Week 14: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Aalaya Elgohery
2024-11-18
# 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 -0.0062314676 -0.0029355732 0.0366062100 0.052133194 4.992311e-02
## 2013-02-28 0.0058912661 -0.0231051173 -0.0129694779 0.016175241 1.267786e-02
## 2013-03-28 0.0009847934 -0.0102354657 0.0129694779 0.040258295 3.726870e-02
## 2013-04-30 0.0096394327 0.0120850197 0.0489676317 0.001222365 1.902953e-02
## 2013-05-31 -0.0202143825 -0.0494831398 -0.0306554215 0.041976570 2.333527e-02
## 2013-06-28 -0.0157776856 -0.0547286850 -0.0271444699 -0.001403236 -1.343377e-02
## 2013-07-31 0.0026874330 0.0131600088 0.0518601691 0.063541440 5.038597e-02
## 2013-08-30 -0.0082981952 -0.0257060498 -0.0197462899 -0.034743650 -3.045181e-02
## 2013-09-30 0.0111438932 0.0695889127 0.0753385049 0.063874010 3.115600e-02
## 2013-10-31 0.0082919401 0.0408614153 0.0320817183 0.034233845 4.526669e-02
## 2013-11-29 -0.0025092846 -0.0025941415 0.0054496221 0.041661256 2.920662e-02
## 2013-12-31 -0.0055832793 -0.0040744762 0.0215279785 0.012891558 2.559638e-02
## 2014-01-31 0.0152920816 -0.0903224453 -0.0534131473 -0.035774586 -3.588402e-02
## 2014-02-28 0.0037561775 0.0332207204 0.0595049311 0.045257160 4.451018e-02
## 2014-03-31 -0.0014809947 0.0380212863 -0.0046023347 0.013315195 8.261019e-03
## 2014-04-30 0.0081833643 0.0077729759 0.0165291395 -0.023184279 6.927470e-03
## 2014-05-30 0.0117211731 0.0290913038 0.0158285760 0.006205544 2.294109e-02
## 2014-06-30 -0.0005755099 0.0237340508 0.0091651849 0.037718406 2.043478e-02
## 2014-07-31 -0.0025124757 0.0135552451 -0.0263794808 -0.052009046 -1.352864e-02
## 2014-08-29 0.0114308608 0.0279046866 0.0018004224 0.043657646 3.870465e-02
## 2014-09-30 -0.0061668757 -0.0808564624 -0.0395985666 -0.061260458 -1.389228e-02
## 2014-10-31 0.0105838326 0.0140961124 -0.0026548905 0.068874740 2.327797e-02
## 2014-11-28 0.0065489703 -0.0155410711 0.0006253892 0.004774026 2.710122e-02
## 2014-12-31 0.0014748274 -0.0404419882 -0.0407467275 0.025295522 -2.540014e-03
## 2015-01-30 0.0203151872 -0.0068958549 0.0062264224 -0.054627733 -3.007699e-02
## 2015-02-27 -0.0089884543 0.0431357892 0.0614506945 0.056914550 5.468208e-02
## 2015-03-31 0.0037405991 -0.0150861389 -0.0143889400 0.010156238 -1.583036e-02
## 2015-04-30 -0.0032330296 0.0662816405 0.0358165849 -0.018417668 9.786126e-03
## 2015-05-29 -0.0043835601 -0.0419111244 0.0019526482 0.007509874 1.277413e-02
## 2015-06-30 -0.0108258984 -0.0297467280 -0.0316786743 0.004171296 -2.052127e-02
## 2015-07-31 0.0085848419 -0.0651780710 0.0201144059 -0.027375444 2.233780e-02
## 2015-08-31 -0.0033631076 -0.0925123356 -0.0771523273 -0.047268268 -6.288651e-02
## 2015-09-30 0.0080814635 -0.0318250626 -0.0451949791 -0.038464967 -2.584723e-02
## 2015-10-30 0.0006846784 0.0618082416 0.0640259730 0.063590124 8.163496e-02
## 2015-11-30 -0.0038978977 -0.0255603382 -0.0075558800 0.024415259 3.648448e-03
## 2015-12-31 -0.0019187167 -0.0389471757 -0.0235949460 -0.052157061 -1.743391e-02
## 2016-01-29 0.0123299140 -0.0516366086 -0.0567579916 -0.060307199 -5.106831e-02
## 2016-02-29 0.0088321845 -0.0082114548 -0.0339139044 0.020605630 -8.263022e-04
## 2016-03-31 0.0087080873 0.1218790433 0.0637459510 0.089910162 6.510015e-02
## 2016-04-29 0.0025462860 0.0040791492 0.0219749270 0.021044159 3.933223e-03
## 2016-05-31 0.0001353141 -0.0376285078 -0.0008559620 0.004397191 1.686880e-02
## 2016-06-30 0.0191670958 0.0445821375 -0.0244915341 0.008292177 3.469884e-03
## 2016-07-29 0.0054294440 0.0524423541 0.0390001936 0.049348382 3.582198e-02
## 2016-08-31 -0.0021558427 0.0087984760 0.0053268624 0.011261111 1.196736e-03
## 2016-09-30 0.0005155527 0.0248727551 0.0132789138 0.008614737 5.805518e-05
## 2016-10-31 -0.0082050601 -0.0083122537 -0.0224035875 -0.038134643 -1.748905e-02
## 2016-11-30 -0.0259899572 -0.0451615271 -0.0179743144 0.125246277 3.617598e-02
## 2016-12-30 0.0025382437 -0.0025298179 0.0267027760 0.031491490 2.006924e-02
## 2017-01-31 0.0021257285 0.0644311431 0.0323817970 -0.012143536 1.773646e-02
## 2017-02-28 0.0064386220 0.0172580171 0.0118366296 0.013428929 3.853904e-02
## 2017-03-31 -0.0005532176 0.0361889820 0.0318055557 -0.006533450 1.249307e-03
## 2017-04-28 0.0090294224 0.0168662855 0.0239521415 0.005107835 9.877090e-03
## 2017-05-31 0.0068469262 0.0280599865 0.0348103340 -0.022862374 1.401437e-02
## 2017-06-30 -0.0001822732 0.0092237649 0.0029559265 0.029151437 6.354618e-03
## 2017-07-31 0.0033339626 0.0565944397 0.0261878679 0.007481739 2.034579e-02
## 2017-08-31 0.0093693321 0.0232437740 -0.0004484333 -0.027564857 2.913517e-03
## 2017-09-29 -0.0057320866 -0.0004461961 0.0233428466 0.082322245 1.994901e-02
## 2017-10-31 0.0009779226 0.0322784749 0.0166536644 0.005915628 2.329075e-02
## 2017-11-30 -0.0014841433 -0.0038968556 0.0068701724 0.036913066 3.010813e-02
## 2017-12-29 0.0047402872 0.0369253929 0.0133982693 -0.003731136 1.205499e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398418e-05 0.0001042034 4.177674e-05 -7.812449e-05 -9.035750e-06
## EEM 1.042034e-04 0.0017547086 1.039017e-03 6.437743e-04 6.795426e-04
## EFA 4.177674e-05 0.0010390173 1.064236e-03 6.490302e-04 6.975403e-04
## IJS -7.812449e-05 0.0006437743 6.490302e-04 1.565448e-03 8.290244e-04
## SPY -9.035750e-06 0.0006795426 6.975403e-04 8.290244e-04 7.408279e-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,] 0.02347486# 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,] 0.0003873695 0.009257143 0.005815632 0.005684469 0.002330248rowSums(component_contribution)## [1] 0.02347486# 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 -0.0062314676 -0.0029355732 0.0366062100 0.052133194 4.992311e-02
## 2013-02-28 0.0058912661 -0.0231051173 -0.0129694779 0.016175241 1.267786e-02
## 2013-03-28 0.0009847934 -0.0102354657 0.0129694779 0.040258295 3.726870e-02
## 2013-04-30 0.0096394327 0.0120850197 0.0489676317 0.001222365 1.902953e-02
## 2013-05-31 -0.0202143825 -0.0494831398 -0.0306554215 0.041976570 2.333527e-02
## 2013-06-28 -0.0157776856 -0.0547286850 -0.0271444699 -0.001403236 -1.343377e-02
## 2013-07-31 0.0026874330 0.0131600088 0.0518601691 0.063541440 5.038597e-02
## 2013-08-30 -0.0082981952 -0.0257060498 -0.0197462899 -0.034743650 -3.045181e-02
## 2013-09-30 0.0111438932 0.0695889127 0.0753385049 0.063874010 3.115600e-02
## 2013-10-31 0.0082919401 0.0408614153 0.0320817183 0.034233845 4.526669e-02
## 2013-11-29 -0.0025092846 -0.0025941415 0.0054496221 0.041661256 2.920662e-02
## 2013-12-31 -0.0055832793 -0.0040744762 0.0215279785 0.012891558 2.559638e-02
## 2014-01-31 0.0152920816 -0.0903224453 -0.0534131473 -0.035774586 -3.588402e-02
## 2014-02-28 0.0037561775 0.0332207204 0.0595049311 0.045257160 4.451018e-02
## 2014-03-31 -0.0014809947 0.0380212863 -0.0046023347 0.013315195 8.261019e-03
## 2014-04-30 0.0081833643 0.0077729759 0.0165291395 -0.023184279 6.927470e-03
## 2014-05-30 0.0117211731 0.0290913038 0.0158285760 0.006205544 2.294109e-02
## 2014-06-30 -0.0005755099 0.0237340508 0.0091651849 0.037718406 2.043478e-02
## 2014-07-31 -0.0025124757 0.0135552451 -0.0263794808 -0.052009046 -1.352864e-02
## 2014-08-29 0.0114308608 0.0279046866 0.0018004224 0.043657646 3.870465e-02
## 2014-09-30 -0.0061668757 -0.0808564624 -0.0395985666 -0.061260458 -1.389228e-02
## 2014-10-31 0.0105838326 0.0140961124 -0.0026548905 0.068874740 2.327797e-02
## 2014-11-28 0.0065489703 -0.0155410711 0.0006253892 0.004774026 2.710122e-02
## 2014-12-31 0.0014748274 -0.0404419882 -0.0407467275 0.025295522 -2.540014e-03
## 2015-01-30 0.0203151872 -0.0068958549 0.0062264224 -0.054627733 -3.007699e-02
## 2015-02-27 -0.0089884543 0.0431357892 0.0614506945 0.056914550 5.468208e-02
## 2015-03-31 0.0037405991 -0.0150861389 -0.0143889400 0.010156238 -1.583036e-02
## 2015-04-30 -0.0032330296 0.0662816405 0.0358165849 -0.018417668 9.786126e-03
## 2015-05-29 -0.0043835601 -0.0419111244 0.0019526482 0.007509874 1.277413e-02
## 2015-06-30 -0.0108258984 -0.0297467280 -0.0316786743 0.004171296 -2.052127e-02
## 2015-07-31 0.0085848419 -0.0651780710 0.0201144059 -0.027375444 2.233780e-02
## 2015-08-31 -0.0033631076 -0.0925123356 -0.0771523273 -0.047268268 -6.288651e-02
## 2015-09-30 0.0080814635 -0.0318250626 -0.0451949791 -0.038464967 -2.584723e-02
## 2015-10-30 0.0006846784 0.0618082416 0.0640259730 0.063590124 8.163496e-02
## 2015-11-30 -0.0038978977 -0.0255603382 -0.0075558800 0.024415259 3.648448e-03
## 2015-12-31 -0.0019187167 -0.0389471757 -0.0235949460 -0.052157061 -1.743391e-02
## 2016-01-29 0.0123299140 -0.0516366086 -0.0567579916 -0.060307199 -5.106831e-02
## 2016-02-29 0.0088321845 -0.0082114548 -0.0339139044 0.020605630 -8.263022e-04
## 2016-03-31 0.0087080873 0.1218790433 0.0637459510 0.089910162 6.510015e-02
## 2016-04-29 0.0025462860 0.0040791492 0.0219749270 0.021044159 3.933223e-03
## 2016-05-31 0.0001353141 -0.0376285078 -0.0008559620 0.004397191 1.686880e-02
## 2016-06-30 0.0191670958 0.0445821375 -0.0244915341 0.008292177 3.469884e-03
## 2016-07-29 0.0054294440 0.0524423541 0.0390001936 0.049348382 3.582198e-02
## 2016-08-31 -0.0021558427 0.0087984760 0.0053268624 0.011261111 1.196736e-03
## 2016-09-30 0.0005155527 0.0248727551 0.0132789138 0.008614737 5.805518e-05
## 2016-10-31 -0.0082050601 -0.0083122537 -0.0224035875 -0.038134643 -1.748905e-02
## 2016-11-30 -0.0259899572 -0.0451615271 -0.0179743144 0.125246277 3.617598e-02
## 2016-12-30 0.0025382437 -0.0025298179 0.0267027760 0.031491490 2.006924e-02
## 2017-01-31 0.0021257285 0.0644311431 0.0323817970 -0.012143536 1.773646e-02
## 2017-02-28 0.0064386220 0.0172580171 0.0118366296 0.013428929 3.853904e-02
## 2017-03-31 -0.0005532176 0.0361889820 0.0318055557 -0.006533450 1.249307e-03
## 2017-04-28 0.0090294224 0.0168662855 0.0239521415 0.005107835 9.877090e-03
## 2017-05-31 0.0068469262 0.0280599865 0.0348103340 -0.022862374 1.401437e-02
## 2017-06-30 -0.0001822732 0.0092237649 0.0029559265 0.029151437 6.354618e-03
## 2017-07-31 0.0033339626 0.0565944397 0.0261878679 0.007481739 2.034579e-02
## 2017-08-31 0.0093693321 0.0232437740 -0.0004484333 -0.027564857 2.913517e-03
## 2017-09-29 -0.0057320866 -0.0004461961 0.0233428466 0.082322245 1.994901e-02
## 2017-10-31 0.0009779226 0.0322784749 0.0166536644 0.005915628 2.329075e-02
## 2017-11-30 -0.0014841433 -0.0038968556 0.0068701724 0.036913066 3.010813e-02
## 2017-12-29 0.0047402872 0.0369253929 0.0133982693 -0.003731136 1.205499e-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 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")
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 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 Portfolio Volatility and Weight",
y = "Percent",
x = NULL)