Apply it to your data 12
Which of the assets the largest contributor to the portfolio volatility?
Spencer Murrin
2023-04-26
# Load packages
# Core
library(tidyverse)
library(tidyquant)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
Choose your stocks from 2012-12-31 to present.
symbols <- c("HMC", "WMT", "TGT")
prices <- tq_get(x = symbols,
get = "stock.prices",
from = "2012-12-31",
to = "2023-04-25")2 Convert prices to returns (monthly)
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 Calculate Component Contribution to Portfolio Volatility
Component Contribution Step-by-Step
# 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## HMC TGT WMT
## 2013-01-31 0.0200998356 0.0207401596 0.0248959215
## 2013-02-28 -0.0066549588 0.0470673617 0.0117958395
## 2013-03-28 0.0263451800 0.0836038329 0.0620732465
## 2013-04-30 0.0439746672 0.0303601401 0.0378938538
## 2013-05-31 -0.0621735609 -0.0099614681 -0.0317802058
## 2013-06-28 -0.0031788525 -0.0092510365 -0.0046873872
## 2013-07-31 -0.0029571990 0.0341195118 0.0452742835
## 2013-08-30 -0.0328436085 -0.1118619627 -0.0596995892
## 2013-09-30 0.0640437702 0.0105272323 0.0133384818
## 2013-10-31 0.0466152820 0.0125805713 0.0370296261
## 2013-11-29 0.0583255324 -0.0069129537 0.0540190449
## 2013-12-31 -0.0199773013 -0.0103775452 -0.0232522335
## 2014-01-31 -0.0974646212 -0.1106960079 -0.0523038937
## 2014-02-28 -0.0397009050 0.1066820566 0.0002674871
## 2014-03-31 -0.0198911029 -0.0329974794 0.0293265369
## 2014-04-30 -0.0594581327 0.0202854596 0.0420195607
## 2014-05-30 0.0549203754 -0.0769022471 -0.0314089587
## 2014-06-30 -0.0002402223 0.0207483820 -0.0223932027
## 2014-07-31 -0.0031485471 0.0279073667 -0.0200475992
## 2014-08-29 -0.0240833990 0.0169978927 0.0323260251
## 2014-09-30 0.0113455078 0.0425314489 0.0127659485
## 2014-10-31 -0.0650832295 -0.0138152997 -0.0026192839
## 2014-11-28 -0.0576712660 0.1874999017 0.1378163776
## 2014-12-31 -0.0214573194 0.0254832182 -0.0135738497
## 2015-01-30 0.0234358641 -0.0307676680 -0.0105347679
## 2015-02-27 0.0922373323 0.0496020406 -0.0124331196
## 2015-03-31 -0.0068034631 0.0659777396 -0.0142310815
## 2015-04-30 0.0232320477 -0.0402790373 -0.0524139873
## 2015-05-29 0.0203699186 0.0128404328 -0.0433512631
## 2015-06-30 -0.0546518440 0.0287063480 -0.0460133698
## 2015-07-31 0.0470248672 0.0026914765 0.0146947913
## 2015-08-31 -0.0758308511 -0.0448221016 -0.0993584484
## 2015-09-30 -0.0462686081 0.0121506650 0.0016979077
## 2015-10-30 0.1025807637 -0.0189940775 -0.1246694221
## 2015-11-30 -0.0136759128 -0.0547335721 0.0275686541
## 2015-12-31 -0.0232171806 0.0015161203 0.0492988632
## 2016-01-29 -0.1669687716 -0.0026202876 0.0793149339
## 2016-02-29 -0.0496973160 0.0882424144 -0.0003016288
## 2016-03-31 0.0682377781 0.0476663391 0.0392703246
## 2016-04-29 -0.0139966361 -0.0343708838 -0.0239372452
## 2016-05-31 0.0371357823 -0.1372352096 0.0641212993
## 2016-06-30 -0.0919533964 0.0150074308 0.0311567814
## 2016-07-29 0.0682819576 0.0759577498 -0.0006851574
## 2016-08-31 0.1275681074 -0.0627265798 -0.0143680361
## 2016-09-30 -0.0574329163 -0.0217474804 0.0094737433
## 2016-10-31 0.0309813130 0.0007280338 -0.0295509617
## 2016-11-30 -0.0030216391 0.1251762441 0.0058384740
## 2016-12-30 -0.0123577178 -0.0670622258 -0.0116432875
## 2017-01-31 0.0179939192 -0.1135002464 -0.0350397876
## 2017-02-28 0.0411989466 -0.0835534105 0.0608891514
## 2017-03-31 -0.0170062708 -0.0628498668 0.0234091685
## 2017-04-28 -0.0390887948 0.0118879433 0.0421084103
## 2017-05-31 -0.0410365836 -0.0018020680 0.0511566238
## 2017-06-30 -0.0195235215 -0.0532513169 -0.0378582092
## 2017-07-31 0.0227407505 0.0804395238 0.0553879644
## 2017-08-31 0.0028509824 -0.0272904153 -0.0180258692
## 2017-09-29 0.0506523860 0.0789559063 0.0008965137
## 2017-10-31 0.0504640714 0.0005083642 0.1109627769
## 2017-11-30 0.0698717551 0.0247791645 0.1076144230
## 2017-12-29 0.0274914471 0.0855496684 0.0207684451
## 2018-01-31 0.0348887845 0.1421908955 0.0764922338
## 2018-02-28 0.0224163187 0.0107467078 -0.1691628230
## 2018-03-29 -0.0324651442 -0.0826207252 -0.0056774142
## 2018-04-30 -0.0107104615 0.0446461175 -0.0057485917
## 2018-05-31 -0.0786855229 0.0125275480 -0.0629873952
## 2018-06-29 -0.0816445365 0.0433596857 0.0369862619
## 2018-07-31 0.0463956745 0.0581796958 0.0409481429
## 2018-08-31 -0.0341715828 0.0889778314 0.0774627690
## 2018-09-28 0.0216028142 0.0080814374 -0.0205518131
## 2018-10-31 -0.0539563840 -0.0533180658 0.0656292489
## 2018-11-30 -0.0116464313 -0.1560244647 -0.0265764899
## 2018-12-31 -0.0552824644 -0.0710992105 -0.0417362936
## 2019-01-31 0.1282718116 0.0994419249 0.0283644816
## 2019-02-28 -0.0617266706 0.0038816480 0.0324429537
## 2019-03-29 -0.0320138365 0.0997558841 -0.0094924042
## 2019-04-30 0.0261548796 -0.0360265133 0.0530144104
## 2019-05-31 -0.1251152129 0.0473594236 -0.0084088417
## 2019-06-28 0.0569595655 0.0737795035 0.0854575277
## 2019-07-31 -0.0378596504 -0.0024277654 -0.0009961233
## 2019-08-30 -0.0502783483 0.2218672784 0.0394580055
## 2019-09-30 0.1049586393 -0.0012153882 0.0379543403
## 2019-10-31 0.0335564199 0.0000000000 -0.0120370555
## 2019-11-29 0.0417558461 0.1623189835 0.0154855924
## 2019-12-31 0.0137124657 0.0252757336 0.0023740140
## 2020-01-31 -0.1006227757 -0.1464843643 -0.0372903940
## 2020-02-28 0.0023411179 -0.0667811361 -0.0613237571
## 2020-03-31 -0.1242897870 -0.1024521624 0.0581106948
## 2020-04-30 0.0683992494 0.1658370196 0.0674661933
## 2020-05-29 0.0798826281 0.1138939583 0.0248286674
## 2020-06-30 -0.0159368157 -0.0198140966 -0.0351084730
## 2020-07-31 -0.0484967636 0.0484207511 0.0772514922
## 2020-08-31 0.0492790018 0.1882718513 0.0745885886
## 2020-09-30 -0.0699157735 0.0402475082 0.0076053150
## 2020-10-30 -0.0033812247 -0.0335903465 -0.0083257524
## 2020-11-30 0.1600602026 0.1691406393 0.0963907867
## 2020-12-31 0.0256519355 -0.0168515315 -0.0545615515
## 2021-01-29 -0.0647037194 0.0259450822 -0.0257178730
## 2021-02-26 0.0439590768 0.0160102396 -0.0782175350
## 2021-03-31 0.1003837894 0.0767328029 0.0486518570
## 2021-04-30 -0.0126626142 0.0453537305 0.0295951624
## 2021-05-28 0.0471600039 0.0938664454 0.0189582893
## 2021-06-30 0.0290057997 0.0632651915 -0.0071363926
## 2021-07-30 -0.0024892172 0.0768491811 0.0107910843
## 2021-08-31 -0.0590291902 -0.0519785598 0.0418679805
## 2021-09-30 0.0259284405 -0.0765903009 -0.0606838050
## 2021-10-29 -0.0361865349 0.1265019373 0.0695572256
## 2021-11-30 -0.0776508507 -0.0592961736 -0.0606288947
## 2021-12-31 0.0387005538 -0.0521915116 0.0324794702
## 2022-01-31 0.0379355855 -0.0487405501 -0.0343091704
## 2022-02-28 0.0336082625 -0.0940889760 -0.0338249225
## 2022-03-31 -0.0639586273 0.0604567191 0.1008100168
## 2022-04-29 -0.0737813917 0.0745690121 0.0269634002
## 2022-05-31 -0.0527981907 -0.3412238153 -0.1698041909
## 2022-06-30 -0.0305834031 -0.1364655946 -0.0563675996
## 2022-07-29 0.0629844441 0.1456890741 0.0826082211
## 2022-08-31 0.0306303499 -0.0125340202 0.0081250670
## 2022-09-30 -0.1920033081 -0.0774525273 -0.0217358900
## 2022-10-31 0.0554070999 0.1015456551 0.0929242133
## 2022-11-30 0.0710357731 0.0232761434 0.0684915859
## 2022-12-30 -0.0692844154 -0.1141982500 -0.0685300595
## 2023-01-31 0.0822610777 0.1440934537 0.0145629779
## 2023-02-28 0.0452922074 -0.0151216005 -0.0121678593
## 2023-03-31 0.0198253161 -0.0171793346 0.0408371631
## 2023-04-24 -0.0129181128 -0.0102558957 0.0353789147# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## HMC TGT WMT
## HMC 0.0035479914 0.001338602 0.0004475078
## TGT 0.0013386019 0.006661768 0.0022292015
## WMT 0.0004475078 0.002229202 0.0027250537# 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, 0.5)
sd_portfolio <- sqrt(t(w) %*% covariance_matrix %*% w)
sd_portfolio## [,1]
## [1,] 0.04643141# 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## HMC TGT WMT
## [1,] 0.007782459 0.0167704 0.02187855rowSums(component_contribution)## [1] 0.04643141# Component contribution in percentage
component_percentages <- (component_contribution / sd_portfolio[1,1]) %>%
round(3) %>%
as_tibble()
component_percentages## # A tibble: 1 × 3
## HMC TGT WMT
## <dbl> <dbl> <dbl>
## 1 0.168 0.361 0.471component_percentages %>%
as_tibble() %>%
gather(key = "asset", value = "contribution")## # A tibble: 3 × 2
## asset contribution
## <chr> <dbl>
## 1 HMC 0.168
## 2 TGT 0.361
## 3 WMT 0.471Component 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## HMC TGT WMT
## 2013-01-31 0.0200998356 0.0207401596 0.0248959215
## 2013-02-28 -0.0066549588 0.0470673617 0.0117958395
## 2013-03-28 0.0263451800 0.0836038329 0.0620732465
## 2013-04-30 0.0439746672 0.0303601401 0.0378938538
## 2013-05-31 -0.0621735609 -0.0099614681 -0.0317802058
## 2013-06-28 -0.0031788525 -0.0092510365 -0.0046873872
## 2013-07-31 -0.0029571990 0.0341195118 0.0452742835
## 2013-08-30 -0.0328436085 -0.1118619627 -0.0596995892
## 2013-09-30 0.0640437702 0.0105272323 0.0133384818
## 2013-10-31 0.0466152820 0.0125805713 0.0370296261
## 2013-11-29 0.0583255324 -0.0069129537 0.0540190449
## 2013-12-31 -0.0199773013 -0.0103775452 -0.0232522335
## 2014-01-31 -0.0974646212 -0.1106960079 -0.0523038937
## 2014-02-28 -0.0397009050 0.1066820566 0.0002674871
## 2014-03-31 -0.0198911029 -0.0329974794 0.0293265369
## 2014-04-30 -0.0594581327 0.0202854596 0.0420195607
## 2014-05-30 0.0549203754 -0.0769022471 -0.0314089587
## 2014-06-30 -0.0002402223 0.0207483820 -0.0223932027
## 2014-07-31 -0.0031485471 0.0279073667 -0.0200475992
## 2014-08-29 -0.0240833990 0.0169978927 0.0323260251
## 2014-09-30 0.0113455078 0.0425314489 0.0127659485
## 2014-10-31 -0.0650832295 -0.0138152997 -0.0026192839
## 2014-11-28 -0.0576712660 0.1874999017 0.1378163776
## 2014-12-31 -0.0214573194 0.0254832182 -0.0135738497
## 2015-01-30 0.0234358641 -0.0307676680 -0.0105347679
## 2015-02-27 0.0922373323 0.0496020406 -0.0124331196
## 2015-03-31 -0.0068034631 0.0659777396 -0.0142310815
## 2015-04-30 0.0232320477 -0.0402790373 -0.0524139873
## 2015-05-29 0.0203699186 0.0128404328 -0.0433512631
## 2015-06-30 -0.0546518440 0.0287063480 -0.0460133698
## 2015-07-31 0.0470248672 0.0026914765 0.0146947913
## 2015-08-31 -0.0758308511 -0.0448221016 -0.0993584484
## 2015-09-30 -0.0462686081 0.0121506650 0.0016979077
## 2015-10-30 0.1025807637 -0.0189940775 -0.1246694221
## 2015-11-30 -0.0136759128 -0.0547335721 0.0275686541
## 2015-12-31 -0.0232171806 0.0015161203 0.0492988632
## 2016-01-29 -0.1669687716 -0.0026202876 0.0793149339
## 2016-02-29 -0.0496973160 0.0882424144 -0.0003016288
## 2016-03-31 0.0682377781 0.0476663391 0.0392703246
## 2016-04-29 -0.0139966361 -0.0343708838 -0.0239372452
## 2016-05-31 0.0371357823 -0.1372352096 0.0641212993
## 2016-06-30 -0.0919533964 0.0150074308 0.0311567814
## 2016-07-29 0.0682819576 0.0759577498 -0.0006851574
## 2016-08-31 0.1275681074 -0.0627265798 -0.0143680361
## 2016-09-30 -0.0574329163 -0.0217474804 0.0094737433
## 2016-10-31 0.0309813130 0.0007280338 -0.0295509617
## 2016-11-30 -0.0030216391 0.1251762441 0.0058384740
## 2016-12-30 -0.0123577178 -0.0670622258 -0.0116432875
## 2017-01-31 0.0179939192 -0.1135002464 -0.0350397876
## 2017-02-28 0.0411989466 -0.0835534105 0.0608891514
## 2017-03-31 -0.0170062708 -0.0628498668 0.0234091685
## 2017-04-28 -0.0390887948 0.0118879433 0.0421084103
## 2017-05-31 -0.0410365836 -0.0018020680 0.0511566238
## 2017-06-30 -0.0195235215 -0.0532513169 -0.0378582092
## 2017-07-31 0.0227407505 0.0804395238 0.0553879644
## 2017-08-31 0.0028509824 -0.0272904153 -0.0180258692
## 2017-09-29 0.0506523860 0.0789559063 0.0008965137
## 2017-10-31 0.0504640714 0.0005083642 0.1109627769
## 2017-11-30 0.0698717551 0.0247791645 0.1076144230
## 2017-12-29 0.0274914471 0.0855496684 0.0207684451
## 2018-01-31 0.0348887845 0.1421908955 0.0764922338
## 2018-02-28 0.0224163187 0.0107467078 -0.1691628230
## 2018-03-29 -0.0324651442 -0.0826207252 -0.0056774142
## 2018-04-30 -0.0107104615 0.0446461175 -0.0057485917
## 2018-05-31 -0.0786855229 0.0125275480 -0.0629873952
## 2018-06-29 -0.0816445365 0.0433596857 0.0369862619
## 2018-07-31 0.0463956745 0.0581796958 0.0409481429
## 2018-08-31 -0.0341715828 0.0889778314 0.0774627690
## 2018-09-28 0.0216028142 0.0080814374 -0.0205518131
## 2018-10-31 -0.0539563840 -0.0533180658 0.0656292489
## 2018-11-30 -0.0116464313 -0.1560244647 -0.0265764899
## 2018-12-31 -0.0552824644 -0.0710992105 -0.0417362936
## 2019-01-31 0.1282718116 0.0994419249 0.0283644816
## 2019-02-28 -0.0617266706 0.0038816480 0.0324429537
## 2019-03-29 -0.0320138365 0.0997558841 -0.0094924042
## 2019-04-30 0.0261548796 -0.0360265133 0.0530144104
## 2019-05-31 -0.1251152129 0.0473594236 -0.0084088417
## 2019-06-28 0.0569595655 0.0737795035 0.0854575277
## 2019-07-31 -0.0378596504 -0.0024277654 -0.0009961233
## 2019-08-30 -0.0502783483 0.2218672784 0.0394580055
## 2019-09-30 0.1049586393 -0.0012153882 0.0379543403
## 2019-10-31 0.0335564199 0.0000000000 -0.0120370555
## 2019-11-29 0.0417558461 0.1623189835 0.0154855924
## 2019-12-31 0.0137124657 0.0252757336 0.0023740140
## 2020-01-31 -0.1006227757 -0.1464843643 -0.0372903940
## 2020-02-28 0.0023411179 -0.0667811361 -0.0613237571
## 2020-03-31 -0.1242897870 -0.1024521624 0.0581106948
## 2020-04-30 0.0683992494 0.1658370196 0.0674661933
## 2020-05-29 0.0798826281 0.1138939583 0.0248286674
## 2020-06-30 -0.0159368157 -0.0198140966 -0.0351084730
## 2020-07-31 -0.0484967636 0.0484207511 0.0772514922
## 2020-08-31 0.0492790018 0.1882718513 0.0745885886
## 2020-09-30 -0.0699157735 0.0402475082 0.0076053150
## 2020-10-30 -0.0033812247 -0.0335903465 -0.0083257524
## 2020-11-30 0.1600602026 0.1691406393 0.0963907867
## 2020-12-31 0.0256519355 -0.0168515315 -0.0545615515
## 2021-01-29 -0.0647037194 0.0259450822 -0.0257178730
## 2021-02-26 0.0439590768 0.0160102396 -0.0782175350
## 2021-03-31 0.1003837894 0.0767328029 0.0486518570
## 2021-04-30 -0.0126626142 0.0453537305 0.0295951624
## 2021-05-28 0.0471600039 0.0938664454 0.0189582893
## 2021-06-30 0.0290057997 0.0632651915 -0.0071363926
## 2021-07-30 -0.0024892172 0.0768491811 0.0107910843
## 2021-08-31 -0.0590291902 -0.0519785598 0.0418679805
## 2021-09-30 0.0259284405 -0.0765903009 -0.0606838050
## 2021-10-29 -0.0361865349 0.1265019373 0.0695572256
## 2021-11-30 -0.0776508507 -0.0592961736 -0.0606288947
## 2021-12-31 0.0387005538 -0.0521915116 0.0324794702
## 2022-01-31 0.0379355855 -0.0487405501 -0.0343091704
## 2022-02-28 0.0336082625 -0.0940889760 -0.0338249225
## 2022-03-31 -0.0639586273 0.0604567191 0.1008100168
## 2022-04-29 -0.0737813917 0.0745690121 0.0269634002
## 2022-05-31 -0.0527981907 -0.3412238153 -0.1698041909
## 2022-06-30 -0.0305834031 -0.1364655946 -0.0563675996
## 2022-07-29 0.0629844441 0.1456890741 0.0826082211
## 2022-08-31 0.0306303499 -0.0125340202 0.0081250670
## 2022-09-30 -0.1920033081 -0.0774525273 -0.0217358900
## 2022-10-31 0.0554070999 0.1015456551 0.0929242133
## 2022-11-30 0.0710357731 0.0232761434 0.0684915859
## 2022-12-30 -0.0692844154 -0.1141982500 -0.0685300595
## 2023-01-31 0.0822610777 0.1440934537 0.0145629779
## 2023-02-28 0.0452922074 -0.0151216005 -0.0121678593
## 2023-03-31 0.0198253161 -0.0171793346 0.0408371631
## 2023-04-24 -0.0129181128 -0.0102558957 0.0353789147calculate_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, .5))## # A tibble: 1 × 3
## HMC TGT WMT
## <dbl> <dbl> <dbl>
## 1 0.168 0.361 0.4716 Plot: Colum Chart of Component Contribution and Weight
plot_data <- asset_returns_wide_tbl %>%
calculate_component_contribution(w = c(.25, .25, .5)) %>%
# Transform to long from
pivot_longer(cols = everything(), names_to = "Asset", values_to = "Contribution") %>%
# Add weights
add_column(weight = c(.25, .25, .5)) %>%
# 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)
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?
Walmart is the largest contributor to the portfolio volatility. Higher stock price volatility often means higher risk for future investment, but usually means a higher return as well. Honda is the lowest contributor to the portfolio volatility and would have smaller gap between stock prices.Looking at the chart, Walmart seems to be the riskier asset in my portfolio compared to the other assets.