Week 14: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Amanda Simpson
2022-11-29
# 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 -0.0062315751 -0.0029358358 0.0366062715 0.052132976 4.992314e-02
## 2013-02-28 0.0058910156 -0.0231048248 -0.0129695485 0.016175510 1.267823e-02
## 2013-03-28 0.0009851287 -0.0102352068 0.0129695485 0.040258487 3.726816e-02
## 2013-04-30 0.0096392326 0.0120846787 0.0489678048 0.001221836 1.903004e-02
## 2013-05-31 -0.0202145329 -0.0494836781 -0.0306558682 0.041976625 2.333506e-02
## 2013-06-28 -0.0157780043 -0.0547281253 -0.0271443950 -0.001403072 -1.343387e-02
## 2013-07-31 0.0026878088 0.0131597634 0.0518604449 0.063541331 5.038584e-02
## 2013-08-30 -0.0082974233 -0.0257054798 -0.0197462369 -0.034743251 -3.045161e-02
## 2013-09-30 0.0111432792 0.0695887098 0.0753385205 0.063873298 3.115592e-02
## 2013-10-31 0.0082923092 0.0408611609 0.0320815816 0.034234385 4.526649e-02
## 2013-11-29 -0.0025105908 -0.0025940684 0.0054496390 0.041660918 2.920743e-02
## 2013-12-31 -0.0055825599 -0.0040740475 0.0215280242 0.012892141 2.559595e-02
## 2014-01-31 0.0152916706 -0.0903228294 -0.0534133267 -0.035775251 -3.588439e-02
## 2014-02-28 0.0037569264 0.0332206312 0.0595050652 0.045257450 4.450989e-02
## 2014-03-31 -0.0014819323 0.0380215360 -0.0046025007 0.013315323 8.261375e-03
## 2014-04-30 0.0081836581 0.0077728543 0.0165292306 -0.023184432 6.927409e-03
## 2014-05-30 0.0117216272 0.0290913105 0.0158285335 0.006205406 2.294156e-02
## 2014-06-30 -0.0005759444 0.0237336330 0.0091655922 0.037718692 2.043469e-02
## 2014-07-31 -0.0025120688 0.0135557354 -0.0263798039 -0.052009416 -1.352885e-02
## 2014-08-29 0.0114308227 0.0279045126 0.0018003560 0.043657874 3.870467e-02
## 2014-09-30 -0.0061670131 -0.0808566992 -0.0395984011 -0.061260293 -1.389230e-02
## 2014-10-31 0.0105843370 0.0140965366 -0.0026548854 0.068874686 2.327790e-02
## 2014-11-28 0.0065487484 -0.0155410573 0.0006252274 0.004773575 2.710153e-02
## 2014-12-31 0.0014751092 -0.0404422589 -0.0407468319 0.025295976 -2.539900e-03
## 2015-01-30 0.0203149499 -0.0068959393 0.0062265907 -0.054628094 -3.007729e-02
## 2015-02-27 -0.0089880331 0.0431363863 0.0614505902 0.056914600 5.468210e-02
## 2015-03-31 0.0037403909 -0.0150865962 -0.0143887692 0.010156405 -1.583036e-02
## 2015-04-30 -0.0032333051 0.0662814080 0.0358165951 -0.018417602 9.786065e-03
## 2015-05-29 -0.0043835034 -0.0419107223 0.0019527689 0.007509937 1.277406e-02
## 2015-06-30 -0.0108257547 -0.0297470158 -0.0316788440 0.004171341 -2.052141e-02
## 2015-07-31 0.0085845634 -0.0651780132 0.0201144055 -0.027375403 2.233803e-02
## 2015-08-31 -0.0033636784 -0.0925122172 -0.0771524349 -0.047268298 -6.288667e-02
## 2015-09-30 0.0080816002 -0.0318249466 -0.0451949070 -0.038464836 -2.584700e-02
## 2015-10-30 0.0006852839 0.0618081097 0.0640260725 0.063589964 8.163477e-02
## 2015-11-30 -0.0038976709 -0.0255603548 -0.0075559842 0.024414968 3.648548e-03
## 2015-12-31 -0.0019189832 -0.0389469630 -0.0235950377 -0.052156987 -1.743346e-02
## 2016-01-29 0.0123295421 -0.0516367885 -0.0567578510 -0.060306912 -5.106896e-02
## 2016-02-29 0.0088318957 -0.0082114300 -0.0339139922 0.020605179 -8.262217e-04
## 2016-03-31 0.0087083361 0.1218788614 0.0637457118 0.089910342 6.510035e-02
## 2016-04-29 0.0025466504 0.0040792678 0.0219752947 0.021044254 3.933541e-03
## 2016-05-31 0.0001352850 -0.0376284126 -0.0008561489 0.004397117 1.686837e-02
## 2016-06-30 0.0191671403 0.0445823102 -0.0244915330 0.008292351 3.469921e-03
## 2016-07-29 0.0054292773 0.0524420211 0.0390002318 0.049348372 3.582186e-02
## 2016-08-31 -0.0021562179 0.0087985285 0.0053268061 0.011261141 1.196687e-03
## 2016-09-30 0.0005156823 0.0248730372 0.0132792447 0.008614539 5.835603e-05
## 2016-10-31 -0.0082050611 -0.0083122664 -0.0224038490 -0.038134852 -1.748925e-02
## 2016-11-30 -0.0259897417 -0.0451616456 -0.0179744407 0.125246484 3.617591e-02
## 2016-12-30 0.0025383656 -0.0025300701 0.0267028708 0.031491784 2.006928e-02
## 2017-01-31 0.0021260283 0.0644312746 0.0323819229 -0.012144001 1.773644e-02
## 2017-02-28 0.0064378729 0.0172580527 0.0118365242 0.013429051 3.853916e-02
## 2017-03-31 -0.0005527346 0.0361888122 0.0318056796 -0.006533345 1.249315e-03
## 2017-04-28 0.0090288611 0.0168666049 0.0239522284 0.005108001 9.877013e-03
## 2017-05-31 0.0068474606 0.0280597471 0.0348102134 -0.022862587 1.401434e-02
## 2017-06-30 -0.0001826990 0.0092237842 0.0029559197 0.029151621 6.354720e-03
## 2017-07-31 0.0033343277 0.0565946333 0.0261878539 0.007481462 2.034598e-02
## 2017-08-31 0.0093692406 0.0232437438 -0.0004482983 -0.027564548 2.913198e-03
## 2017-09-29 -0.0057319258 -0.0004462966 0.0233428581 0.082321800 1.994928e-02
## 2017-10-31 0.0009778856 0.0322785406 0.0166536403 0.005915994 2.329059e-02
## 2017-11-30 -0.0014839332 -0.0038971054 0.0068697606 0.036913188 3.010813e-02
## 2017-12-29 0.0047399550 0.0369256124 0.0133985337 -0.003731148 1.205489e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398349e-05 0.0001042066 4.178069e-05 -7.812247e-05 -9.033003e-06
## EEM 1.042066e-04 0.0017547084 1.039017e-03 6.437720e-04 6.795431e-04
## EFA 4.178069e-05 0.0010390174 1.064239e-03 6.490287e-04 6.975411e-04
## IJS -7.812247e-05 0.0006437720 6.490287e-04 1.565449e-03 8.290259e-04
## SPY -9.033003e-06 0.0006795431 6.975411e-04 8.290259e-04 7.408295e-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,] 0.02347488# 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,] 0.0003873914 0.009257138 0.005815638 0.005684464 0.002330252rowSums(component_contribution)## [1] 0.02347488# 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 -0.0062315751 -0.0029358358 0.0366062715 0.052132976 4.992314e-02
## 2013-02-28 0.0058910156 -0.0231048248 -0.0129695485 0.016175510 1.267823e-02
## 2013-03-28 0.0009851287 -0.0102352068 0.0129695485 0.040258487 3.726816e-02
## 2013-04-30 0.0096392326 0.0120846787 0.0489678048 0.001221836 1.903004e-02
## 2013-05-31 -0.0202145329 -0.0494836781 -0.0306558682 0.041976625 2.333506e-02
## 2013-06-28 -0.0157780043 -0.0547281253 -0.0271443950 -0.001403072 -1.343387e-02
## 2013-07-31 0.0026878088 0.0131597634 0.0518604449 0.063541331 5.038584e-02
## 2013-08-30 -0.0082974233 -0.0257054798 -0.0197462369 -0.034743251 -3.045161e-02
## 2013-09-30 0.0111432792 0.0695887098 0.0753385205 0.063873298 3.115592e-02
## 2013-10-31 0.0082923092 0.0408611609 0.0320815816 0.034234385 4.526649e-02
## 2013-11-29 -0.0025105908 -0.0025940684 0.0054496390 0.041660918 2.920743e-02
## 2013-12-31 -0.0055825599 -0.0040740475 0.0215280242 0.012892141 2.559595e-02
## 2014-01-31 0.0152916706 -0.0903228294 -0.0534133267 -0.035775251 -3.588439e-02
## 2014-02-28 0.0037569264 0.0332206312 0.0595050652 0.045257450 4.450989e-02
## 2014-03-31 -0.0014819323 0.0380215360 -0.0046025007 0.013315323 8.261375e-03
## 2014-04-30 0.0081836581 0.0077728543 0.0165292306 -0.023184432 6.927409e-03
## 2014-05-30 0.0117216272 0.0290913105 0.0158285335 0.006205406 2.294156e-02
## 2014-06-30 -0.0005759444 0.0237336330 0.0091655922 0.037718692 2.043469e-02
## 2014-07-31 -0.0025120688 0.0135557354 -0.0263798039 -0.052009416 -1.352885e-02
## 2014-08-29 0.0114308227 0.0279045126 0.0018003560 0.043657874 3.870467e-02
## 2014-09-30 -0.0061670131 -0.0808566992 -0.0395984011 -0.061260293 -1.389230e-02
## 2014-10-31 0.0105843370 0.0140965366 -0.0026548854 0.068874686 2.327790e-02
## 2014-11-28 0.0065487484 -0.0155410573 0.0006252274 0.004773575 2.710153e-02
## 2014-12-31 0.0014751092 -0.0404422589 -0.0407468319 0.025295976 -2.539900e-03
## 2015-01-30 0.0203149499 -0.0068959393 0.0062265907 -0.054628094 -3.007729e-02
## 2015-02-27 -0.0089880331 0.0431363863 0.0614505902 0.056914600 5.468210e-02
## 2015-03-31 0.0037403909 -0.0150865962 -0.0143887692 0.010156405 -1.583036e-02
## 2015-04-30 -0.0032333051 0.0662814080 0.0358165951 -0.018417602 9.786065e-03
## 2015-05-29 -0.0043835034 -0.0419107223 0.0019527689 0.007509937 1.277406e-02
## 2015-06-30 -0.0108257547 -0.0297470158 -0.0316788440 0.004171341 -2.052141e-02
## 2015-07-31 0.0085845634 -0.0651780132 0.0201144055 -0.027375403 2.233803e-02
## 2015-08-31 -0.0033636784 -0.0925122172 -0.0771524349 -0.047268298 -6.288667e-02
## 2015-09-30 0.0080816002 -0.0318249466 -0.0451949070 -0.038464836 -2.584700e-02
## 2015-10-30 0.0006852839 0.0618081097 0.0640260725 0.063589964 8.163477e-02
## 2015-11-30 -0.0038976709 -0.0255603548 -0.0075559842 0.024414968 3.648548e-03
## 2015-12-31 -0.0019189832 -0.0389469630 -0.0235950377 -0.052156987 -1.743346e-02
## 2016-01-29 0.0123295421 -0.0516367885 -0.0567578510 -0.060306912 -5.106896e-02
## 2016-02-29 0.0088318957 -0.0082114300 -0.0339139922 0.020605179 -8.262217e-04
## 2016-03-31 0.0087083361 0.1218788614 0.0637457118 0.089910342 6.510035e-02
## 2016-04-29 0.0025466504 0.0040792678 0.0219752947 0.021044254 3.933541e-03
## 2016-05-31 0.0001352850 -0.0376284126 -0.0008561489 0.004397117 1.686837e-02
## 2016-06-30 0.0191671403 0.0445823102 -0.0244915330 0.008292351 3.469921e-03
## 2016-07-29 0.0054292773 0.0524420211 0.0390002318 0.049348372 3.582186e-02
## 2016-08-31 -0.0021562179 0.0087985285 0.0053268061 0.011261141 1.196687e-03
## 2016-09-30 0.0005156823 0.0248730372 0.0132792447 0.008614539 5.835603e-05
## 2016-10-31 -0.0082050611 -0.0083122664 -0.0224038490 -0.038134852 -1.748925e-02
## 2016-11-30 -0.0259897417 -0.0451616456 -0.0179744407 0.125246484 3.617591e-02
## 2016-12-30 0.0025383656 -0.0025300701 0.0267028708 0.031491784 2.006928e-02
## 2017-01-31 0.0021260283 0.0644312746 0.0323819229 -0.012144001 1.773644e-02
## 2017-02-28 0.0064378729 0.0172580527 0.0118365242 0.013429051 3.853916e-02
## 2017-03-31 -0.0005527346 0.0361888122 0.0318056796 -0.006533345 1.249315e-03
## 2017-04-28 0.0090288611 0.0168666049 0.0239522284 0.005108001 9.877013e-03
## 2017-05-31 0.0068474606 0.0280597471 0.0348102134 -0.022862587 1.401434e-02
## 2017-06-30 -0.0001826990 0.0092237842 0.0029559197 0.029151621 6.354720e-03
## 2017-07-31 0.0033343277 0.0565946333 0.0261878539 0.007481462 2.034598e-02
## 2017-08-31 0.0093692406 0.0232437438 -0.0004482983 -0.027564548 2.913198e-03
## 2017-09-29 -0.0057319258 -0.0004462966 0.0233428581 0.082321800 1.994928e-02
## 2017-10-31 0.0009778856 0.0322785406 0.0166536403 0.005915994 2.329059e-02
## 2017-11-30 -0.0014839332 -0.0038971054 0.0068697606 0.036913188 3.010813e-02
## 2017-12-29 0.0047399550 0.0369256124 0.0133985337 -0.003731148 1.205489e-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 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)) +
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)