Week 14: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Olivia Salesky
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 -0.0062309613 -0.0029356428 0.0366062037 0.052132988 4.992264e-02
## 2013-02-28 0.0058913558 -0.0231051614 -0.0129692061 0.016175620 1.267842e-02
## 2013-03-28 0.0009846970 -0.0102350949 0.0129692061 0.040258004 3.726781e-02
## 2013-04-30 0.0096393225 0.0120847929 0.0489677005 0.001222323 1.903039e-02
## 2013-05-31 -0.0202144393 -0.0494835595 -0.0306556961 0.041976899 2.333540e-02
## 2013-06-28 -0.0157779198 -0.0547281186 -0.0271443950 -0.001403539 -1.343444e-02
## 2013-07-31 0.0026878081 0.0131596382 0.0518605098 0.063541626 5.038585e-02
## 2013-08-30 -0.0082980421 -0.0257057968 -0.0197463901 -0.034743418 -3.045118e-02
## 2013-09-30 0.0111438972 0.0695890268 0.0753385269 0.063873533 3.115559e-02
## 2013-10-31 0.0082916864 0.0408612744 0.0320817229 0.034234079 4.526690e-02
## 2013-11-29 -0.0025097162 -0.0025939543 0.0054495796 0.041661156 2.920723e-02
## 2013-12-31 -0.0055829045 -0.0040747038 0.0215281785 0.012892059 2.559576e-02
## 2014-01-31 0.0152916680 -0.0903223382 -0.0534133996 -0.035775318 -3.588450e-02
## 2014-02-28 0.0037570167 0.0332203569 0.0595051947 0.045257436 4.451048e-02
## 2014-03-31 -0.0014819319 0.0380217478 -0.0046026346 0.013315406 8.260990e-03
## 2014-04-30 0.0081835657 0.0077728543 0.0165293051 -0.023184105 6.927502e-03
## 2014-05-30 0.0117213798 0.0290910017 0.0158284565 0.006205078 2.294147e-02
## 2014-06-30 -0.0005754420 0.0237341337 0.0091654436 0.037718774 2.043469e-02
## 2014-07-31 -0.0025126610 0.0135553272 -0.0263799576 -0.052009416 -1.352885e-02
## 2014-08-29 0.0114308247 0.0279048341 0.0018006595 0.043657715 3.870432e-02
## 2014-09-30 -0.0061673593 -0.0808568044 -0.0395986345 -0.061260388 -1.389195e-02
## 2014-10-31 0.0105850255 0.0140965366 -0.0026547278 0.068874860 2.327790e-02
## 2014-11-28 0.0065483204 -0.0155412572 0.0006253064 0.004773654 2.710144e-02
## 2014-12-31 0.0014753610 -0.0404419698 -0.0407468286 0.025295919 -2.540158e-03
## 2015-01-30 0.0203152712 -0.0068957890 0.0062267332 -0.054628037 -3.007694e-02
## 2015-02-27 -0.0089886786 0.0431360321 0.0614503653 0.056914676 5.468202e-02
## 2015-03-31 0.0037402198 -0.0150861321 -0.0143886327 0.010156329 -1.583028e-02
## 2015-04-30 -0.0032327235 0.0662810586 0.0358163834 -0.018417813 9.785894e-03
## 2015-05-29 -0.0043832535 -0.0419108359 0.0019528441 0.007509996 1.277440e-02
## 2015-06-30 -0.0108260910 -0.0297467851 -0.0316789216 0.004171569 -2.052157e-02
## 2015-07-31 0.0085848134 -0.0651781303 0.0201144071 -0.027375713 2.233811e-02
## 2015-08-31 -0.0033638412 -0.0925124571 -0.0771524204 -0.047268289 -6.288694e-02
## 2015-09-30 0.0080815129 -0.0318247067 -0.0451948454 -0.038464611 -2.584709e-02
## 2015-10-30 0.0006856949 0.0618085753 0.0640260725 0.063589904 8.163529e-02
## 2015-11-30 -0.0038984075 -0.0255608204 -0.0075559234 0.024414950 3.648471e-03
## 2015-12-31 -0.0019189838 -0.0389470340 -0.0235951816 -0.052156828 -1.743388e-02
## 2016-01-29 0.0123298685 -0.0516367176 -0.0567576800 -0.060307169 -5.106853e-02
## 2016-02-29 0.0088315655 -0.0082116560 -0.0339139210 0.020605438 -8.263966e-04
## 2016-03-31 0.0087089830 0.1218790873 0.0637456380 0.089910413 6.510018e-02
## 2016-04-29 0.0025460072 0.0040791682 0.0219750423 0.021044231 3.933542e-03
## 2016-05-31 0.0001355272 -0.0376283820 -0.0008560654 0.004397040 1.686862e-02
## 2016-06-30 0.0191669870 0.0445821813 -0.0244914495 0.008292162 3.469841e-03
## 2016-07-29 0.0054292888 0.0524424066 0.0390003965 0.049348504 3.582202e-02
## 2016-08-31 -0.0021559095 0.0087987130 0.0053266413 0.011261070 1.196687e-03
## 2016-09-30 0.0005156823 0.0248726650 0.0132791638 0.008614803 5.796024e-05
## 2016-10-31 -0.0082049151 -0.0083121444 -0.0224036234 -0.038134900 -1.748925e-02
## 2016-11-30 -0.0259898102 -0.0451617676 -0.0179745854 0.125246386 3.617623e-02
## 2016-12-30 0.0025382059 -0.0025301341 0.0267030347 0.031491736 2.006905e-02
## 2017-01-31 0.0021257104 0.0644314586 0.0323817590 -0.012144064 1.773659e-02
## 2017-02-28 0.0064380329 0.0172576968 0.0118364457 0.013428755 3.853916e-02
## 2017-03-31 -0.0005528189 0.0361891619 0.0318056821 -0.006532923 1.249175e-03
## 2017-04-28 0.0090291870 0.0168662675 0.0239522302 0.005107939 9.877296e-03
## 2017-05-31 0.0068476155 0.0280599708 0.0348101443 -0.022862651 1.401413e-02
## 2017-06-30 -0.0001827819 0.0092238919 0.0029560630 0.029151917 6.354928e-03
## 2017-07-31 0.0033342548 0.0565943473 0.0261877148 0.007481460 2.034584e-02
## 2017-08-31 0.0093696188 0.0232439220 -0.0004481592 -0.027564351 2.913331e-03
## 2017-09-29 -0.0057326956 -0.0004461971 0.0233427901 0.082321270 1.994902e-02
## 2017-10-31 0.0009780402 0.0322784411 0.0166535746 0.005915878 2.329080e-02
## 2017-11-30 -0.0014836139 -0.0038971054 0.0068702098 0.036913503 3.010775e-02
## 2017-12-29 0.0047397901 0.0369256124 0.0133981527 -0.003731344 1.205521e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398472e-05 0.0001042095 4.178302e-05 -7.812059e-05 -9.030964e-06
## EEM 1.042095e-04 0.0017547102 1.039017e-03 6.437742e-04 6.795430e-04
## EFA 4.178302e-05 0.0010390169 1.064238e-03 6.490297e-04 6.975417e-04
## IJS -7.812059e-05 0.0006437742 6.490297e-04 1.565450e-03 8.290249e-04
## SPY -9.030964e-06 0.0006795430 6.975417e-04 8.290249e-04 7.408301e-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,] 0.0003874131 0.009257143 0.005815635 0.005684468 0.002330251rowSums(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 -0.0062309613 -0.0029356428 0.0366062037 0.052132988 4.992264e-02
## 2013-02-28 0.0058913558 -0.0231051614 -0.0129692061 0.016175620 1.267842e-02
## 2013-03-28 0.0009846970 -0.0102350949 0.0129692061 0.040258004 3.726781e-02
## 2013-04-30 0.0096393225 0.0120847929 0.0489677005 0.001222323 1.903039e-02
## 2013-05-31 -0.0202144393 -0.0494835595 -0.0306556961 0.041976899 2.333540e-02
## 2013-06-28 -0.0157779198 -0.0547281186 -0.0271443950 -0.001403539 -1.343444e-02
## 2013-07-31 0.0026878081 0.0131596382 0.0518605098 0.063541626 5.038585e-02
## 2013-08-30 -0.0082980421 -0.0257057968 -0.0197463901 -0.034743418 -3.045118e-02
## 2013-09-30 0.0111438972 0.0695890268 0.0753385269 0.063873533 3.115559e-02
## 2013-10-31 0.0082916864 0.0408612744 0.0320817229 0.034234079 4.526690e-02
## 2013-11-29 -0.0025097162 -0.0025939543 0.0054495796 0.041661156 2.920723e-02
## 2013-12-31 -0.0055829045 -0.0040747038 0.0215281785 0.012892059 2.559576e-02
## 2014-01-31 0.0152916680 -0.0903223382 -0.0534133996 -0.035775318 -3.588450e-02
## 2014-02-28 0.0037570167 0.0332203569 0.0595051947 0.045257436 4.451048e-02
## 2014-03-31 -0.0014819319 0.0380217478 -0.0046026346 0.013315406 8.260990e-03
## 2014-04-30 0.0081835657 0.0077728543 0.0165293051 -0.023184105 6.927502e-03
## 2014-05-30 0.0117213798 0.0290910017 0.0158284565 0.006205078 2.294147e-02
## 2014-06-30 -0.0005754420 0.0237341337 0.0091654436 0.037718774 2.043469e-02
## 2014-07-31 -0.0025126610 0.0135553272 -0.0263799576 -0.052009416 -1.352885e-02
## 2014-08-29 0.0114308247 0.0279048341 0.0018006595 0.043657715 3.870432e-02
## 2014-09-30 -0.0061673593 -0.0808568044 -0.0395986345 -0.061260388 -1.389195e-02
## 2014-10-31 0.0105850255 0.0140965366 -0.0026547278 0.068874860 2.327790e-02
## 2014-11-28 0.0065483204 -0.0155412572 0.0006253064 0.004773654 2.710144e-02
## 2014-12-31 0.0014753610 -0.0404419698 -0.0407468286 0.025295919 -2.540158e-03
## 2015-01-30 0.0203152712 -0.0068957890 0.0062267332 -0.054628037 -3.007694e-02
## 2015-02-27 -0.0089886786 0.0431360321 0.0614503653 0.056914676 5.468202e-02
## 2015-03-31 0.0037402198 -0.0150861321 -0.0143886327 0.010156329 -1.583028e-02
## 2015-04-30 -0.0032327235 0.0662810586 0.0358163834 -0.018417813 9.785894e-03
## 2015-05-29 -0.0043832535 -0.0419108359 0.0019528441 0.007509996 1.277440e-02
## 2015-06-30 -0.0108260910 -0.0297467851 -0.0316789216 0.004171569 -2.052157e-02
## 2015-07-31 0.0085848134 -0.0651781303 0.0201144071 -0.027375713 2.233811e-02
## 2015-08-31 -0.0033638412 -0.0925124571 -0.0771524204 -0.047268289 -6.288694e-02
## 2015-09-30 0.0080815129 -0.0318247067 -0.0451948454 -0.038464611 -2.584709e-02
## 2015-10-30 0.0006856949 0.0618085753 0.0640260725 0.063589904 8.163529e-02
## 2015-11-30 -0.0038984075 -0.0255608204 -0.0075559234 0.024414950 3.648471e-03
## 2015-12-31 -0.0019189838 -0.0389470340 -0.0235951816 -0.052156828 -1.743388e-02
## 2016-01-29 0.0123298685 -0.0516367176 -0.0567576800 -0.060307169 -5.106853e-02
## 2016-02-29 0.0088315655 -0.0082116560 -0.0339139210 0.020605438 -8.263966e-04
## 2016-03-31 0.0087089830 0.1218790873 0.0637456380 0.089910413 6.510018e-02
## 2016-04-29 0.0025460072 0.0040791682 0.0219750423 0.021044231 3.933542e-03
## 2016-05-31 0.0001355272 -0.0376283820 -0.0008560654 0.004397040 1.686862e-02
## 2016-06-30 0.0191669870 0.0445821813 -0.0244914495 0.008292162 3.469841e-03
## 2016-07-29 0.0054292888 0.0524424066 0.0390003965 0.049348504 3.582202e-02
## 2016-08-31 -0.0021559095 0.0087987130 0.0053266413 0.011261070 1.196687e-03
## 2016-09-30 0.0005156823 0.0248726650 0.0132791638 0.008614803 5.796024e-05
## 2016-10-31 -0.0082049151 -0.0083121444 -0.0224036234 -0.038134900 -1.748925e-02
## 2016-11-30 -0.0259898102 -0.0451617676 -0.0179745854 0.125246386 3.617623e-02
## 2016-12-30 0.0025382059 -0.0025301341 0.0267030347 0.031491736 2.006905e-02
## 2017-01-31 0.0021257104 0.0644314586 0.0323817590 -0.012144064 1.773659e-02
## 2017-02-28 0.0064380329 0.0172576968 0.0118364457 0.013428755 3.853916e-02
## 2017-03-31 -0.0005528189 0.0361891619 0.0318056821 -0.006532923 1.249175e-03
## 2017-04-28 0.0090291870 0.0168662675 0.0239522302 0.005107939 9.877296e-03
## 2017-05-31 0.0068476155 0.0280599708 0.0348101443 -0.022862651 1.401413e-02
## 2017-06-30 -0.0001827819 0.0092238919 0.0029560630 0.029151917 6.354928e-03
## 2017-07-31 0.0033342548 0.0565943473 0.0261877148 0.007481460 2.034584e-02
## 2017-08-31 0.0093696188 0.0232439220 -0.0004481592 -0.027564351 2.913331e-03
## 2017-09-29 -0.0057326956 -0.0004461971 0.0233427901 0.082321270 1.994902e-02
## 2017-10-31 0.0009780402 0.0322784411 0.0166535746 0.005915878 2.329080e-02
## 2017-11-30 -0.0014836139 -0.0038971054 0.0068702098 0.036913503 3.010775e-02
## 2017-12-29 0.0047397901 0.0369256124 0.0133981527 -0.003731344 1.205521e-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)