Week 13: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Gannon Stewart
2023-04-25
# 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 -0.0062306319 -0.0029350924 0.0366061757 0.052133040 4.992303e-02
## 2013-02-28 0.0058911593 -0.0231053950 -0.0129691395 0.016175587 1.267838e-02
## 2013-03-28 0.0009845243 -0.0102351118 0.0129691395 0.040257950 3.726836e-02
## 2013-04-30 0.0096397453 0.0120847681 0.0489679329 0.001222476 1.902962e-02
## 2013-05-31 -0.0202148068 -0.0494834238 -0.0306558102 0.041976617 2.333530e-02
## 2013-06-28 -0.0157775348 -0.0547284477 -0.0271445512 -0.001403091 -1.343421e-02
## 2013-07-31 0.0026874539 0.0131598125 0.0518606179 0.063541133 5.038614e-02
## 2013-08-30 -0.0082982301 -0.0257058122 -0.0197463849 -0.034743104 -3.045133e-02
## 2013-09-30 0.0111436453 0.0695890421 0.0753385007 0.063873514 3.115605e-02
## 2013-10-31 0.0082922834 0.0408612799 0.0320817073 0.034233892 4.526603e-02
## 2013-11-29 -0.0025098786 -0.0025941888 0.0054497573 0.041661214 2.920708e-02
## 2013-12-31 -0.0055828202 -0.0040740977 0.0215280098 0.012892145 2.559670e-02
## 2014-01-31 0.0152910874 -0.0903227907 -0.0534134386 -0.035775144 -3.588462e-02
## 2014-02-28 0.0037572021 0.0332206166 0.0595051909 0.045256946 4.451019e-02
## 2014-03-31 -0.0014817567 0.0380218568 -0.0046027569 0.013315383 8.261304e-03
## 2014-04-30 0.0081832844 0.0077726767 0.0165295734 -0.023184057 6.927086e-03
## 2014-05-30 0.0117219155 0.0290910706 0.0158282756 0.006205138 2.294165e-02
## 2014-06-30 -0.0005759939 0.0237339251 0.0091652306 0.037718891 2.043435e-02
## 2014-07-31 -0.0025121621 0.0135553808 -0.0263795809 -0.052009399 -1.352859e-02
## 2014-08-29 0.0114310309 0.0279047915 0.0018002278 0.043657667 3.870472e-02
## 2014-09-30 -0.0061675020 -0.0808568916 -0.0395983087 -0.061260226 -1.389208e-02
## 2014-10-31 0.0105846887 0.0140967699 -0.0026548127 0.068874846 2.327744e-02
## 2014-11-28 0.0065484188 -0.0155414346 0.0006253148 0.004773623 2.710147e-02
## 2014-12-31 0.0014752012 -0.0404420932 -0.0407466701 0.025295689 -2.539942e-03
## 2015-01-30 0.0203154344 -0.0068956260 0.0062265031 -0.054628070 -3.007721e-02
## 2015-02-27 -0.0089880866 0.0431358088 0.0614506029 0.056914746 5.468230e-02
## 2015-03-31 0.0037400788 -0.0150862412 -0.0143887693 0.010156418 -1.583039e-02
## 2015-04-30 -0.0032328950 0.0662813542 0.0358164231 -0.018417774 9.786066e-03
## 2015-05-29 -0.0043837555 -0.0419107892 0.0019526919 0.007509952 1.277408e-02
## 2015-06-30 -0.0108252116 -0.0297466579 -0.0316786710 0.004171319 -2.052151e-02
## 2015-07-31 0.0085845574 -0.0651780755 0.0201145100 -0.027375320 2.233815e-02
## 2015-08-31 -0.0033636164 -0.0925124157 -0.0771525110 -0.047268233 -6.288659e-02
## 2015-09-30 0.0080810055 -0.0318248596 -0.0451948664 -0.038464844 -2.584702e-02
## 2015-10-30 0.0006853394 0.0618080610 0.0640258639 0.063589755 8.163478e-02
## 2015-11-30 -0.0038978720 -0.0255602592 -0.0075557791 0.024415330 3.648755e-03
## 2015-12-31 -0.0019189096 -0.0389471503 -0.0235951165 -0.052157030 -1.743371e-02
## 2016-01-29 0.0123297225 -0.0516366816 -0.0567577476 -0.060306852 -5.106870e-02
## 2016-02-29 0.0088318463 -0.0082115380 -0.0339138891 0.020605130 -8.264513e-04
## 2016-03-31 0.0087088852 0.1218792034 0.0637455001 0.089910297 6.510026e-02
## 2016-04-29 0.0025461086 0.0040788845 0.0219753752 0.021044214 3.933534e-03
## 2016-05-31 0.0001353674 -0.0376283948 -0.0008560587 0.004397021 1.686847e-02
## 2016-06-30 0.0191665713 0.0445823977 -0.0244917258 0.008292459 3.469808e-03
## 2016-07-29 0.0054298583 0.0524421804 0.0390001995 0.049348374 3.582195e-02
## 2016-08-31 -0.0021561182 0.0087984416 0.0053270066 0.011261139 1.196796e-03
## 2016-09-30 0.0005157718 0.0248730626 0.0132790225 0.008614622 5.813242e-05
## 2016-10-31 -0.0082056509 -0.0083123531 -0.0224037254 -0.038135055 -1.748925e-02
## 2016-11-30 -0.0259890984 -0.0451620121 -0.0179743636 0.125246568 3.617611e-02
## 2016-12-30 0.0025383600 -0.0025297675 0.0267029495 0.031491998 2.006901e-02
## 2017-01-31 0.0021262975 0.0644314144 0.0323817944 -0.012144399 1.773628e-02
## 2017-02-28 0.0064372557 0.0172578913 0.0118363811 0.013429306 3.853948e-02
## 2017-03-31 -0.0005531165 0.0361887638 0.0318056750 -0.006532896 1.249205e-03
## 2017-04-28 0.0090296920 0.0168665141 0.0239523104 0.005107519 9.877324e-03
## 2017-05-31 0.0068473289 0.0280599633 0.0348101251 -0.022862494 1.401398e-02
## 2017-06-30 -0.0001825774 0.0092238315 0.0029558687 0.029151651 6.354851e-03
## 2017-07-31 0.0033343782 0.0565943842 0.0261880413 0.007481124 2.034599e-02
## 2017-08-31 0.0093692250 0.0232438852 -0.0004484364 -0.027564384 2.913193e-03
## 2017-09-29 -0.0057324393 -0.0004460776 0.0233427746 0.082321842 1.994919e-02
## 2017-10-31 0.0009780437 0.0322784075 0.0166538426 0.005915767 2.329072e-02
## 2017-11-30 -0.0014841321 -0.0038969506 0.0068700026 0.036913299 3.010792e-02
## 2017-12-29 0.0047405248 0.0369251471 0.0133982350 -0.003730781 1.205490e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398342e-05 0.0001042115 0.0000417841 -7.811823e-05 -9.030912e-06
## EEM 1.042115e-04 0.0017547117 0.0010390168 6.437728e-04 6.795428e-04
## EFA 4.178410e-05 0.0010390168 0.0010642377 6.490277e-04 6.975406e-04
## IJS -7.811823e-05 0.0006437728 0.0006490277 1.565448e-03 8.290245e-04
## SPY -9.030912e-06 0.0006795428 0.0006975406 8.290245e-04 7.408298e-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,] 0.0003874223 0.009257148 0.005815633 0.005684461 0.002330249rowSums(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
# 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 -0.0062306319 -0.0029350924 0.0366061757 0.052133040 4.992303e-02
## 2013-02-28 0.0058911593 -0.0231053950 -0.0129691395 0.016175587 1.267838e-02
## 2013-03-28 0.0009845243 -0.0102351118 0.0129691395 0.040257950 3.726836e-02
## 2013-04-30 0.0096397453 0.0120847681 0.0489679329 0.001222476 1.902962e-02
## 2013-05-31 -0.0202148068 -0.0494834238 -0.0306558102 0.041976617 2.333530e-02
## 2013-06-28 -0.0157775348 -0.0547284477 -0.0271445512 -0.001403091 -1.343421e-02
## 2013-07-31 0.0026874539 0.0131598125 0.0518606179 0.063541133 5.038614e-02
## 2013-08-30 -0.0082982301 -0.0257058122 -0.0197463849 -0.034743104 -3.045133e-02
## 2013-09-30 0.0111436453 0.0695890421 0.0753385007 0.063873514 3.115605e-02
## 2013-10-31 0.0082922834 0.0408612799 0.0320817073 0.034233892 4.526603e-02
## 2013-11-29 -0.0025098786 -0.0025941888 0.0054497573 0.041661214 2.920708e-02
## 2013-12-31 -0.0055828202 -0.0040740977 0.0215280098 0.012892145 2.559670e-02
## 2014-01-31 0.0152910874 -0.0903227907 -0.0534134386 -0.035775144 -3.588462e-02
## 2014-02-28 0.0037572021 0.0332206166 0.0595051909 0.045256946 4.451019e-02
## 2014-03-31 -0.0014817567 0.0380218568 -0.0046027569 0.013315383 8.261304e-03
## 2014-04-30 0.0081832844 0.0077726767 0.0165295734 -0.023184057 6.927086e-03
## 2014-05-30 0.0117219155 0.0290910706 0.0158282756 0.006205138 2.294165e-02
## 2014-06-30 -0.0005759939 0.0237339251 0.0091652306 0.037718891 2.043435e-02
## 2014-07-31 -0.0025121621 0.0135553808 -0.0263795809 -0.052009399 -1.352859e-02
## 2014-08-29 0.0114310309 0.0279047915 0.0018002278 0.043657667 3.870472e-02
## 2014-09-30 -0.0061675020 -0.0808568916 -0.0395983087 -0.061260226 -1.389208e-02
## 2014-10-31 0.0105846887 0.0140967699 -0.0026548127 0.068874846 2.327744e-02
## 2014-11-28 0.0065484188 -0.0155414346 0.0006253148 0.004773623 2.710147e-02
## 2014-12-31 0.0014752012 -0.0404420932 -0.0407466701 0.025295689 -2.539942e-03
## 2015-01-30 0.0203154344 -0.0068956260 0.0062265031 -0.054628070 -3.007721e-02
## 2015-02-27 -0.0089880866 0.0431358088 0.0614506029 0.056914746 5.468230e-02
## 2015-03-31 0.0037400788 -0.0150862412 -0.0143887693 0.010156418 -1.583039e-02
## 2015-04-30 -0.0032328950 0.0662813542 0.0358164231 -0.018417774 9.786066e-03
## 2015-05-29 -0.0043837555 -0.0419107892 0.0019526919 0.007509952 1.277408e-02
## 2015-06-30 -0.0108252116 -0.0297466579 -0.0316786710 0.004171319 -2.052151e-02
## 2015-07-31 0.0085845574 -0.0651780755 0.0201145100 -0.027375320 2.233815e-02
## 2015-08-31 -0.0033636164 -0.0925124157 -0.0771525110 -0.047268233 -6.288659e-02
## 2015-09-30 0.0080810055 -0.0318248596 -0.0451948664 -0.038464844 -2.584702e-02
## 2015-10-30 0.0006853394 0.0618080610 0.0640258639 0.063589755 8.163478e-02
## 2015-11-30 -0.0038978720 -0.0255602592 -0.0075557791 0.024415330 3.648755e-03
## 2015-12-31 -0.0019189096 -0.0389471503 -0.0235951165 -0.052157030 -1.743371e-02
## 2016-01-29 0.0123297225 -0.0516366816 -0.0567577476 -0.060306852 -5.106870e-02
## 2016-02-29 0.0088318463 -0.0082115380 -0.0339138891 0.020605130 -8.264513e-04
## 2016-03-31 0.0087088852 0.1218792034 0.0637455001 0.089910297 6.510026e-02
## 2016-04-29 0.0025461086 0.0040788845 0.0219753752 0.021044214 3.933534e-03
## 2016-05-31 0.0001353674 -0.0376283948 -0.0008560587 0.004397021 1.686847e-02
## 2016-06-30 0.0191665713 0.0445823977 -0.0244917258 0.008292459 3.469808e-03
## 2016-07-29 0.0054298583 0.0524421804 0.0390001995 0.049348374 3.582195e-02
## 2016-08-31 -0.0021561182 0.0087984416 0.0053270066 0.011261139 1.196796e-03
## 2016-09-30 0.0005157718 0.0248730626 0.0132790225 0.008614622 5.813242e-05
## 2016-10-31 -0.0082056509 -0.0083123531 -0.0224037254 -0.038135055 -1.748925e-02
## 2016-11-30 -0.0259890984 -0.0451620121 -0.0179743636 0.125246568 3.617611e-02
## 2016-12-30 0.0025383600 -0.0025297675 0.0267029495 0.031491998 2.006901e-02
## 2017-01-31 0.0021262975 0.0644314144 0.0323817944 -0.012144399 1.773628e-02
## 2017-02-28 0.0064372557 0.0172578913 0.0118363811 0.013429306 3.853948e-02
## 2017-03-31 -0.0005531165 0.0361887638 0.0318056750 -0.006532896 1.249205e-03
## 2017-04-28 0.0090296920 0.0168665141 0.0239523104 0.005107519 9.877324e-03
## 2017-05-31 0.0068473289 0.0280599633 0.0348101251 -0.022862494 1.401398e-02
## 2017-06-30 -0.0001825774 0.0092238315 0.0029558687 0.029151651 6.354851e-03
## 2017-07-31 0.0033343782 0.0565943842 0.0261880413 0.007481124 2.034599e-02
## 2017-08-31 0.0093692250 0.0232438852 -0.0004484364 -0.027564384 2.913193e-03
## 2017-09-29 -0.0057324393 -0.0004460776 0.0233427746 0.082321842 1.994919e-02
## 2017-10-31 0.0009780437 0.0322784075 0.0166538426 0.005915767 2.329072e-02
## 2017-11-30 -0.0014841321 -0.0038969506 0.0068700026 0.036913299 3.010792e-02
## 2017-12-29 0.0047405248 0.0369251471 0.0133982350 -0.003730781 1.205490e-02calculate_component_contribution <- function(.data, w) {
covariance_matrix <- cov(asset_returns_wide_tbl)
# 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_return_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 NaN NaN NaN NaN NaN5 Visualizing Component Contribution
Column Chart of Component contribution
plot_data <- asset_return_wide_tbl %>%
calculate_component_contribution(w = c(.25, .25, .2,.2, .1)) %>%
#Transform to long from
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 from
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 Potfolio Volatility and Weight",
y = "percent",
x = NULL)