Week 14: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Kyle Shearer
2023-04-17
# 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 -0.0062308973 -0.0029356242 0.0366063378 0.052133052 4.992321e-02
## 2013-02-28 0.0058917696 -0.0231052854 -0.0129693913 0.016175295 1.267813e-02
## 2013-03-28 0.0009842597 -0.0102353449 0.0129693913 0.040258641 3.726795e-02
## 2013-04-30 0.0096393114 0.0120849155 0.0489677137 0.001222502 1.903008e-02
## 2013-05-31 -0.0202143711 -0.0494833437 -0.0306555699 0.041976213 2.333518e-02
## 2013-06-28 -0.0157779683 -0.0547282638 -0.0271444801 -0.001402893 -1.343387e-02
## 2013-07-31 0.0026873488 0.0131596862 0.0518602840 0.063541668 5.038547e-02
## 2013-08-30 -0.0082977825 -0.0257056207 -0.0197462997 -0.034743927 -3.045145e-02
## 2013-09-30 0.0111435623 0.0695889134 0.0753385893 0.063873622 3.115649e-02
## 2013-10-31 0.0082923648 0.0408613952 0.0320817073 0.034234160 4.526635e-02
## 2013-11-29 -0.0025096918 -0.0025941018 0.0054497573 0.041661273 2.920686e-02
## 2013-12-31 -0.0055829008 -0.0040746191 0.0215279323 0.012892060 2.559601e-02
## 2014-01-31 0.0152916041 -0.0903225351 -0.0534133611 -0.035775378 -3.588423e-02
## 2014-02-28 0.0037569464 0.0332205572 0.0595051139 0.045257588 4.451039e-02
## 2014-03-31 -0.0014819403 0.0380218614 -0.0046025445 0.013315074 8.261115e-03
## 2014-04-30 0.0081830194 0.0077725603 0.0165292858 -0.023184383 6.927275e-03
## 2014-05-30 0.0117217348 0.0290911913 0.0158286525 0.006205221 2.294137e-02
## 2014-06-30 -0.0005754629 0.0237339556 0.0091652100 0.037718756 2.043491e-02
## 2014-07-31 -0.0025121613 0.0135555467 -0.0263797850 -0.052009244 -1.352887e-02
## 2014-08-29 0.0114306797 0.0279046023 0.0018005131 0.043657889 3.870463e-02
## 2014-09-30 -0.0061675020 -0.0808564664 -0.0395985939 -0.061260385 -1.389218e-02
## 2014-10-31 0.0105849340 0.0140961089 -0.0026548127 0.068875004 2.327806e-02
## 2014-11-28 0.0065488492 -0.0155412080 0.0006253148 0.004773682 2.710112e-02
## 2014-12-31 0.0014741052 -0.0404418564 -0.0407466701 0.025295606 -2.539767e-03
## 2015-01-30 0.0203156922 -0.0068956555 0.0062265031 -0.054627819 -3.007720e-02
## 2015-02-27 -0.0089878365 0.0431358049 0.0614506608 0.056914571 5.468203e-02
## 2015-03-31 0.0037399041 -0.0150860034 -0.0143888272 0.010156264 -1.583056e-02
## 2015-04-30 -0.0032331467 0.0662811397 0.0358165742 -0.018417754 9.786068e-03
## 2015-05-29 -0.0043832519 -0.0419108998 0.0019525408 0.007510009 1.277434e-02
## 2015-06-30 -0.0108257092 -0.0297465687 -0.0316786710 0.004171471 -2.052108e-02
## 2015-07-31 0.0085848903 -0.0651783550 0.0201143002 -0.027375528 2.233780e-02
## 2015-08-31 -0.0033640359 -0.0925121558 -0.0771523012 -0.047268394 -6.288684e-02
## 2015-09-30 0.0080814250 -0.0318252165 -0.0451949311 -0.038464677 -2.584720e-02
## 2015-10-30 0.0006855911 0.0618082470 0.0640260094 0.063589830 8.163496e-02
## 2015-11-30 -0.0038980358 -0.0255602272 -0.0075559415 0.024415326 3.648502e-03
## 2015-12-31 -0.0019191627 -0.0389471530 -0.0235952019 -0.052157269 -1.743371e-02
## 2016-01-29 0.0123298007 -0.0516366096 -0.0567576690 -0.060306770 -5.106844e-02
## 2016-02-29 0.0088317716 -0.0082115380 -0.0339139835 0.020605130 -8.262749e-04
## 2016-03-31 0.0087090469 0.1218789326 0.0637458542 0.089910375 6.510035e-02
## 2016-04-29 0.0025459487 0.0040792901 0.0219752038 0.021044346 3.933193e-03
## 2016-05-31 0.0001351970 -0.0376287047 -0.0008563104 0.004397173 1.686881e-02
## 2016-06-30 0.0191673824 0.0445825058 -0.0244913881 0.008292247 3.469641e-03
## 2016-07-29 0.0054294607 0.0524423744 0.0390001135 0.049348367 3.582187e-02
## 2016-08-31 -0.0021562743 0.0087984720 0.0053268421 0.011260870 1.197118e-03
## 2016-09-30 0.0005158448 0.0248729973 0.0132791871 0.008614747 5.773848e-05
## 2016-10-31 -0.0082050945 -0.0083123524 -0.0224037254 -0.038134761 -1.748925e-02
## 2016-11-30 -0.0259897303 -0.0451620402 -0.0179744481 0.125246339 3.617619e-02
## 2016-12-30 0.0025381882 -0.0025300922 0.0267029517 0.031491618 2.006909e-02
## 2017-01-31 0.0021261372 0.0644317961 0.0323818767 -0.012143973 1.773680e-02
## 2017-02-28 0.0064378338 0.0172577695 0.0118364598 0.013428833 3.853888e-02
## 2017-03-31 -0.0005524766 0.0361888793 0.0318056725 -0.006532724 1.249276e-03
## 2017-04-28 0.0090287971 0.0168664838 0.0239521597 0.005107708 9.877179e-03
## 2017-05-31 0.0068472455 0.0280597953 0.0348104153 -0.022862671 1.401426e-02
## 2017-06-30 -0.0001829763 0.0092239144 0.0029558502 0.029151640 6.354713e-03
## 2017-07-31 0.0033350288 0.0565943842 0.0261877742 0.007481668 2.034586e-02
## 2017-08-31 0.0093691413 0.0232438852 -0.0004481744 -0.027564741 2.913399e-03
## 2017-09-29 -0.0057320432 -0.0004463555 0.0233427189 0.082321842 1.994898e-02
## 2017-10-31 0.0009773248 0.0322786854 0.0166537732 0.005915767 2.329079e-02
## 2017-11-30 -0.0014836529 -0.0038972207 0.0068698021 0.036913524 3.010798e-02
## 2017-12-29 0.0047404514 0.0369257721 0.0133982532 -0.003731331 1.205515e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398446e-05 0.0001042121 4.178401e-05 -7.811947e-05 -9.030545e-06
## EEM 1.042121e-04 0.0017547099 1.039017e-03 6.437725e-04 6.795418e-04
## EFA 4.178401e-05 0.0010390169 1.064238e-03 6.490309e-04 6.975412e-04
## IJS -7.811947e-05 0.0006437725 6.490309e-04 1.565452e-03 8.290263e-04
## SPY -9.030545e-06 0.0006795418 6.975412e-04 8.290263e-04 7.408287e-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,] 0.000387424 0.009257141 0.005815637 0.00568447 0.002330249rowSums(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 -0.0062308973 -0.0029356242 0.0366063378 0.052133052 4.992321e-02
## 2013-02-28 0.0058917696 -0.0231052854 -0.0129693913 0.016175295 1.267813e-02
## 2013-03-28 0.0009842597 -0.0102353449 0.0129693913 0.040258641 3.726795e-02
## 2013-04-30 0.0096393114 0.0120849155 0.0489677137 0.001222502 1.903008e-02
## 2013-05-31 -0.0202143711 -0.0494833437 -0.0306555699 0.041976213 2.333518e-02
## 2013-06-28 -0.0157779683 -0.0547282638 -0.0271444801 -0.001402893 -1.343387e-02
## 2013-07-31 0.0026873488 0.0131596862 0.0518602840 0.063541668 5.038547e-02
## 2013-08-30 -0.0082977825 -0.0257056207 -0.0197462997 -0.034743927 -3.045145e-02
## 2013-09-30 0.0111435623 0.0695889134 0.0753385893 0.063873622 3.115649e-02
## 2013-10-31 0.0082923648 0.0408613952 0.0320817073 0.034234160 4.526635e-02
## 2013-11-29 -0.0025096918 -0.0025941018 0.0054497573 0.041661273 2.920686e-02
## 2013-12-31 -0.0055829008 -0.0040746191 0.0215279323 0.012892060 2.559601e-02
## 2014-01-31 0.0152916041 -0.0903225351 -0.0534133611 -0.035775378 -3.588423e-02
## 2014-02-28 0.0037569464 0.0332205572 0.0595051139 0.045257588 4.451039e-02
## 2014-03-31 -0.0014819403 0.0380218614 -0.0046025445 0.013315074 8.261115e-03
## 2014-04-30 0.0081830194 0.0077725603 0.0165292858 -0.023184383 6.927275e-03
## 2014-05-30 0.0117217348 0.0290911913 0.0158286525 0.006205221 2.294137e-02
## 2014-06-30 -0.0005754629 0.0237339556 0.0091652100 0.037718756 2.043491e-02
## 2014-07-31 -0.0025121613 0.0135555467 -0.0263797850 -0.052009244 -1.352887e-02
## 2014-08-29 0.0114306797 0.0279046023 0.0018005131 0.043657889 3.870463e-02
## 2014-09-30 -0.0061675020 -0.0808564664 -0.0395985939 -0.061260385 -1.389218e-02
## 2014-10-31 0.0105849340 0.0140961089 -0.0026548127 0.068875004 2.327806e-02
## 2014-11-28 0.0065488492 -0.0155412080 0.0006253148 0.004773682 2.710112e-02
## 2014-12-31 0.0014741052 -0.0404418564 -0.0407466701 0.025295606 -2.539767e-03
## 2015-01-30 0.0203156922 -0.0068956555 0.0062265031 -0.054627819 -3.007720e-02
## 2015-02-27 -0.0089878365 0.0431358049 0.0614506608 0.056914571 5.468203e-02
## 2015-03-31 0.0037399041 -0.0150860034 -0.0143888272 0.010156264 -1.583056e-02
## 2015-04-30 -0.0032331467 0.0662811397 0.0358165742 -0.018417754 9.786068e-03
## 2015-05-29 -0.0043832519 -0.0419108998 0.0019525408 0.007510009 1.277434e-02
## 2015-06-30 -0.0108257092 -0.0297465687 -0.0316786710 0.004171471 -2.052108e-02
## 2015-07-31 0.0085848903 -0.0651783550 0.0201143002 -0.027375528 2.233780e-02
## 2015-08-31 -0.0033640359 -0.0925121558 -0.0771523012 -0.047268394 -6.288684e-02
## 2015-09-30 0.0080814250 -0.0318252165 -0.0451949311 -0.038464677 -2.584720e-02
## 2015-10-30 0.0006855911 0.0618082470 0.0640260094 0.063589830 8.163496e-02
## 2015-11-30 -0.0038980358 -0.0255602272 -0.0075559415 0.024415326 3.648502e-03
## 2015-12-31 -0.0019191627 -0.0389471530 -0.0235952019 -0.052157269 -1.743371e-02
## 2016-01-29 0.0123298007 -0.0516366096 -0.0567576690 -0.060306770 -5.106844e-02
## 2016-02-29 0.0088317716 -0.0082115380 -0.0339139835 0.020605130 -8.262749e-04
## 2016-03-31 0.0087090469 0.1218789326 0.0637458542 0.089910375 6.510035e-02
## 2016-04-29 0.0025459487 0.0040792901 0.0219752038 0.021044346 3.933193e-03
## 2016-05-31 0.0001351970 -0.0376287047 -0.0008563104 0.004397173 1.686881e-02
## 2016-06-30 0.0191673824 0.0445825058 -0.0244913881 0.008292247 3.469641e-03
## 2016-07-29 0.0054294607 0.0524423744 0.0390001135 0.049348367 3.582187e-02
## 2016-08-31 -0.0021562743 0.0087984720 0.0053268421 0.011260870 1.197118e-03
## 2016-09-30 0.0005158448 0.0248729973 0.0132791871 0.008614747 5.773848e-05
## 2016-10-31 -0.0082050945 -0.0083123524 -0.0224037254 -0.038134761 -1.748925e-02
## 2016-11-30 -0.0259897303 -0.0451620402 -0.0179744481 0.125246339 3.617619e-02
## 2016-12-30 0.0025381882 -0.0025300922 0.0267029517 0.031491618 2.006909e-02
## 2017-01-31 0.0021261372 0.0644317961 0.0323818767 -0.012143973 1.773680e-02
## 2017-02-28 0.0064378338 0.0172577695 0.0118364598 0.013428833 3.853888e-02
## 2017-03-31 -0.0005524766 0.0361888793 0.0318056725 -0.006532724 1.249276e-03
## 2017-04-28 0.0090287971 0.0168664838 0.0239521597 0.005107708 9.877179e-03
## 2017-05-31 0.0068472455 0.0280597953 0.0348104153 -0.022862671 1.401426e-02
## 2017-06-30 -0.0001829763 0.0092239144 0.0029558502 0.029151640 6.354713e-03
## 2017-07-31 0.0033350288 0.0565943842 0.0261877742 0.007481668 2.034586e-02
## 2017-08-31 0.0093691413 0.0232438852 -0.0004481744 -0.027564741 2.913399e-03
## 2017-09-29 -0.0057320432 -0.0004463555 0.0233427189 0.082321842 1.994898e-02
## 2017-10-31 0.0009773248 0.0322786854 0.0166537732 0.005915767 2.329079e-02
## 2017-11-30 -0.0014836529 -0.0038972207 0.0068698021 0.036913524 3.010798e-02
## 2017-12-29 0.0047404514 0.0369257721 0.0133982532 -0.003731331 1.205515e-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(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
plot_data <- asset_returns_wide_tbl %>%
calculate_component_contribution(w = c(0.25, 0.25, 0.2, 0.2, 0.1)) %>%
# 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")
6 Rolling Component Contribution
Column Chart of Component Contribution and Weight
plot_data <- asset_returns_wide_tbl %>%
calculate_component_contribution(w = c(0.25, 0.25, 0.2, 0.2, 0.1)) %>%
# Transform to long form
pivot_longer(cols = everything(), names_to = "Asset", values_to = "Contribution") %>%
# Add weights
add_column(weight = c(0.25, 0.25, 0.2, 0.2, 0.1)) %>%
# 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)