Week 14: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Marcello Popa
2025-10-19
# 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 -0.0062311910 -0.0029353724 0.0366059316 0.052133205 4.992336e-02
## 2013-02-28 0.0058914433 -0.0231052291 -0.0129692870 0.016175342 1.267786e-02
## 2013-03-28 0.0009847193 -0.0102352304 0.0129692870 0.040258193 3.726813e-02
## 2013-04-30 0.0096390033 0.0120851259 0.0489679870 0.001222230 1.903017e-02
## 2013-05-31 -0.0202137936 -0.0494836945 -0.0306558629 0.041976398 2.333549e-02
## 2013-06-28 -0.0157783258 -0.0547282154 -0.0271445331 -0.001402705 -1.343502e-02
## 2013-07-31 0.0026878019 0.0131595421 0.0518605845 0.063541045 5.038630e-02
## 2013-08-30 -0.0082983740 -0.0257055786 -0.0197465144 -0.034743293 -3.045088e-02
## 2013-09-30 0.0111441319 0.0695892020 0.0753388719 0.063873532 3.115546e-02
## 2013-10-31 0.0082920931 0.0408610491 0.0320814876 0.034234257 4.526674e-02
## 2013-11-29 -0.0025102055 -0.0025941928 0.0054498449 0.041661243 2.920711e-02
## 2013-12-31 -0.0055827477 -0.0040743565 0.0215279241 0.012891635 2.559626e-02
## 2014-01-31 0.0152911043 -0.0903224723 -0.0534133482 -0.035774811 -3.588455e-02
## 2014-02-28 0.0037577119 0.0332204176 0.0595050030 0.045257340 4.451004e-02
## 2014-03-31 -0.0014817480 0.0380215189 -0.0046027327 0.013315310 8.261400e-03
## 2014-04-30 0.0081831624 0.0077727936 0.0165295035 -0.023184763 6.927654e-03
## 2014-05-30 0.0117217396 0.0290913110 0.0158285221 0.006205615 2.294097e-02
## 2014-06-30 -0.0005753663 0.0237338294 0.0091653391 0.037718814 2.043492e-02
## 2014-07-31 -0.0025131032 0.0135558000 -0.0263800492 -0.052009333 -1.352879e-02
## 2014-08-29 0.0114310008 0.0279047127 0.0018008695 0.043657621 3.870468e-02
## 2014-09-30 -0.0061667859 -0.0808569957 -0.0395985334 -0.061260320 -1.389199e-02
## 2014-10-31 0.0105842641 0.0140964574 -0.0026548515 0.068874963 2.327770e-02
## 2014-11-28 0.0065486146 -0.0155413274 0.0006254112 0.004773651 2.710113e-02
## 2014-12-31 0.0014749715 -0.0404420005 -0.0407468077 0.025295599 -2.539825e-03
## 2015-01-30 0.0203152636 -0.0068955733 0.0062264504 -0.054627890 -3.007673e-02
## 2015-02-27 -0.0089881166 0.0431360190 0.0614505033 0.056914610 5.468151e-02
## 2015-03-31 0.0037401666 -0.0150860017 -0.0143888748 0.010156466 -1.583032e-02
## 2015-04-30 -0.0032333261 0.0662809406 0.0358167407 -0.018417724 9.785788e-03
## 2015-05-29 -0.0043836278 -0.0419109266 0.0019528670 0.007509938 1.277460e-02
## 2015-06-30 -0.0108254173 -0.0297465852 -0.0316789152 0.004171207 -2.052132e-02
## 2015-07-31 0.0085844084 -0.0651782066 0.0201143349 -0.027375272 2.233793e-02
## 2015-08-31 -0.0033638779 -0.0925121920 -0.0771524198 -0.047268269 -6.288672e-02
## 2015-09-30 0.0080819006 -0.0318250996 -0.0451949346 -0.038464836 -2.584725e-02
## 2015-10-30 0.0006851779 0.0618084156 0.0640261620 0.063589925 8.163508e-02
## 2015-11-30 -0.0038976155 -0.0255605417 -0.0075558944 0.024415111 3.648681e-03
## 2015-12-31 -0.0019187153 -0.0389472098 -0.0235952201 -0.052157166 -1.743403e-02
## 2016-01-29 0.0123298299 -0.0516363969 -0.0567577917 -0.060306990 -5.106842e-02
## 2016-02-29 0.0088314028 -0.0082117681 -0.0339140194 0.020605304 -8.265218e-04
## 2016-03-31 0.0087084161 0.1218789596 0.0637457622 0.089910313 6.510035e-02
## 2016-04-29 0.0025467434 0.0040794461 0.0219751912 0.021044400 3.933516e-03
## 2016-05-31 0.0001352418 -0.0376286687 -0.0008560850 0.004397027 1.686876e-02
## 2016-06-30 0.0191665372 0.0445824244 -0.0244916138 0.008292248 3.469675e-03
## 2016-07-29 0.0054296821 0.0524422271 0.0390002419 0.049348431 3.582199e-02
## 2016-08-31 -0.0021566153 0.0087984061 0.0053267601 0.011261131 1.196402e-03
## 2016-09-30 0.0005164791 0.0248729807 0.0132794159 0.008614383 5.827065e-05
## 2016-10-31 -0.0082053659 -0.0083120758 -0.0224039192 -0.038134530 -1.748889e-02
## 2016-11-30 -0.0259898026 -0.0451619435 -0.0179742274 0.125246458 3.617591e-02
## 2016-12-30 0.0025385079 -0.0025300489 0.0267027282 0.031491989 2.006898e-02
## 2017-01-31 0.0021256769 0.0644315409 0.0323819116 -0.012144270 1.773672e-02
## 2017-02-28 0.0064378722 0.0172575919 0.0118363502 0.013428459 3.853932e-02
## 2017-03-31 -0.0005527707 0.0361891550 0.0318055948 -0.006532369 1.248973e-03
## 2017-04-28 0.0090288150 0.0168661777 0.0239524099 0.005107638 9.877081e-03
## 2017-05-31 0.0068480651 0.0280602412 0.0348101442 -0.022863056 1.401428e-02
## 2017-06-30 -0.0001828290 0.0092235488 0.0029559261 0.029152084 6.354867e-03
## 2017-07-31 0.0033344929 0.0565945349 0.0261879539 0.007481281 2.034559e-02
## 2017-08-31 0.0093695040 0.0232437164 -0.0004482150 -0.027564463 2.913710e-03
## 2017-09-29 -0.0057327868 -0.0004459528 0.0233426686 0.082321556 1.994886e-02
## 2017-10-31 0.0009779149 0.0322783953 0.0166535135 0.005916216 2.329082e-02
## 2017-11-30 -0.0014838854 -0.0038968195 0.0068704448 0.036913260 3.010821e-02
## 2017-12-29 0.0047405116 0.0369252206 0.0133981361 -0.003730966 1.205501e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398379e-05 0.0001042098 4.178396e-05 -7.812013e-05 -9.030836e-06
## EEM 1.042098e-04 0.0017547102 1.039018e-03 6.437713e-04 6.795411e-04
## EFA 4.178396e-05 0.0010390185 1.064240e-03 6.490302e-04 6.975417e-04
## IJS -7.812013e-05 0.0006437713 6.490302e-04 1.565448e-03 8.290226e-04
## SPY -9.030836e-06 0.0006795411 6.975417e-04 8.290226e-04 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,] 0.02347491# 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,] 0.0003874144 0.00925714 0.005815647 0.005684459 0.002330247rowSums(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
asset_returns_wide_tbl <- asset_returns_tbl %>%
pivot_wider(names_from = asset, values_from = returns) %>%
column_to_rownames(var = "date")
calculate_component_contribution <- function(asset_returns_wide_tbl, w) {
covariance_matrix <- cov(asset_returns_wide_tbl)
sd_portfolio <- sqrt(t(w) %*% covariance_matrix %*% w)
component_contribution <- (t(w) %*% covariance_matrix * w) / sd_portfolio[1,1]
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") 