849026 0.0489678953 0.001222163 1.903030e-02
## 2013-05-31 -0.0202136301 -0.0494837218 -0.0306558616 0.041976486 2.333515e-02
## 2013-06-28 -0.0157790017 -0.0547282663 -0.0271442942 -0.001403043 -1.343435e-02
## 2013-07-31 0.0026873392 0.0131597606 0.0518602606 0.063541452 5.038578e-02
## 2013-08-30 -0.0082978167 -0.0257054834 -0.0197462899 -0.034743279 -3.045103e-02
## 2013-09-30 0.0111446506 0.0695885319 0.0753386693 0.063873556 3.115622e-02
## 2013-10-31 0.0082914658 0.0408614153 0.0320816335 0.034234195 4.526667e-02
## 2013-11-29 -0.0025100362 -0.0025941415 0.0054495424 0.041660925 2.920651e-02
## 2013-12-31 -0.0055829044 -0.0040741329 0.0215281336 0.012892370 2.559638e-02
## 2014-01-31 0.0152914329 -0.0903229138 -0.0534133024 -0.035775319 -3.588453e-02
## 2014-02-28 0.0037566444 0.0332207850 0.0595051622 0.045257568 4.451019e-02
## 2014-03-31 -0.0014808095 0.0380215801 -0.0046026433 0.013314955 8.261218e-03
## 2014-04-30 0.0081829052 0.0077728584 0.0165291408 -0.023184279 6.927471e-03
## 2014-05-30 0.0117218179 0.0290911880 0.0158286522 0.006205384 2.294109e-02
## 2014-06-30 -0.0005758743 0.0237337214 0.0091654820 0.037718567 2.043479e-02
## 2014-07-31 -0.0025122026 0.0135557911 -0.0263800066 -0.052009454 -1.352855e-02
## 2014-08-29 0.0114307715 0.0279046807 0.0018006511 0.043658288 3.870465e-02
## 2014-09-30 -0.0061673311 -0.0808569014 -0.0395984874 -0.061260692 -1.389219e-02
## 2014-10-31 0.0105844686 0.0140965659 -0.0026548903 0.068874818 2.327788e-02
## 2014-11-28 0.0065489703 -0.0155414106 0.0006251511 0.004773794 2.710122e-02
## 2014-12-31 0.0014750949 -0.0404421120 -0.0407465688 0.025295977 -2.539838e-03
## 2015-01-30 0.0203152692 -0.0068958566 0.0062263403 -0.054628351 -3.007708e-02
## 2015-02-27 -0.0089879221 0.0431362586 0.0614508539 0.056914568 5.468224e-02
## 2015-03-31 0.0037398053 -0.0150863686 -0.0143889389 0.010156389 -1.583045e-02
## 2015-04-30 -0.0032334700 0.0662814223 0.0358165822 -0.018417519 9.785951e-03
## 2015-05-29 -0.0043833847 -0.0419110200 0.0019525726 0.007509649 1.277379e-02
## 2015-06-30 -0.0108250055 -0.0297464970 -0.0316784407 0.004171671 -2.052093e-02
## 2015-07-31 0.0085842148 -0.0651781257 0.0201141723 -0.027375517 2.233772e-02
## 2015-08-31 -0.0033638194 -0.0925124668 -0.0771523273 -0.047268345 -6.288669e-02
## 2015-09-30 0.0080818217 -0.0318248523 -0.0451948066 -0.038464799 -2.584705e-02
## 2015-10-30 0.0006853845 0.0618082331 0.0640258814 0.063589878 8.163505e-02
## 2015-11-30 -0.0038981617 -0.0255604030 -0.0075559609 0.024414954 3.648704e-03
## 2015-12-31 -0.0019191601 -0.0389471020 -0.0235949460 -0.052156758 -1.743365e-02
## 2016-01-29 0.0123294789 -0.0516368254 -0.0567578149 -0.060306689 -5.106865e-02
## 2016-02-29 0.0088319300 -0.0082114554 -0.0339139897 0.020604949 -8.265769e-04
## 2016-03-31 0.0087088708 0.1218789852 0.0637457739 0.089910260 6.510007e-02
## 2016-04-29 0.0025461146 0.0040793491 0.0219749289 0.021044238 3.933736e-03
## 2016-05-31 0.0001357437 -0.0376286433 -0.0008558782 0.004397116 1.686829e-02
## 2016-06-30 0.0191666728 0.0445823386 -0.0244916202 0.008292550 3.470052e-03
## 2016-07-29 0.0054297811 0.0524419089 0.0390001141 0.049348371 3.582166e-02
## 2016-08-31 -0.0021562627 0.0087989755 0.0053269456 0.011260829 1.197301e-03
## 2016-09-30 0.0005158048 0.0248726900 0.0132791585 0.008614876 5.757072e-05
## 2016-10-31 -0.0082052308 -0.0083120694 -0.0224038330 -0.038134929 -1.748905e-02
## 2016-11-30 -0.0259894448 -0.0451619603 -0.0179741467 0.125246366 3.617599e-02
## 2016-12-30 0.0025378099 -0.0025299463 0.0267025268 0.031492233 2.006940e-02
## 2017-01-31 0.0021263343 0.0644315195 0.0323819616 -0.012144276 1.773623e-02
## 2017-02-28 0.0064377606 0.0172576608 0.0118364721 0.013428623 3.853934e-02
## 2017-03-31 -0.0005527881 0.0361891043 0.0318057896 -0.006532958 1.249307e-03
## 2017-04-28 0.0090290824 0.0168665113 0.0239521397 0.005107774 9.877017e-03
## 2017-05-31 0.0068477752 0.0280599834 0.0348102595 -0.022862689 1.401423e-02
## 2017-06-30 -0.0001826963 0.0092236560 0.0029559982 0.029151874 6.354832e-03
## 2017-07-31 0.0033344687 0.0565944397 0.0261877263 0.007481738 2.034579e-02
## 2017-08-31 0.0093692439 0.0232437740 -0.0004482935 -0.027564791 2.913448e-03
## 2017-09-29 -0.0057325044 -0.0004461961 0.0233429133 0.082321138 1.994915e-02
## 2017-10-31 0.0009780905 0.0322784749 0.0166536621 0.005916547 2.329061e-02
## 2017-11-30 -0.0014841430 -0.0038969524 0.0068698379 0.036913286 3.010826e-02
## 2017-12-29 0.0047403701 0.0369254897 0.0133982062 -0.003731136 1.205487e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398345e-05 0.0001042114 4.178228e-05 -7.811897e-05 -9.031071e-06
## EEM 1.042114e-04 0.0017547123 1.039018e-03 6.437735e-04 6.795431e-04
## EFA 4.178228e-05 0.0010390178 1.064237e-03 6.490308e-04 6.975407e-04
## IJS -7.811897e-05 0.0006437735 6.490308e-04 1.565450e-03 8.290248e-04
## SPY -9.031071e-06 0.0006795431 6.975407e-04 8.290248e-04 7.408271e-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,] 0.0003874164 0.009257151 0.005815634 0.005684469 0.002330248rowSums(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")
asset_returns_wide_tbl## AGG EEM EFA IJS SPY
## 2013-01-31 -0.0062313750 -0.0029354630 0.0366063075 0.052133543 4.992272e-02
## 2013-02-28 0.0058912661 -0.0231051173 -0.0129694791 0.016175455 1.267848e-02
## 2013-03-28 0.0009850712 -0.0102351227 0.0129694791 0.040258194 3.726772e-02
## 2013-04-30 0.0096393383 0.0120849026 0.0489678953 0.001222163 1.903030e-02
## 2013-05-31 -0.0202136301 -0.0494837218 -0.0306558616 0.041976486 2.333515e-02
## 2013-06-28 -0.0157790017 -0.0547282663 -0.0271442942 -0.001403043 -1.343435e-02
## 2013-07-31 0.0026873392 0.0131597606 0.0518602606 0.063541452 5.038578e-02
## 2013-08-30 -0.0082978167 -0.0257054834 -0.0197462899 -0.034743279 -3.045103e-02
## 2013-09-30 0.0111446506 0.0695885319 0.0753386693 0.063873556 3.115622e-02
## 2013-10-31 0.0082914658 0.0408614153 0.0320816335 0.034234195 4.526667e-02
## 2013-11-29 -0.0025100362 -0.0025941415 0.0054495424 0.041660925 2.920651e-02
## 2013-12-31 -0.0055829044 -0.0040741329 0.0215281336 0.012892370 2.559638e-02
## 2014-01-31 0.0152914329 -0.0903229138 -0.0534133024 -0.035775319 -3.588453e-02
## 2014-02-28 0.0037566444 0.0332207850 0.0595051622 0.045257568 4.451019e-02
## 2014-03-31 -0.0014808095 0.0380215801 -0.0046026433 0.013314955 8.261218e-03
## 2014-04-30 0.0081829052 0.0077728584 0.0165291408 -0.023184279 6.927471e-03
## 2014-05-30 0.0117218179 0.0290911880 0.0158286522 0.006205384 2.294109e-02
## 2014-06-30 -0.0005758743 0.0237337214 0.0091654820 0.037718567 2.043479e-02
## 2014-07-31 -0.0025122026 0.0135557911 -0.0263800066 -0.052009454 -1.352855e-02
## 2014-08-29 0.0114307715 0.0279046807 0.0018006511 0.043658288 3.870465e-02
## 2014-09-30 -0.0061673311 -0.0808569014 -0.0395984874 -0.061260692 -1.389219e-02
## 2014-10-31 0.0105844686 0.0140965659 -0.0026548903 0.068874818 2.327788e-02
## 2014-11-28 0.0065489703 -0.0155414106 0.0006251511 0.004773794 2.710122e-02
## 2014-12-31 0.0014750949 -0.0404421120 -0.0407465688 0.025295977 -2.539838e-03
## 2015-01-30 0.0203152692 -0.0068958566 0.0062263403 -0.054628351 -3.007708e-02
## 2015-02-27 -0.0089879221 0.0431362586 0.0614508539 0.056914568 5.468224e-02
## 2015-03-31 0.0037398053 -0.0150863686 -0.0143889389 0.010156389 -1.583045e-02
## 2015-04-30 -0.0032334700 0.0662814223 0.0358165822 -0.018417519 9.785951e-03
## 2015-05-29 -0.0043833847 -0.0419110200 0.0019525726 0.007509649 1.277379e-02
## 2015-06-30 -0.0108250055 -0.0297464970 -0.0316784407 0.004171671 -2.052093e-02
## 2015-07-31 0.0085842148 -0.0651781257 0.0201141723 -0.027375517 2.233772e-02
## 2015-08-31 -0.0033638194 -0.0925124668 -0.0771523273 -0.047268345 -6.288669e-02
## 2015-09-30 0.0080818217 -0.0318248523 -0.0451948066 -0.038464799 -2.584705e-02
## 2015-10-30 0.0006853845 0.0618082331 0.0640258814 0.063589878 8.163505e-02
## 2015-11-30 -0.0038981617 -0.0255604030 -0.0075559609 0.024414954 3.648704e-03
## 2015-12-31 -0.0019191601 -0.0389471020 -0.0235949460 -0.052156758 -1.743365e-02
## 2016-01-29 0.0123294789 -0.0516368254 -0.0567578149 -0.060306689 -5.106865e-02
## 2016-02-29 0.0088319300 -0.0082114554 -0.0339139897 0.020604949 -8.265769e-04
## 2016-03-31 0.0087088708 0.1218789852 0.0637457739 0.089910260 6.510007e-02
## 2016-04-29 0.0025461146 0.0040793491 0.0219749289 0.021044238 3.933736e-03
## 2016-05-31 0.0001357437 -0.0376286433 -0.0008558782 0.004397116 1.686829e-02
## 2016-06-30 0.0191666728 0.0445823386 -0.0244916202 0.008292550 3.470052e-03
## 2016-07-29 0.0054297811 0.0524419089 0.0390001141 0.049348371 3.582166e-02
## 2016-08-31 -0.0021562627 0.0087989755 0.0053269456 0.011260829 1.197301e-03
## 2016-09-30 0.0005158048 0.0248726900 0.0132791585 0.008614876 5.757072e-05
## 2016-10-31 -0.0082052308 -0.0083120694 -0.0224038330 -0.038134929 -1.748905e-02
## 2016-11-30 -0.0259894448 -0.0451619603 -0.0179741467 0.125246366 3.617599e-02
## 2016-12-30 0.0025378099 -0.0025299463 0.0267025268 0.031492233 2.006940e-02
## 2017-01-31 0.0021263343 0.0644315195 0.0323819616 -0.012144276 1.773623e-02
## 2017-02-28 0.0064377606 0.0172576608 0.0118364721 0.013428623 3.853934e-02
## 2017-03-31 -0.0005527881 0.0361891043 0.0318057896 -0.006532958 1.249307e-03
## 2017-04-28 0.0090290824 0.0168665113 0.0239521397 0.005107774 9.877017e-03
## 2017-05-31 0.0068477752 0.0280599834 0.0348102595 -0.022862689 1.401423e-02
## 2017-06-30 -0.0001826963 0.0092236560 0.0029559982 0.029151874 6.354832e-03
## 2017-07-31 0.0033344687 0.0565944397 0.0261877263 0.007481738 2.034579e-02
## 2017-08-31 0.0093692439 0.0232437740 -0.0004482935 -0.027564791 2.913448e-03
## 2017-09-29 -0.0057325044 -0.0004461961 0.0233429133 0.082321138 1.994915e-02
## 2017-10-31 0.0009780905 0.0322784749 0.0166536621 0.005916547 2.329061e-02
## 2017-11-30 -0.0014841430 -0.0038969524 0.0068698379 0.036913286 3.010826e-02
## 2017-12-29 0.0047403701 0.0369254897 0.0133982062 -0.003731136 1.205487e-02# Custom function
calculate_component_contribution <- function(.data, w) {
# Covariance of asset returns
covariance_matrix <- cov(.data)
# 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
Column Chart of component Contribution and Weight
asset_returns_wide_tbl %>%
calculate_component_contribution(w = c(0.25,0.25,0.2,0.2,0.1)) %>%
pivot_longer(cols = everything(), names_to = "Asset", values_to = "Contribution")%>%
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")
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") +
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)
## 6 Rolling Component Contribution