Week 14: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Ryan Berg
2024-11-24
# 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 -0.0062318388 -0.0029353531 0.0366062066 0.052133194 4.992336e-02
## 2013-02-28 0.0058914520 -0.0231052330 -0.0129695687 0.016175347 1.267798e-02
## 2013-03-28 0.0009851637 -0.0102350107 0.0129695687 0.040257887 3.726749e-02
## 2013-04-30 0.0096391531 0.0120847911 0.0489674545 0.001222668 1.903072e-02
## 2013-05-31 -0.0202140044 -0.0494833772 -0.0306553350 0.041976377 2.333503e-02
## 2013-06-28 -0.0157784372 -0.0547285103 -0.0271445615 -0.001403043 -1.343423e-02
## 2013-07-31 0.0026870543 0.0131599478 0.0518603476 0.063541349 5.038588e-02
## 2013-08-30 -0.0082973395 -0.0257057991 -0.0197464655 -0.034743276 -3.045114e-02
## 2013-09-30 0.0111435118 0.0695890226 0.0753387580 0.063873462 3.115588e-02
## 2013-10-31 0.0082922221 0.0408614058 0.0320816335 0.034234195 4.526636e-02
## 2013-11-29 -0.0025094722 -0.0025940269 0.0054495424 0.041660925 2.920724e-02
## 2013-12-31 -0.0055837520 -0.0040743604 0.0215281336 0.012892046 2.559627e-02
## 2014-01-31 0.0152919957 -0.0903227778 -0.0534132206 -0.035775331 -3.588484e-02
## 2014-02-28 0.0037567361 0.0332202922 0.0595047722 0.045257503 4.451040e-02
## 2014-03-31 -0.0014815519 0.0380219391 -0.0046024125 0.013315276 8.261611e-03
## 2014-04-30 0.0081833688 0.0077726260 0.0165294466 -0.023184119 6.927566e-03
## 2014-05-30 0.0117218169 0.0290914162 0.0158282739 0.006205222 2.294079e-02
## 2014-06-30 -0.0005756920 0.0237337188 0.0091655576 0.037718725 2.043497e-02
## 2014-07-31 -0.0025126586 0.0135555730 -0.0263800086 -0.052009450 -1.352892e-02
## 2014-08-29 0.0114313154 0.0279046837 0.0018006513 0.043657894 3.870483e-02
## 2014-09-30 -0.0061675106 -0.0808567961 -0.0395984113 -0.061260214 -1.389247e-02
## 2014-10-31 0.0105841970 0.0140965659 -0.0026548903 0.068874574 2.327788e-02
## 2014-11-28 0.0065494174 -0.0155416393 0.0006253098 0.004773949 2.710122e-02
## 2014-12-31 0.0014744702 -0.0404420024 -0.0407469754 0.025295524 -2.539662e-03
## 2015-01-30 0.0203154493 -0.0068954378 0.0062268346 -0.054627737 -3.007726e-02
## 2015-02-27 -0.0089885401 0.0431360737 0.0614504530 0.056914555 5.468199e-02
## 2015-03-31 0.0037402471 -0.0150863669 -0.0143887845 0.010156164 -1.583028e-02
## 2015-04-30 -0.0032329421 0.0662815240 0.0358164310 -0.018417519 9.786039e-03
## 2015-05-29 -0.0043832065 -0.0419112382 0.0019529501 0.007509949 1.277413e-02
## 2015-06-30 -0.0108254481 -0.0297467314 -0.0316789785 0.004171296 -2.052118e-02
## 2015-07-31 0.0085843035 -0.0651779538 0.0201144838 -0.027375519 2.233755e-02
## 2015-08-31 -0.0033634631 -0.0925122670 -0.0771524098 -0.047268188 -6.288643e-02
## 2015-09-30 0.0080810235 -0.0318249895 -0.0451948966 -0.038464796 -2.584714e-02
## 2015-10-30 0.0006855612 0.0618082331 0.0640260539 0.063589951 8.163479e-02
## 2015-11-30 -0.0038982509 -0.0255605396 -0.0075557978 0.024415027 3.648620e-03
## 2015-12-31 -0.0019188056 -0.0389468944 -0.0235954429 -0.052156908 -1.743331e-02
## 2016-01-29 0.0123299162 -0.0516368216 -0.0567576577 -0.060306684 -5.106874e-02
## 2016-02-29 0.0088318385 -0.0082116810 -0.0339139958 0.020604695 -8.263021e-04
## 2016-03-31 0.0087083502 0.1218791360 0.0637459567 0.089910352 6.510015e-02
## 2016-04-29 0.0025465444 0.0040793491 0.0219749289 0.021044615 3.933479e-03
## 2016-05-31 0.0001352282 -0.0376285743 -0.0008561300 0.004397040 1.686855e-02
## 2016-06-30 0.0191666761 0.0445821375 -0.0244914543 0.008292177 3.469549e-03
## 2016-07-29 0.0054295306 0.0524425421 0.0390002001 0.049348449 3.582207e-02
## 2016-08-31 -0.0021557596 0.0087982260 0.0053268633 0.011261109 1.196978e-03
## 2016-09-30 0.0005160566 0.0248731807 0.0132793221 0.008614736 5.773221e-05
## 2016-10-31 -0.0082053127 -0.0083124950 -0.0224039973 -0.038134998 -1.748914e-02
## 2016-11-30 -0.0259896119 -0.0451615214 -0.0179741483 0.125246556 3.617607e-02
## 2016-12-30 0.0025378964 -0.0025300097 0.0267027760 0.031491796 2.006933e-02
## 2017-01-31 0.0021258151 0.0644312672 0.0323817970 -0.012143968 1.773631e-02
## 2017-02-28 0.0064381065 0.0172579571 0.0118365508 0.013428745 3.853949e-02
## 2017-03-31 -0.0005527881 0.0361888681 0.0318056345 -0.006533390 1.248867e-03
## 2017-04-28 0.0090289972 0.0168663993 0.0239522905 0.005108329 9.877456e-03
## 2017-05-31 0.0068477758 0.0280600953 0.0348101850 -0.022862934 1.401416e-02
## 2017-06-30 -0.0001828656 0.0092236560 0.0029558548 0.029151872 6.354690e-03
## 2017-07-31 0.0033343008 0.0565944397 0.0261878698 0.007481555 2.034579e-02
## 2017-08-31 0.0093689136 0.0232438736 -0.0004482236 -0.027564795 2.913656e-03
## 2017-09-29 -0.0057315843 -0.0004461961 0.0233429117 0.082321953 1.994901e-02
## 2017-10-31 0.0009777545 0.0322784718 0.0166535938 0.005915857 2.329068e-02
## 2017-11-30 -0.0014838910 -0.0038969521 0.0068699713 0.036913176 3.010813e-02
## 2017-12-29 0.0047402860 0.0369252995 0.0133983361 -0.003731247 1.205493e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398398e-05 0.0001042076 4.178037e-05 -7.812141e-05 -9.033462e-06
## EEM 1.042076e-04 0.0017547126 1.039018e-03 6.437746e-04 6.795440e-04
## EFA 4.178037e-05 0.0010390184 1.064238e-03 6.490318e-04 6.975416e-04
## IJS -7.812141e-05 0.0006437746 6.490318e-04 1.565448e-03 8.290252e-04
## SPY -9.033462e-06 0.0006795440 6.975416e-04 8.290252e-04 7.408286e-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,] 0.0003873959 0.009257152 0.005815638 0.005684469 0.00233025rowSums(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 -0.0062318388 -0.0029353531 0.0366062066 0.052133194 4.992336e-02
## 2013-02-28 0.0058914520 -0.0231052330 -0.0129695687 0.016175347 1.267798e-02
## 2013-03-28 0.0009851637 -0.0102350107 0.0129695687 0.040257887 3.726749e-02
## 2013-04-30 0.0096391531 0.0120847911 0.0489674545 0.001222668 1.903072e-02
## 2013-05-31 -0.0202140044 -0.0494833772 -0.0306553350 0.041976377 2.333503e-02
## 2013-06-28 -0.0157784372 -0.0547285103 -0.0271445615 -0.001403043 -1.343423e-02
## 2013-07-31 0.0026870543 0.0131599478 0.0518603476 0.063541349 5.038588e-02
## 2013-08-30 -0.0082973395 -0.0257057991 -0.0197464655 -0.034743276 -3.045114e-02
## 2013-09-30 0.0111435118 0.0695890226 0.0753387580 0.063873462 3.115588e-02
## 2013-10-31 0.0082922221 0.0408614058 0.0320816335 0.034234195 4.526636e-02
## 2013-11-29 -0.0025094722 -0.0025940269 0.0054495424 0.041660925 2.920724e-02
## 2013-12-31 -0.0055837520 -0.0040743604 0.0215281336 0.012892046 2.559627e-02
## 2014-01-31 0.0152919957 -0.0903227778 -0.0534132206 -0.035775331 -3.588484e-02
## 2014-02-28 0.0037567361 0.0332202922 0.0595047722 0.045257503 4.451040e-02
## 2014-03-31 -0.0014815519 0.0380219391 -0.0046024125 0.013315276 8.261611e-03
## 2014-04-30 0.0081833688 0.0077726260 0.0165294466 -0.023184119 6.927566e-03
## 2014-05-30 0.0117218169 0.0290914162 0.0158282739 0.006205222 2.294079e-02
## 2014-06-30 -0.0005756920 0.0237337188 0.0091655576 0.037718725 2.043497e-02
## 2014-07-31 -0.0025126586 0.0135555730 -0.0263800086 -0.052009450 -1.352892e-02
## 2014-08-29 0.0114313154 0.0279046837 0.0018006513 0.043657894 3.870483e-02
## 2014-09-30 -0.0061675106 -0.0808567961 -0.0395984113 -0.061260214 -1.389247e-02
## 2014-10-31 0.0105841970 0.0140965659 -0.0026548903 0.068874574 2.327788e-02
## 2014-11-28 0.0065494174 -0.0155416393 0.0006253098 0.004773949 2.710122e-02
## 2014-12-31 0.0014744702 -0.0404420024 -0.0407469754 0.025295524 -2.539662e-03
## 2015-01-30 0.0203154493 -0.0068954378 0.0062268346 -0.054627737 -3.007726e-02
## 2015-02-27 -0.0089885401 0.0431360737 0.0614504530 0.056914555 5.468199e-02
## 2015-03-31 0.0037402471 -0.0150863669 -0.0143887845 0.010156164 -1.583028e-02
## 2015-04-30 -0.0032329421 0.0662815240 0.0358164310 -0.018417519 9.786039e-03
## 2015-05-29 -0.0043832065 -0.0419112382 0.0019529501 0.007509949 1.277413e-02
## 2015-06-30 -0.0108254481 -0.0297467314 -0.0316789785 0.004171296 -2.052118e-02
## 2015-07-31 0.0085843035 -0.0651779538 0.0201144838 -0.027375519 2.233755e-02
## 2015-08-31 -0.0033634631 -0.0925122670 -0.0771524098 -0.047268188 -6.288643e-02
## 2015-09-30 0.0080810235 -0.0318249895 -0.0451948966 -0.038464796 -2.584714e-02
## 2015-10-30 0.0006855612 0.0618082331 0.0640260539 0.063589951 8.163479e-02
## 2015-11-30 -0.0038982509 -0.0255605396 -0.0075557978 0.024415027 3.648620e-03
## 2015-12-31 -0.0019188056 -0.0389468944 -0.0235954429 -0.052156908 -1.743331e-02
## 2016-01-29 0.0123299162 -0.0516368216 -0.0567576577 -0.060306684 -5.106874e-02
## 2016-02-29 0.0088318385 -0.0082116810 -0.0339139958 0.020604695 -8.263021e-04
## 2016-03-31 0.0087083502 0.1218791360 0.0637459567 0.089910352 6.510015e-02
## 2016-04-29 0.0025465444 0.0040793491 0.0219749289 0.021044615 3.933479e-03
## 2016-05-31 0.0001352282 -0.0376285743 -0.0008561300 0.004397040 1.686855e-02
## 2016-06-30 0.0191666761 0.0445821375 -0.0244914543 0.008292177 3.469549e-03
## 2016-07-29 0.0054295306 0.0524425421 0.0390002001 0.049348449 3.582207e-02
## 2016-08-31 -0.0021557596 0.0087982260 0.0053268633 0.011261109 1.196978e-03
## 2016-09-30 0.0005160566 0.0248731807 0.0132793221 0.008614736 5.773221e-05
## 2016-10-31 -0.0082053127 -0.0083124950 -0.0224039973 -0.038134998 -1.748914e-02
## 2016-11-30 -0.0259896119 -0.0451615214 -0.0179741483 0.125246556 3.617607e-02
## 2016-12-30 0.0025378964 -0.0025300097 0.0267027760 0.031491796 2.006933e-02
## 2017-01-31 0.0021258151 0.0644312672 0.0323817970 -0.012143968 1.773631e-02
## 2017-02-28 0.0064381065 0.0172579571 0.0118365508 0.013428745 3.853949e-02
## 2017-03-31 -0.0005527881 0.0361888681 0.0318056345 -0.006533390 1.248867e-03
## 2017-04-28 0.0090289972 0.0168663993 0.0239522905 0.005108329 9.877456e-03
## 2017-05-31 0.0068477758 0.0280600953 0.0348101850 -0.022862934 1.401416e-02
## 2017-06-30 -0.0001828656 0.0092236560 0.0029558548 0.029151872 6.354690e-03
## 2017-07-31 0.0033343008 0.0565944397 0.0261878698 0.007481555 2.034579e-02
## 2017-08-31 0.0093689136 0.0232438736 -0.0004482236 -0.027564795 2.913656e-03
## 2017-09-29 -0.0057315843 -0.0004461961 0.0233429117 0.082321953 1.994901e-02
## 2017-10-31 0.0009777545 0.0322784718 0.0166535938 0.005915857 2.329068e-02
## 2017-11-30 -0.0014838910 -0.0038969521 0.0068699713 0.036913176 3.010813e-02
## 2017-12-29 0.0047402860 0.0369252995 0.0133983361 -0.003731247 1.205493e-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 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)) +
theme(plot.title = element_text(hjust = 0.5)) +
theme_tq() +
labs(title = "Percent Contribution to Portfolio Volatility and Weight", y = "Percent",
x = NULL)