Apply it to your data 12
Which of the assets the largest contributor to the portfolio volatility?
Takeru Ito
2025-11-19
# 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.
1 Import stock prices
symbols <- c("AAPL", "TGT", "AMZN", "WMT", "PEP")
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## AAPL AMZN PEP TGT
## 2013-01-31 -1.555889e-01 0.0566799395 0.0625911683 0.0207399364
## 2013-02-28 -2.561096e-02 -0.0046435024 0.0464266350 0.0470671838
## 2013-03-28 2.850330e-03 0.0083654162 0.0431368037 0.0836041496
## 2013-04-30 2.711615e-04 -0.0487507497 0.0415950987 0.0303598241
## 2013-05-31 2.217173e-02 0.0588686246 -0.0208286184 -0.0099611675
## 2013-06-28 -1.258958e-01 0.0310507506 0.0195320071 -0.0092512085
## 2013-07-31 1.321022e-01 0.0813355350 0.0211702203 0.0341193490
## 2013-08-30 8.044322e-02 -0.0695574090 -0.0466793531 -0.1118616188
## 2013-09-30 -2.172386e-02 0.1067688897 0.0042184476 0.0105269024
## 2013-10-31 9.201510e-02 0.1521839116 0.0561302315 0.0125809791
## 2013-11-29 6.770799e-02 0.0781496860 0.0043905080 -0.0069133995
## 2013-12-31 8.862879e-03 0.0130490386 -0.0113592004 -0.0103772510
## 2014-01-31 -1.139498e-01 -0.1059765119 -0.0316006713 -0.1106960080
## 2014-02-28 5.591854e-02 0.0094619003 -0.0036150290 0.1066821271
## 2014-03-31 1.975607e-02 -0.0737086161 0.0489951972 -0.0329978216
## 2014-04-30 9.476128e-02 -0.1007565303 0.0282205738 0.0202853927
## 2014-05-30 7.576540e-02 0.0273091844 0.0280123802 -0.0769022135
## 2014-06-30 2.728618e-02 0.0383836202 0.0188216406 0.0207489687
## 2014-07-31 2.832615e-02 -0.0369768154 -0.0139767466 0.0279067617
## 2014-08-29 7.465195e-02 0.0799468404 0.0486280911 0.0169978674
## 2014-09-30 -1.722061e-02 -0.0502010184 0.0135742371 0.0425319434
## 2014-10-31 6.948891e-02 -0.0540982347 0.0325508040 -0.0138153886
## 2014-11-28 1.007307e-01 0.1031187277 0.0400521890 0.1874998166
## 2014-12-31 -7.460629e-02 -0.0872368614 -0.0503893945 0.0254832748
## 2015-01-30 5.961177e-02 0.1330922557 -0.0082826795 -0.0307675545
## 2015-02-27 9.601610e-02 0.0697992426 0.0539662358 0.0496021165
## 2015-03-31 -3.187455e-02 -0.0214295755 -0.0278572653 0.0659769989
## 2015-04-30 5.769772e-03 0.1253212736 -0.0052424692 -0.0402785800
## 2015-05-29 4.434124e-02 0.0175090293 0.0136777299 0.0128402106
## 2015-06-30 -3.793831e-02 0.0112589814 -0.0252227650 0.0287064164
## 2015-07-31 -3.348063e-02 0.2111621090 0.0317391278 0.0026916360
## 2015-08-31 -6.848917e-02 -0.0443525782 -0.0361411998 -0.0448221894
## 2015-09-30 -2.205791e-02 -0.0019516837 0.0223621774 0.0121510349
## 2015-10-30 8.011270e-02 0.2010808743 0.0803525832 -0.0189944304
## 2015-11-30 -5.821348e-03 0.0602956777 -0.0200650898 -0.0547336205
## 2015-12-31 -1.167903e-01 0.0165440008 0.0045818655 0.0015158699
## 2016-01-29 -7.822345e-02 -0.1410054620 -0.0062246328 -0.0026201718
## 2016-02-29 -1.288088e-03 -0.0605352209 -0.0150162051 0.0882424844
## 2016-03-31 1.197460e-01 0.0717834363 0.0536582301 0.0476669211
## 2016-04-29 -1.507313e-01 0.1053453760 0.0046729064 -0.0343712324
## 2016-05-31 6.931429e-02 0.0915002899 -0.0175382309 -0.1372355970
## 2016-06-30 -4.359633e-02 -0.0099694639 0.0535411636 0.0150075932
## 2016-07-29 8.623519e-02 0.0586021229 0.0277405386 0.0759581171
## 2016-08-31 2.337661e-02 0.0135476418 -0.0130754680 -0.0627265606
## 2016-09-30 6.344806e-02 0.0848953908 0.0187459848 -0.0217478023
## 2016-10-31 4.324889e-03 -0.0583893058 -0.0145391694 0.0007275473
## 2016-11-30 -2.183761e-02 -0.0509721927 -0.0611560485 0.1251765740
## 2016-12-30 4.684099e-02 -0.0009330556 0.0442609018 -0.0670618677
## 2017-01-31 4.664178e-02 0.0936394059 -0.0081573438 -0.1135005300
## 2017-02-28 1.255549e-01 0.0258446800 0.0616556740 -0.0835533873
## 2017-03-31 4.754169e-02 0.0479423007 0.0201644701 -0.0628499147
## 2017-04-28 -6.986092e-05 0.0424566944 0.0126145579 0.0118878203
## 2017-05-31 6.560791e-02 0.0725778018 0.0380442043 -0.0018016474
## 2017-06-30 -5.891590e-02 -0.0271286156 -0.0118784061 -0.0532516131
## 2017-07-31 3.218012e-02 0.0202278808 0.0096513462 0.0804397045
## 2017-08-31 1.016529e-01 -0.0072953953 -0.0006017527 -0.0272904770
## 2017-09-29 -6.213458e-02 -0.0198260355 -0.0378631524 0.0789560154
## 2017-10-31 9.240350e-02 0.1395154056 -0.0108275356 0.0005084695
## 2017-11-30 2.007531e-02 0.0626577318 0.0624075714 0.0247790384
## 2017-12-29 -1.536326e-02 -0.0062057845 0.0287617232 0.0855496098
## WMT
## 2013-01-31 0.0248963913
## 2013-02-28 0.0117957358
## 2013-03-28 0.0620732336
## 2013-04-30 0.0378932666
## 2013-05-31 -0.0317795670
## 2013-06-28 -0.0046878858
## 2013-07-31 0.0452745145
## 2013-08-30 -0.0596996795
## 2013-09-30 0.0133391599
## 2013-10-31 0.0370285815
## 2013-11-29 0.0540191996
## 2013-12-31 -0.0232522450
## 2014-01-31 -0.0523036082
## 2014-02-28 0.0002675095
## 2014-03-31 0.0293260735
## 2014-04-30 0.0420198962
## 2014-05-30 -0.0314092566
## 2014-06-30 -0.0223929236
## 2014-07-31 -0.0200473363
## 2014-08-29 0.0323259003
## 2014-09-30 0.0127659115
## 2014-10-31 -0.0026192415
## 2014-11-28 0.1378162397
## 2014-12-31 -0.0135735995
## 2015-01-30 -0.0105351112
## 2015-02-27 -0.0124328896
## 2015-03-31 -0.0142313553
## 2015-04-30 -0.0524138480
## 2015-05-29 -0.0433513037
## 2015-06-30 -0.0460136507
## 2015-07-31 0.0146950821
## 2015-08-31 -0.0993580345
## 2015-09-30 0.0016974198
## 2015-10-30 -0.1246696153
## 2015-11-30 0.0275687911
## 2015-12-31 0.0492990864
## 2016-01-29 0.0793149329
## 2016-02-29 -0.0003019371
## 2016-03-31 0.0392706623
## 2016-04-29 -0.0239371028
## 2016-05-31 0.0641212881
## 2016-06-30 0.0311567244
## 2016-07-29 -0.0006849209
## 2016-08-31 -0.0143683082
## 2016-09-30 0.0094733768
## 2016-10-31 -0.0295503588
## 2016-11-30 0.0058383167
## 2016-12-30 -0.0116430074
## 2017-01-31 -0.0350401409
## 2017-02-28 0.0608888664
## 2017-03-31 0.0234095158
## 2017-04-28 0.0421083629
## 2017-05-31 0.0511562822
## 2017-06-30 -0.0378577120
## 2017-07-31 0.0553877522
## 2017-08-31 -0.0180254181
## 2017-09-29 0.0008961626
## 2017-10-31 0.1109625570
## 2017-11-30 0.1076146601
## 2017-12-29 0.0207685161# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AAPL AMZN PEP TGT WMT
## AAPL 4.830146e-03 0.0015511133 0.0006789485 -1.384739e-05 0.0006412761
## AMZN 1.551113e-03 0.0054660218 0.0008712211 -2.147201e-04 0.0003511319
## PEP 6.789485e-04 0.0008712211 0.0010461777 2.506920e-04 0.0004913971
## TGT -1.384739e-05 -0.0002147201 0.0002506920 3.709011e-03 0.0009852575
## WMT 6.412761e-04 0.0003511319 0.0004913971 9.852575e-04 0.0022213949# 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,] 0.03620391# 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## AAPL AMZN PEP TGT WMT
## [1,] 0.01237755 0.01326305 0.003845198 0.004603505 0.002114612rowSums(component_contribution)## [1] 0.03620391# Component contribution in percentage
component_percentages <- (component_contribution / sd_portfolio[1,1]) %>%
round(3) %>%
as_tibble()
component_percentages## # A tibble: 1 × 5
## AAPL AMZN PEP TGT WMT
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.342 0.366 0.106 0.127 0.058component_percentages %>%
as_tibble() %>%
gather(key = "asset", value = "contribution")## # A tibble: 5 × 2
## asset contribution
## <chr> <dbl>
## 1 AAPL 0.342
## 2 AMZN 0.366
## 3 PEP 0.106
## 4 TGT 0.127
## 5 WMT 0.0586 Plot: Colum Chart of Component Contribution and Weight
# 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
## AAPL AMZN PEP TGT WMT
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.342 0.366 0.106 0.127 0.058# 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 Portfolio Volatility and weight",
y = "percent",
x = "asset") 
Which of the assets in your portfolio the largest contributor to the
portfolio volatility? Do you think your portfolio risk is concentrated
in any one asset?
AAPL is the largest contributor to the portfolio’s volatility, and while risk isn’t concentrated in only one asset, it is somewhat heavier in AAPL and AMZN than in the others.