Week 14: Code along 12
CHAPTER 10
Joseph Frates
2025-11-17
# 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 -0.0062309008 -0.002935032 0.0366059316 0.052133308 4.992270e-02
## 2013-02-28 0.0058910567 -0.023105689 -0.0129690974 0.016175232 1.267799e-02
## 2013-03-28 0.0009848158 -0.010234998 0.0129690974 0.040257880 3.726843e-02
## 2013-04-30 0.0096392903 0.012084894 0.0489679870 0.001222744 1.902992e-02
## 2013-05-31 -0.0202139843 -0.049483402 -0.0306555872 0.041976681 2.333514e-02
## 2013-06-28 -0.0157784247 -0.054728469 -0.0271447143 -0.001403099 -1.343408e-02
## 2013-07-31 0.0026879993 0.013159862 0.0518603108 0.063541125 5.038627e-02
## 2013-08-30 -0.0082983732 -0.025705575 -0.0197462437 -0.034743763 -3.045155e-02
## 2013-09-30 0.0111439341 0.069588829 0.0753385261 0.063873994 3.115592e-02
## 2013-10-31 0.0082918989 0.040861059 0.0320817420 0.034233988 4.526662e-02
## 2013-11-29 -0.0025097175 -0.002593842 0.0054495999 0.041661076 2.920700e-02
## 2013-12-31 -0.0055833363 -0.004074474 0.0215282490 0.012891966 2.559595e-02
## 2014-01-31 0.0152912071 -0.090322601 -0.0534135125 -0.035774976 -3.588445e-02
## 2014-02-28 0.0037574237 0.033220422 0.0595050079 0.045257177 4.451005e-02
## 2014-03-31 -0.0014808797 0.038021524 -0.0046024936 0.013315313 8.261302e-03
## 2014-04-30 0.0081824896 0.007773151 0.0165292653 -0.023184437 6.927853e-03
## 2014-05-30 0.0117219334 0.029090843 0.0158286006 0.006205451 2.294126e-02
## 2014-06-30 -0.0005762189 0.023734060 0.0091651859 0.037718814 2.043435e-02
## 2014-07-31 -0.0025121562 0.013555689 -0.0263795816 -0.052009250 -1.352841e-02
## 2014-08-29 0.0114313774 0.027904391 0.0018003196 0.043657856 3.870449e-02
## 2014-09-30 -0.0061675399 -0.080856446 -0.0395984613 -0.061260638 -1.389209e-02
## 2014-10-31 0.0105851102 0.014096456 -0.0026548519 0.068874884 2.327752e-02
## 2014-11-28 0.0065480550 -0.015541326 0.0006251659 0.004773337 2.710168e-02
## 2014-12-31 0.0014754354 -0.040441996 -0.0407463134 0.025295915 -2.539914e-03
## 2015-01-30 0.0203148037 -0.006895942 0.0062263652 -0.054627652 -3.007710e-02
## 2015-02-27 -0.0089875682 0.043136265 0.0614504237 0.056914448 5.468205e-02
## 2015-03-31 0.0037401652 -0.015086181 -0.0143886336 0.010156466 -1.583032e-02
## 2015-04-30 -0.0032334165 0.066281232 0.0358165012 -0.018417570 9.785698e-03
## 2015-05-29 -0.0043836266 -0.041911155 0.0019527115 0.007509707 1.277408e-02
## 2015-06-30 -0.0108250421 -0.029746529 -0.0316787621 0.004171207 -2.052089e-02
## 2015-07-31 0.0085842184 -0.065178275 0.0201144152 -0.027375274 2.233793e-02
## 2015-08-31 -0.0033638763 -0.092512275 -0.0771523348 -0.047268355 -6.288680e-02
## 2015-09-30 0.0080816215 -0.031824888 -0.0451949307 -0.038465098 -2.584735e-02
## 2015-10-30 0.0006851777 0.061808142 0.0640258227 0.063590031 8.163517e-02
## 2015-11-30 -0.0038983516 -0.025560268 -0.0075556441 0.024415275 3.648335e-03
## 2015-12-31 -0.0019189932 -0.038947137 -0.0235950480 -0.052156763 -1.743377e-02
## 2016-01-29 0.0123302958 -0.051636623 -0.0567578728 -0.060306975 -5.106843e-02
## 2016-02-29 0.0088316770 -0.008211692 -0.0339139220 0.020605128 -8.260582e-04
## 2016-03-31 0.0087088647 0.121879106 0.0637456621 0.089910384 6.510042e-02
## 2016-04-29 0.0025461171 0.004079241 0.0219751028 0.021044167 3.932995e-03
## 2016-05-31 0.0001355098 -0.037628532 -0.0008560850 0.004397256 1.686851e-02
## 2016-06-30 0.0191668000 0.044582357 -0.0244916138 0.008292095 3.470100e-03
## 2016-07-29 0.0054295064 0.052442166 0.0390002419 0.049348431 3.582166e-02
## 2016-08-31 -0.0021564405 0.008798726 0.0053269298 0.011261131 1.196892e-03
## 2016-09-30 0.0005161298 0.024872727 0.0132789111 0.008614665 5.794374e-05
## 2016-10-31 -0.0082047505 -0.008312139 -0.0224034129 -0.038134959 -1.748914e-02
## 2016-11-30 -0.0259904210 -0.045161884 -0.0179745731 0.125246798 3.617616e-02
## 2016-12-30 0.0025382379 -0.002529917 0.0267029875 0.031491544 2.006914e-02
## 2017-01-31 0.0021261272 0.064431352 0.0323818267 -0.012144083 1.773656e-02
## 2017-02-28 0.0064380503 0.017258200 0.0118364314 0.013428710 3.853903e-02
## 2017-03-31 -0.0005531281 0.036188787 0.0318057497 -0.006532745 1.249270e-03
## 2017-04-28 0.0090295244 0.016866291 0.0239520970 0.005107514 9.877155e-03
## 2017-05-31 0.0068472691 0.028059788 0.0348101469 -0.022862550 1.401449e-02
## 2017-06-30 -0.0001830050 0.009223772 0.0029560003 0.029151768 6.354505e-03
## 2017-07-31 0.0033351957 0.056594640 0.0261880260 0.007481714 2.034594e-02
## 2017-08-31 0.0093688057 0.023243714 -0.0004483592 -0.027564899 2.913357e-03
## 2017-09-29 -0.0057320898 -0.000446055 0.0233428112 0.082321566 1.994914e-02
## 2017-10-31 0.0009779146 0.032278395 0.0166537895 0.005916449 2.329081e-02
## 2017-11-30 -0.0014843220 -0.003897018 0.0068696856 0.036913032 3.010795e-02
## 2017-12-29 0.0047404250 0.036925324 0.0133984810 -0.003731191 1.205495e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398424e-05 0.0001042127 4.178319e-05 -0.0000781181 -9.030421e-06
## EEM 1.042127e-04 0.0017547085 1.039016e-03 0.0006437744 6.795429e-04
## EFA 4.178319e-05 0.0010390164 1.064236e-03 0.0006490293 6.975395e-04
## IJS -7.811810e-05 0.0006437744 6.490293e-04 0.0015654508 8.290245e-04
## SPY -9.030421e-06 0.0006795429 6.975395e-04 0.0008290245 7.408289e-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,] 0.0003874265 0.009257144 0.005815627 0.005684472 0.002330248rowSums(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")
# Custom function
calculate_component_contribution <- function(asset_returns_wide_tbl, w) {
# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
# Standard deviation of portfolio
sd_portfolio <- sqrt(t(w) %*% covariance_matrix %*% w)
# Component contribution
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
# Figure 10.1 Contribution to Standard Deviation ----
asset_returns_wide_tbl %>%
calculate_component_contribution(w = c(0.25,0.25,0.2,0.2,0.1)) %>%
gather(key = "asset", value = "contribution") %>%
ggplot(aes(asset, contribution)) +
geom_col(fill = "cornflowerblue") +
theme(plot.title = element_text(hjust = 0.5)) +
scale_y_continuous(labels = scales::percent_format(accuracy = 1)) +
labs(title = "Percent Contribution to Portfolio Standard Deviation",
y = "Percent Contribution to Risk",
x = NULL)
# Figure 10.2 Weight versus Contribution ----
asset_returns_wide_tbl %>%
calculate_component_contribution(w = c(0.25,0.25,0.2,0.2,0.1)) %>%
gather(key = "asset", value = "contribution") %>%
add_column(weights = c(0.25,0.25,0.2,0.2,0.1)) %>%
pivot_longer(cols = c(contribution, weights), names_to = "type", values_to = "value") %>%
ggplot(aes(asset, value, fill = type)) +
geom_col(position = "dodge") +
theme(plot.title = element_text(hjust = 0.5)) +
scale_y_continuous(labels = scales::percent_format(accuracy = 1)) +
theme_tq() +
scale_fill_tq() +
labs(title = "Percent Contribution to Volatility",
y = "percent",
x = "asset") 