Apply it to your data 12
Which of the assets the largest contributor to the portfolio volatility?
Ashley Trogler
2024-06-22
# 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
Choose your stocks from 2012-12-31 to present.
symbols <- c("WMT", "TGT", "COST")
prices <- tq_get(x = symbols,
get = "stock.prices",
from = "2012-12-31",
to = "2024-06-22")
prices## # A tibble: 8,664 × 8
## symbol date open high low close volume adjusted
## <chr> <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 WMT 2012-12-31 22.5 22.8 22.5 22.7 21037500 17.8
## 2 WMT 2013-01-02 23.0 23.1 22.8 23.1 31172400 18.1
## 3 WMT 2013-01-03 23.1 23.1 22.8 22.9 26730300 18.0
## 4 WMT 2013-01-04 22.9 23.1 22.8 23.0 19314000 18.0
## 5 WMT 2013-01-07 22.9 23.0 22.7 22.8 18604200 17.9
## 6 WMT 2013-01-08 22.8 23.0 22.7 22.9 17600700 17.9
## 7 WMT 2013-01-09 22.9 22.9 22.7 22.9 15165600 17.9
## 8 WMT 2013-01-10 22.9 23.0 22.6 22.8 34361400 17.9
## 9 WMT 2013-01-11 22.9 22.9 22.7 22.9 18673500 17.9
## 10 WMT 2013-01-14 22.8 22.9 22.7 22.8 16471200 17.8
## # ℹ 8,654 more rows2 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
asset_returns_wide_tbl <- asset_returns_tbl %>%
pivot_wider(names_from = asset, values_from = returns) %>%
column_to_rownames(var = "date")
asset_returns_wide_tbl## COST TGT WMT
## 2013-01-31 0.0359118563 0.0207397882 0.0248962777
## 2013-02-28 -0.0076475360 0.0470677222 0.0117953957
## 2013-03-28 0.0464884672 0.0836036093 0.0620734366
## 2013-04-30 0.0216287224 0.0303599578 0.0378939522
## 2013-05-31 0.0137933633 -0.0099612184 -0.0317802181
## 2013-06-28 0.0085374763 -0.0092511918 -0.0046875807
## 2013-07-31 0.0601083565 0.0341188690 0.0452740639
## 2013-08-30 -0.0458223790 -0.1118611724 -0.0596997724
## 2013-09-30 0.0290718441 0.0105273528 0.0133391984
## 2013-10-31 0.0242754411 0.0125805355 0.0370288807
## 2013-11-29 0.0635978788 -0.0069131646 0.0540192970
## 2013-12-31 -0.0524560565 -0.0103776577 -0.0232520007
## 2014-01-31 -0.0575835901 -0.1106955873 -0.0523041023
## 2014-02-28 0.0414544398 0.1066821378 0.0002678000
## 2014-03-31 -0.0448253631 -0.0329979090 0.0293262185
## 2014-04-30 0.0351902242 0.0202852304 0.0420196598
## 2014-05-30 0.0059920526 -0.0769022289 -0.0314088932
## 2014-06-30 -0.0074399681 0.0207485560 -0.0223931078
## 2014-07-31 0.0234830968 0.0279074480 -0.0200476361
## 2014-08-29 0.0296726310 0.0169975620 0.0323258119
## 2014-09-30 0.0344191177 0.0425319191 0.0127657392
## 2014-10-31 0.0622568237 -0.0138156491 -0.0026188998
## 2014-11-28 0.0661378445 0.1875001408 0.1378160845
## 2014-12-31 -0.0026068347 0.0254832349 -0.0135732956
## 2015-01-30 0.0087098909 -0.0307673434 -0.0105355974
## 2015-02-27 0.0623771013 0.0496017116 -0.0124326417
## 2015-03-31 0.0304253328 0.0659774514 -0.0142314497
## 2015-04-30 -0.0546596110 -0.0402788970 -0.0524135580
## 2015-05-29 -0.0032207262 0.0128401962 -0.0433514846
## 2015-06-30 -0.0542544934 0.0287064969 -0.0460133786
## 2015-07-31 0.0730815717 0.0026914443 0.0146949522
## 2015-08-31 -0.0340551354 -0.0448221582 -0.0993586562
## 2015-09-30 0.0317641347 0.0121514322 0.0016978405
## 2015-10-30 0.0895906655 -0.0189945892 -0.1246694338
## 2015-11-30 0.0232363056 -0.0547337416 0.0275686559
## 2015-12-31 0.0004952755 0.0015160492 0.0492992864
## 2016-01-29 -0.0664305203 -0.0026203738 0.0793144370
## 2016-02-29 -0.0045318319 0.0882423884 -0.0003013328
## 2016-03-31 0.0490978470 0.0476667364 0.0392707965
## 2016-04-29 -0.0588890840 -0.0343705859 -0.0239374847
## 2016-05-31 0.0043109151 -0.1372357830 0.0641211295
## 2016-06-30 0.0540990540 0.0150075140 0.0311566542
## 2016-07-29 0.0628096873 0.0759581505 -0.0006845999
## 2016-08-31 -0.0284742385 -0.0627264342 -0.0143682067
## 2016-09-30 -0.0609213806 -0.0217480981 0.0094731350
## 2016-10-31 -0.0308969373 0.0007279391 -0.0295502795
## 2016-11-30 0.0181081526 0.1251765314 0.0058382102
## 2016-12-30 0.0644926878 -0.0670619619 -0.0116433546
## 2017-01-31 0.0237000197 -0.1135005374 -0.0350394339
## 2017-02-28 0.0802950288 -0.0835533344 0.0608887230
## 2017-03-31 -0.0550492954 -0.0628498742 0.0234090972
## 2017-04-28 0.0569661568 0.0118879148 0.0421086241
## 2017-05-31 0.0587797992 -0.0018019267 0.0511562327
## 2017-06-30 -0.1206068371 -0.0532515388 -0.0378576663
## 2017-07-31 -0.0089185560 0.0804398100 0.0553878975
## 2017-08-31 -0.0080370039 -0.0272904554 -0.0180256193
## 2017-09-29 0.0470447943 0.0789557917 0.0008961231
## 2017-10-31 -0.0197321073 0.0005084595 0.1109630688
## 2017-11-30 0.1383320749 0.0247791585 0.1076142859
## 2017-12-29 0.0091214520 0.0855494777 0.0207684225
## 2018-01-31 0.0459411880 0.1421912708 0.0764919556
## 2018-02-28 -0.0179104366 0.0107465788 -0.1691627116
## 2018-03-29 -0.0130234896 -0.0826209563 -0.0056771898
## 2018-04-30 0.0452894056 0.0446462662 -0.0057487134
## 2018-05-31 0.0083743626 0.0125275346 -0.0629875063
## 2018-06-29 0.0527602865 0.0433597975 0.0369864449
## 2018-07-31 0.0455078228 0.0581794746 0.0409478591
## 2018-08-31 0.0663289443 0.0889776424 0.0774628374
## 2018-09-28 0.0074785908 0.0080818676 -0.0205518569
## 2018-10-31 -0.0269698628 -0.0533180943 0.0656295145
## 2018-11-30 0.0138982976 -0.1560250187 -0.0265767650
## 2018-12-31 -0.1269314370 -0.0710987430 -0.0417365288
## 2019-01-31 0.0522180692 0.0994421956 0.0283648380
## 2019-02-28 0.0216654347 0.0038811670 0.0324433018
## 2019-03-29 0.1016324236 0.0997557218 -0.0094927667
## 2019-04-30 0.0139030115 -0.0360263069 0.0530141786
## 2019-05-31 -0.0218347883 0.0473595390 -0.0084085450
## 2019-06-28 0.0980461487 0.0737793346 0.0854575766
## 2019-07-31 0.0421255935 -0.0024273432 -0.0009961644
## 2019-08-30 0.0693118656 0.2218670392 0.0394579920
## 2019-09-30 -0.0228189354 -0.0012152654 0.0379543711
## 2019-10-31 0.0329301277 0.0000000000 -0.0120373070
## 2019-11-29 0.0090467358 0.1623186105 0.0154858494
## 2019-12-31 -0.0198412448 0.0252759556 0.0023740623
## 2020-01-31 0.0387074313 -0.1464845700 -0.0372905292
## 2020-02-28 -0.0810563170 -0.0667810587 -0.0613235734
## 2020-03-31 0.0140923364 -0.1024521322 0.0581106668
## 2020-04-30 0.0630696791 0.1658372065 0.0674659426
## 2020-05-29 0.0178919995 0.1138938005 0.0248291095
## 2020-06-30 -0.0171991064 -0.0198141103 -0.0351086241
## 2020-07-31 0.0731777316 0.0484208443 0.0772516530
## 2020-08-31 0.0657703112 0.1882718481 0.0745884877
## 2020-09-30 0.0208926128 0.0402476399 0.0076050694
## 2020-10-30 0.0092730308 -0.0335904896 -0.0083254558
## 2020-11-30 0.0912040167 0.1691405095 0.0963904023
## 2020-12-31 -0.0131568740 -0.0168514053 -0.0545611601
## 2021-01-29 -0.0668094741 0.0259450317 -0.0257181668
## 2021-02-26 -0.0607610812 0.0160103058 -0.0782172925
## 2021-03-31 0.0628754937 0.0767328273 0.0486515442
## 2021-04-30 0.0562815715 0.0453535882 0.0295953916
## 2021-05-28 0.0164726709 0.0938665279 0.0189582671
## 2021-06-30 0.0449723170 0.0632652250 -0.0071365835
## 2021-07-30 0.0844259272 0.0768492173 0.0107912082
## 2021-08-31 0.0582399344 -0.0519786925 0.0418682054
## 2021-09-30 -0.0135716308 -0.0765902091 -0.0606839831
## 2021-10-29 0.0913578036 0.1265019698 0.0695571065
## 2021-11-30 0.0928770027 -0.0592961897 -0.0606288087
## 2021-12-31 0.0511728240 -0.0521915401 0.0324795396
## 2022-01-31 -0.1167773929 -0.0487405512 -0.0343092312
## 2022-02-28 0.0290841490 -0.0940889867 -0.0338250137
## 2022-03-31 0.1034616875 0.0604566694 0.1008101558
## 2022-04-29 -0.0781044907 0.0745690586 0.0269633655
## 2022-05-31 -0.1314594789 -0.3412236863 -0.1698041668
## 2022-06-30 0.0276274452 -0.1364655852 -0.0563675841
## 2022-07-29 0.1234132837 0.1456888697 0.0826081991
## 2022-08-31 -0.0361144843 -0.0125338930 0.0081250417
## 2022-09-30 -0.1003084089 -0.0774525323 -0.0217357908
## 2022-10-31 0.0618563544 0.1015456621 0.0929241750
## 2022-11-30 0.0725757513 0.0232761217 0.0684916163
## 2022-12-30 -0.1665906326 -0.1141983311 -0.0685300635
## 2023-01-31 0.1130549133 0.1440936163 0.0145630640
## 2023-02-28 -0.0524475710 -0.0151216610 -0.0121680534
## 2023-03-31 0.0258717045 -0.0171793421 0.0408372578
## 2023-04-28 0.0126990200 -0.0487450396 0.0235918739
## 2023-05-31 0.0185209767 -0.1795999093 -0.0237416193
## 2023-06-30 0.0510997638 0.0073812991 0.0678437301
## 2023-07-31 0.0405678126 0.0340609050 0.0169068907
## 2023-08-31 -0.0186364188 -0.0669316857 0.0206048845
## 2023-09-29 0.0281466463 -0.1349887673 -0.0166185178
## 2023-10-31 -0.0224102040 0.0019877341 0.0215263029
## 2023-11-30 0.0722446165 0.1990889251 -0.0483956693
## 2023-12-29 0.1300909610 0.0623595611 0.0162177168
## 2024-01-31 0.0513780419 -0.0237310867 0.0470820912
## 2024-02-29 0.0696229645 0.1022452202 0.0620581818
## 2024-03-28 -0.0152523574 0.1474205982 0.0296685011
## 2024-04-30 -0.0117661258 -0.0960553701 -0.0137217305
## 2024-05-31 0.1136275203 -0.0235389825 0.1060150757
## 2024-06-21 0.0463476781 -0.0663844762 0.0321715698calculate_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(.45, .35, .2))## # A tibble: 1 × 3
## COST TGT WMT
## <dbl> <dbl> <dbl>
## 1 0.39 0.478 0.1336 Plot: Colum Chart of Component Contribution and Weight
plot_data <-asset_returns_wide_tbl %>%
calculate_component_contribution(w = c(0.4, 0.35, 0.25)) %>%
#Transform to long form
pivot_longer(cols = everything(), names_to = "Asset", values_to = "Contribution") %>%
# Add weights
add_column(weight = c(0.4, 0.35, 0.25)) %>%
# 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 Porfolio 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?
The largest contributor in this profloio is Target, but not by as much as I would have thought. Target is sitting below 50% around 48% followed by Costco at around 34% and Walmart at around 17%. I don't think this portfolio is concentrated in anyone asset, I do feel that Target has the most concentration data wise, but having Costco so close behind I don't see how the majoirity would be within Target. Therefore, I feel this portfolio is not concentrated in any one asset instead divded amoung all 3.