Week 14: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Will Haney
2022-09-19
# 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 -0.0062307093 -0.0029352588 0.0366063164 0.052133325 4.992283e-02
## 2013-02-28 0.0058909615 -0.0231053426 -0.0129693806 0.016175558 1.267792e-02
## 2013-03-28 0.0009851049 -0.0102349956 0.0129693806 0.040257880 3.726806e-02
## 2013-04-30 0.0096392903 0.0120846592 0.0489676260 0.001222538 1.903040e-02
## 2013-05-31 -0.0202140816 -0.0494834626 -0.0306555956 0.041976098 2.333467e-02
## 2013-06-28 -0.0157781297 -0.0547284085 -0.0271443442 -0.001402607 -1.343408e-02
## 2013-07-31 0.0026876045 0.0131598622 0.0518602163 0.063541329 5.038617e-02
## 2013-08-30 -0.0082980766 -0.0257056404 -0.0197460608 -0.034743670 -3.045110e-02
## 2013-09-30 0.0111432449 0.0695888937 0.0753383432 0.063874084 3.115569e-02
## 2013-10-31 0.0082922937 0.0408612923 0.0320818242 0.034233811 4.526662e-02
## 2013-11-29 -0.0025097180 -0.0025941928 0.0054495177 0.041661246 2.920721e-02
## 2013-12-31 -0.0055828460 -0.0040743565 0.0215279293 0.012892048 2.559625e-02
## 2014-01-31 0.0152912026 -0.0903225366 -0.0534131927 -0.035775396 -3.588506e-02
## 2014-02-28 0.0037573262 0.0332204819 0.0595050873 0.045257351 4.451046e-02
## 2014-03-31 -0.0014818452 0.0380219380 -0.0046026528 0.013315233 8.261201e-03
## 2014-04-30 0.0081838369 0.0077724933 0.0165293451 -0.023183947 6.927655e-03
## 2014-05-30 0.0117206960 0.0290911922 0.0158286006 0.006205040 2.294117e-02
## 2014-06-30 -0.0005748932 0.0237340549 0.0091653391 0.037718659 2.043435e-02
## 2014-07-31 -0.0025125343 0.0135553522 -0.0263798134 -0.052009345 -1.352822e-02
## 2014-08-29 0.0114306231 0.0279049351 0.0018005552 0.043657949 3.870440e-02
## 2014-09-30 -0.0061676372 -0.0808566440 -0.0395986182 -0.061260230 -1.389190e-02
## 2014-10-31 0.0105848358 0.0140961057 -0.0026546063 0.068874794 2.327798e-02
## 2014-11-28 0.0065490819 -0.0155408578 0.0006250839 0.004773494 2.710122e-02
## 2014-12-31 0.0014751570 -0.0404423479 -0.0407465623 0.025296062 -2.540092e-03
## 2015-01-30 0.0203149873 -0.0068957571 0.0062266198 -0.054628196 -3.007655e-02
## 2015-02-27 -0.0089878424 0.0431359626 0.0614504932 0.056914686 5.468115e-02
## 2015-03-31 0.0037398006 -0.0150862429 -0.0143888725 0.010156465 -1.583006e-02
## 2015-04-30 -0.0032327769 0.0662814118 0.0358166571 -0.018417877 9.785700e-03
## 2015-05-29 -0.0043834422 -0.0419109218 0.0019525556 0.007509862 1.277434e-02
## 2015-06-30 -0.0108258764 -0.0297469427 -0.0316788424 0.004171512 -2.052080e-02
## 2015-07-31 0.0085848688 -0.0651779659 0.0201144955 -0.027375424 2.233775e-02
## 2015-08-31 -0.0033641537 -0.0925122625 -0.0771524198 -0.047268433 -6.288680e-02
## 2015-09-30 0.0080820820 -0.0318250291 -0.0451949346 -0.038464757 -2.584716e-02
## 2015-10-30 0.0006848106 0.0618082789 0.0640259117 0.063589930 8.163490e-02
## 2015-11-30 -0.0038979835 -0.0255604049 -0.0075557282 0.024415269 3.648594e-03
## 2015-12-31 -0.0019187159 -0.0389470640 -0.0235953082 -0.052157408 -1.743368e-02
## 2016-01-29 0.0123297422 -0.0516367731 -0.0567574374 -0.060306477 -5.106860e-02
## 2016-02-29 0.0088316770 -0.0082114604 -0.0339142959 0.020605041 -8.264291e-04
## 2016-03-31 0.0087086856 0.1218788821 0.0637460333 0.089910306 6.510035e-02
## 2016-04-29 0.0025455816 0.0040792413 0.0219749278 0.021044169 3.933342e-03
## 2016-05-31 0.0001362244 -0.0376283222 -0.0008559985 0.004397257 1.686842e-02
## 2016-06-30 0.0191668877 0.0445823504 -0.0244916138 0.008292171 3.470270e-03
## 2016-07-29 0.0054294187 0.0524420950 0.0389999859 0.049348503 3.582150e-02
## 2016-08-31 -0.0021565278 0.0087987255 0.0053271858 0.011261130 1.197056e-03
## 2016-09-30 0.0005161299 0.0248725391 0.0132789949 0.008614594 5.786201e-05
## 2016-10-31 -0.0082052793 -0.0083122655 -0.0224035823 -0.038134666 -1.748890e-02
## 2016-11-30 -0.0259891726 -0.0451615672 -0.0179744875 0.125246117 3.617583e-02
## 2016-12-30 0.0025374253 -0.0025300489 0.0267028177 0.031491556 2.006922e-02
## 2017-01-31 0.0021266671 0.0644315409 0.0323820788 -0.012143517 1.773641e-02
## 2017-02-28 0.0064376907 0.0172577131 0.0118363492 0.013428770 3.853926e-02
## 2017-03-31 -0.0005527706 0.0361890338 0.0318056710 -0.006533058 1.249344e-03
## 2017-04-28 0.0090292555 0.0168664077 0.0239521757 0.005107702 9.877227e-03
## 2017-05-31 0.0068474445 0.0280597877 0.0348103694 -0.022862612 1.401427e-02
## 2017-06-30 -0.0001828290 0.0092239939 0.0029557777 0.029152077 6.354649e-03
## 2017-07-31 0.0033345803 0.0565943133 0.0261880981 0.007481341 2.034580e-02
## 2017-08-31 0.0093688942 0.0232439210 -0.0004486475 -0.027564708 2.913287e-03
## 2017-09-29 -0.0057322650 -0.0004463619 0.0233428866 0.082321610 1.994914e-02
## 2017-10-31 0.0009780894 0.0322784018 0.0166537225 0.005916215 2.329061e-02
## 2017-11-30 -0.0014841472 -0.0038967208 0.0068700998 0.036913256 3.010848e-02
## 2017-12-29 0.0047405986 0.0369250326 0.0133980709 -0.003731078 1.205455e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398274e-05 0.0001042096 4.178302e-05 -7.811891e-05 -9.029716e-06
## EEM 1.042096e-04 0.0017547081 1.039017e-03 6.437744e-04 6.795429e-04
## EFA 4.178302e-05 0.0010390169 1.064237e-03 6.490298e-04 6.975396e-04
## IJS -7.811891e-05 0.0006437744 6.490298e-04 1.565448e-03 8.290220e-04
## SPY -9.029716e-06 0.0006795429 6.975396e-04 8.290220e-04 7.408255e-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,] 0.0234749# 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,] 0.0003874131 0.009257141 0.005815634 0.005684468 0.002330247rowSums(component_contribution)## [1] 0.0234749# 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 -0.0062307093 -0.0029352588 0.0366063164 0.052133325 4.992283e-02
## 2013-02-28 0.0058909615 -0.0231053426 -0.0129693806 0.016175558 1.267792e-02
## 2013-03-28 0.0009851049 -0.0102349956 0.0129693806 0.040257880 3.726806e-02
## 2013-04-30 0.0096392903 0.0120846592 0.0489676260 0.001222538 1.903040e-02
## 2013-05-31 -0.0202140816 -0.0494834626 -0.0306555956 0.041976098 2.333467e-02
## 2013-06-28 -0.0157781297 -0.0547284085 -0.0271443442 -0.001402607 -1.343408e-02
## 2013-07-31 0.0026876045 0.0131598622 0.0518602163 0.063541329 5.038617e-02
## 2013-08-30 -0.0082980766 -0.0257056404 -0.0197460608 -0.034743670 -3.045110e-02
## 2013-09-30 0.0111432449 0.0695888937 0.0753383432 0.063874084 3.115569e-02
## 2013-10-31 0.0082922937 0.0408612923 0.0320818242 0.034233811 4.526662e-02
## 2013-11-29 -0.0025097180 -0.0025941928 0.0054495177 0.041661246 2.920721e-02
## 2013-12-31 -0.0055828460 -0.0040743565 0.0215279293 0.012892048 2.559625e-02
## 2014-01-31 0.0152912026 -0.0903225366 -0.0534131927 -0.035775396 -3.588506e-02
## 2014-02-28 0.0037573262 0.0332204819 0.0595050873 0.045257351 4.451046e-02
## 2014-03-31 -0.0014818452 0.0380219380 -0.0046026528 0.013315233 8.261201e-03
## 2014-04-30 0.0081838369 0.0077724933 0.0165293451 -0.023183947 6.927655e-03
## 2014-05-30 0.0117206960 0.0290911922 0.0158286006 0.006205040 2.294117e-02
## 2014-06-30 -0.0005748932 0.0237340549 0.0091653391 0.037718659 2.043435e-02
## 2014-07-31 -0.0025125343 0.0135553522 -0.0263798134 -0.052009345 -1.352822e-02
## 2014-08-29 0.0114306231 0.0279049351 0.0018005552 0.043657949 3.870440e-02
## 2014-09-30 -0.0061676372 -0.0808566440 -0.0395986182 -0.061260230 -1.389190e-02
## 2014-10-31 0.0105848358 0.0140961057 -0.0026546063 0.068874794 2.327798e-02
## 2014-11-28 0.0065490819 -0.0155408578 0.0006250839 0.004773494 2.710122e-02
## 2014-12-31 0.0014751570 -0.0404423479 -0.0407465623 0.025296062 -2.540092e-03
## 2015-01-30 0.0203149873 -0.0068957571 0.0062266198 -0.054628196 -3.007655e-02
## 2015-02-27 -0.0089878424 0.0431359626 0.0614504932 0.056914686 5.468115e-02
## 2015-03-31 0.0037398006 -0.0150862429 -0.0143888725 0.010156465 -1.583006e-02
## 2015-04-30 -0.0032327769 0.0662814118 0.0358166571 -0.018417877 9.785700e-03
## 2015-05-29 -0.0043834422 -0.0419109218 0.0019525556 0.007509862 1.277434e-02
## 2015-06-30 -0.0108258764 -0.0297469427 -0.0316788424 0.004171512 -2.052080e-02
## 2015-07-31 0.0085848688 -0.0651779659 0.0201144955 -0.027375424 2.233775e-02
## 2015-08-31 -0.0033641537 -0.0925122625 -0.0771524198 -0.047268433 -6.288680e-02
## 2015-09-30 0.0080820820 -0.0318250291 -0.0451949346 -0.038464757 -2.584716e-02
## 2015-10-30 0.0006848106 0.0618082789 0.0640259117 0.063589930 8.163490e-02
## 2015-11-30 -0.0038979835 -0.0255604049 -0.0075557282 0.024415269 3.648594e-03
## 2015-12-31 -0.0019187159 -0.0389470640 -0.0235953082 -0.052157408 -1.743368e-02
## 2016-01-29 0.0123297422 -0.0516367731 -0.0567574374 -0.060306477 -5.106860e-02
## 2016-02-29 0.0088316770 -0.0082114604 -0.0339142959 0.020605041 -8.264291e-04
## 2016-03-31 0.0087086856 0.1218788821 0.0637460333 0.089910306 6.510035e-02
## 2016-04-29 0.0025455816 0.0040792413 0.0219749278 0.021044169 3.933342e-03
## 2016-05-31 0.0001362244 -0.0376283222 -0.0008559985 0.004397257 1.686842e-02
## 2016-06-30 0.0191668877 0.0445823504 -0.0244916138 0.008292171 3.470270e-03
## 2016-07-29 0.0054294187 0.0524420950 0.0389999859 0.049348503 3.582150e-02
## 2016-08-31 -0.0021565278 0.0087987255 0.0053271858 0.011261130 1.197056e-03
## 2016-09-30 0.0005161299 0.0248725391 0.0132789949 0.008614594 5.786201e-05
## 2016-10-31 -0.0082052793 -0.0083122655 -0.0224035823 -0.038134666 -1.748890e-02
## 2016-11-30 -0.0259891726 -0.0451615672 -0.0179744875 0.125246117 3.617583e-02
## 2016-12-30 0.0025374253 -0.0025300489 0.0267028177 0.031491556 2.006922e-02
## 2017-01-31 0.0021266671 0.0644315409 0.0323820788 -0.012143517 1.773641e-02
## 2017-02-28 0.0064376907 0.0172577131 0.0118363492 0.013428770 3.853926e-02
## 2017-03-31 -0.0005527706 0.0361890338 0.0318056710 -0.006533058 1.249344e-03
## 2017-04-28 0.0090292555 0.0168664077 0.0239521757 0.005107702 9.877227e-03
## 2017-05-31 0.0068474445 0.0280597877 0.0348103694 -0.022862612 1.401427e-02
## 2017-06-30 -0.0001828290 0.0092239939 0.0029557777 0.029152077 6.354649e-03
## 2017-07-31 0.0033345803 0.0565943133 0.0261880981 0.007481341 2.034580e-02
## 2017-08-31 0.0093688942 0.0232439210 -0.0004486475 -0.027564708 2.913287e-03
## 2017-09-29 -0.0057322650 -0.0004463619 0.0233428866 0.082321610 1.994914e-02
## 2017-10-31 0.0009780894 0.0322784018 0.0166537225 0.005916215 2.329061e-02
## 2017-11-30 -0.0014841472 -0.0038967208 0.0068700998 0.036913256 3.010848e-02
## 2017-12-29 0.0047405986 0.0369250326 0.0133980709 -0.003731078 1.205455e-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 on 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 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 = 0.5)) +
theme_tq() +
labs(title = "Percent Contribution to Portfolio Volatility and Weight", y = "Percent",
x = NULL)