Apply it to your data 12
Which of the assets the largest contributor to the portfolio volatility?
Julius Mondschein
2024-06-25
# 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("NVDA", "MSFT", "TSLA", "AMD")
prices <- tq_get(x = symbols,
get = "stock.prices",
from = "2012-12-31",
to = "2024-06-24")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
# 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## AMD MSFT NVDA TSLA
## 2013-01-31 0.080042631 0.027328140 0.000000000 0.102078114
## 2013-02-28 -0.043228694 0.020914748 0.038221638 -0.074128640
## 2013-03-28 0.023810626 0.028720544 0.013338473 0.084208138
## 2013-04-30 0.100643521 0.145776685 0.070706518 0.354111531
## 2013-05-31 0.349557500 0.059941424 0.054651647 0.593716684
## 2013-06-28 0.019802609 -0.010368475 -0.030166672 0.093672163
## 2013-07-31 -0.079021973 -0.081394714 0.028091702 0.223739522
## 2013-08-30 -0.142285017 0.054854545 0.026269924 0.229971642
## 2013-09-30 0.152839195 -0.003599743 0.053460626 0.134706620
## 2013-10-31 -0.131658393 0.062037930 -0.024066347 -0.189806595
## 2013-11-29 0.086012929 0.081562332 0.032034957 -0.228409405
## 2013-12-31 0.061270767 -0.019063465 0.026566803 0.167108541
## 2014-01-31 -0.120694197 0.011429005 -0.020176837 0.187261714
## 2014-02-28 0.078471606 0.019814700 0.162107429 0.299722785
## 2014-03-31 0.077759411 0.067617272 -0.025904067 -0.160783242
## 2014-04-30 0.019753709 -0.014498323 0.030788240 -0.002690122
## 2014-05-30 -0.022250646 0.020307610 0.032886765 -0.000577422
## 2014-06-30 0.046406386 0.018393254 -0.024508429 0.144457224
## 2014-07-31 -0.069163352 0.034413273 -0.057729831 -0.072372676
## 2014-08-29 0.064378658 0.057485178 0.110060177 0.188794007
## 2014-09-30 -0.201203738 0.020264417 -0.052782660 -0.105566477
## 2014-10-31 -0.197092916 0.012645820 0.057399186 -0.004046477
## 2014-11-28 -0.003577818 0.024439082 0.074852373 0.011599801
## 2014-12-31 -0.043963081 -0.028858042 -0.044863790 -0.094774519
## 2015-01-30 -0.038172628 -0.139546984 -0.043318911 -0.088365289
## 2015-02-27 0.190716820 0.089036290 0.142699056 -0.001277808
## 2015-03-31 -0.148805873 -0.075529835 -0.052582251 -0.074350051
## 2015-04-30 -0.170452010 0.179201546 0.058908748 0.180226808
## 2015-05-29 0.008810621 -0.030803793 0.001459857 0.103899574
## 2015-06-30 0.051293347 -0.059571313 -0.095717138 0.067300935
## 2015-07-31 -0.217948801 0.056150602 -0.007988106 -0.007896616
## 2015-08-31 -0.064193162 -0.063950746 0.123595437 -0.066366250
## 2015-09-30 -0.051002506 0.016860711 0.092150870 -0.002653519
## 2015-10-30 0.209091727 0.173394894 0.140555674 -0.182659777
## 2015-11-30 0.107245540 0.038686179 0.115404956 0.106828586
## 2015-12-31 0.195650415 0.020577982 0.038347215 0.041471519
## 2016-01-29 -0.265854608 -0.007054322 -0.118048303 -0.227360626
## 2016-02-29 -0.027651504 -0.072344108 0.071923572 0.003810669
## 2016-03-31 0.286513083 0.082036541 0.127654846 0.179948109
## 2016-04-29 0.219628629 -0.102086925 -0.002810731 0.046721797
## 2016-05-31 0.252565652 0.067842329 0.276388533 -0.075597968
## 2016-06-30 0.117539811 -0.035138342 0.006187785 -0.050296440
## 2016-07-29 0.288654408 0.102267934 0.194444076 0.100785334
## 2016-08-31 0.075772552 0.019880851 0.073468916 -0.102058091
## 2016-09-30 -0.068510397 0.002433661 0.110693810 -0.038366372
## 2016-10-31 0.045269423 0.039487601 0.037805045 -0.031364583
## 2016-11-30 0.208935186 0.012390994 0.260525340 -0.043041267
## 2016-12-30 0.241162087 0.030721627 0.146435639 0.120665178
## 2017-01-31 -0.089419301 0.039598006 0.022602211 0.164624916
## 2017-02-28 0.332469208 -0.004373182 -0.071875087 -0.007730364
## 2017-03-31 0.006204787 0.028960656 0.070843835 0.107278727
## 2017-04-28 -0.089826957 0.038718291 -0.043434290 0.120916212
## 2017-05-31 -0.172743565 0.025672836 0.326022326 0.082295892
## 2017-06-30 0.109106841 -0.013115062 0.001453729 0.058654468
## 2017-07-31 0.086677465 0.053249786 0.117044802 -0.111459860
## 2017-08-31 -0.045855434 0.033388955 0.042639710 0.095543446
## 2017-09-29 -0.019418086 -0.003751961 0.053600823 -0.042474144
## 2017-10-31 -0.148545524 0.110342156 0.145700326 -0.028457409
## 2017-11-30 -0.009140779 0.016841111 -0.029244711 -0.070862541
## 2017-12-29 -0.057644734 0.016145579 -0.036583514 0.008061928
## 2018-01-31 0.290111036 0.104998052 0.239240354 0.129254571
## 2018-02-28 -0.126279741 -0.008450808 -0.014958848 -0.032266877
## 2018-03-29 -0.186458876 -0.027022804 -0.043969366 -0.253920408
## 2018-04-30 0.079353598 0.024353113 -0.029312649 0.099254576
## 2018-05-31 0.232656934 0.059652267 0.115145163 -0.031698139
## 2018-06-29 0.087800110 -0.002329768 -0.062544768 0.186043257
## 2018-07-31 0.201155761 0.073020915 0.033048653 -0.140021491
## 2018-08-31 0.317113754 0.061088402 0.137075494 0.011737389
## 2018-09-28 0.204779675 0.017997510 0.001210380 -0.130439038
## 2018-10-31 -0.528461644 -0.068387097 -0.287373431 0.242170576
## 2018-11-30 0.156736193 0.041798001 -0.253667113 0.038271580
## 2018-12-31 -0.143100857 -0.087790625 -0.202283670 -0.051761952
## 2019-01-31 0.279386699 0.027768869 0.073974250 -0.080628789
## 2019-02-28 -0.036716646 0.074511259 0.071593897 0.041032981
## 2019-03-29 0.081186244 0.051409264 0.151869779 -0.133656413
## 2019-04-30 0.079439632 0.101963388 0.007987876 -0.159123803
## 2019-05-31 -0.007994204 -0.050746912 -0.288679947 -0.253945372
## 2019-06-28 0.102547402 0.079843677 0.192591631 0.188012109
## 2019-07-31 0.002630713 0.017096995 0.026972510 0.078092373
## 2019-08-30 0.032312988 0.014924704 -0.006208304 -0.068516948
## 2019-09-30 -0.081448072 0.008451044 0.038414536 0.065449565
## 2019-10-31 0.157348653 0.030739153 0.143946986 0.268061253
## 2019-11-29 0.143100874 0.057761450 0.076031728 0.046592176
## 2019-12-31 0.158192829 0.040901384 0.082162827 0.237359743
## 2020-01-31 0.024554311 0.076455956 0.004790859 0.441578342
## 2020-02-28 -0.032874943 -0.046764912 0.133626936 0.026424253
## 2020-03-31 0.000000000 -0.026900207 -0.024248349 -0.242781458
## 2020-04-30 0.141443063 0.127800617 0.103279464 0.400209535
## 2020-05-29 0.026557731 0.025074131 0.194461918 0.065730500
## 2020-06-30 -0.022367226 0.104863934 0.068216413 0.257108657
## 2020-07-31 0.386468079 0.007343402 0.111189501 0.281420674
## 2020-08-31 0.159505216 0.097808886 0.231105475 0.554719320
## 2020-09-30 -0.102282260 -0.069775287 0.011895549 -0.149762306
## 2020-10-30 -0.085249927 -0.038086127 -0.076501232 -0.100371771
## 2020-11-30 0.207589583 0.058326085 0.066921537 0.380308519
## 2020-12-31 -0.010305505 0.038264400 -0.025900028 0.217730753
## 2021-01-29 -0.068478958 0.041997470 -0.005010623 0.117343701
## 2021-02-26 -0.013282561 0.004109382 0.054293175 -0.161038203
## 2021-03-31 -0.073771271 0.014482934 -0.026723395 -0.011269836
## 2021-04-30 0.038975739 0.067286239 0.117298031 0.060292565
## 2021-05-28 -0.019048206 -0.007656595 0.079071150 -0.126372343
## 2021-06-30 0.159523669 0.081569607 0.208332116 0.083547955
## 2021-07-30 0.122680138 0.050423677 -0.025494210 0.010973846
## 2021-08-31 0.041774537 0.059768825 0.138204256 0.068224268
## 2021-09-30 -0.073246845 -0.068406124 -0.077484855 0.052632612
## 2021-10-29 0.155648945 0.162366311 0.210396084 0.362230202
## 2021-11-30 0.275527434 -0.001283055 0.245338542 0.027237848
## 2021-12-31 -0.095815465 0.017184243 -0.105149811 -0.079968440
## 2022-01-31 -0.230729542 -0.078334353 -0.183267225 -0.120597475
## 2022-02-28 0.076555710 -0.037922248 -0.004133154 -0.073397011
## 2022-03-31 -0.120482480 0.031364756 0.112575749 0.213504290
## 2022-04-29 -0.245712033 -0.105212625 -0.386065597 -0.213125289
## 2022-05-31 0.174849100 -0.018242815 0.006716877 -0.138340062
## 2022-06-30 -0.286700804 -0.056909474 -0.208219114 -0.118657126
## 2022-07-29 0.211383814 0.089014539 0.180792144 0.280480149
## 2022-08-31 -0.107161630 -0.068989111 -0.185089196 -0.075250271
## 2022-09-30 -0.292287949 -0.115710273 -0.217576827 -0.038313992
## 2022-10-31 -0.053488672 -0.003311622 0.106044023 -0.153346760
## 2022-11-30 0.256609830 0.097329043 0.226461913 -0.155866121
## 2022-12-30 -0.181111434 -0.061923720 -0.146693749 -0.457813194
## 2023-01-31 0.148643655 0.032773642 0.290330387 0.340915767
## 2023-02-28 0.044631101 0.008977423 0.172531382 0.171904973
## 2023-03-31 0.220952299 0.144863386 0.179536580 0.008471140
## 2023-04-28 -0.092284450 0.063692768 -0.001008526 -0.233183710
## 2023-05-31 0.279677610 0.068691305 0.310008254 0.216021889
## 2023-06-30 -0.037054001 0.036330672 0.111729704 0.249689452
## 2023-07-31 0.004292397 -0.013659548 0.099530583 0.021391609
## 2023-08-31 -0.078906991 -0.022476429 0.054674115 -0.035588260
## 2023-09-29 -0.027814218 -0.037330893 -0.126218698 -0.030929027
## 2023-10-31 -0.042923335 0.068420561 -0.064546193 -0.219831983
## 2023-11-30 0.207055468 0.115954969 0.137050216 0.178463656
## 2023-12-29 0.196105829 -0.007603225 0.057262968 0.034390133
## 2024-01-31 0.128899206 0.055700698 0.217059049 -0.282704160
## 2024-02-29 0.138134928 0.041447426 0.251388505 0.075015304
## 2024-03-28 -0.064576574 0.016971445 0.132939772 -0.138383423
## 2024-04-30 -0.130678165 -0.077540252 -0.044746588 0.041724969
## 2024-05-31 0.052397554 0.065966581 0.238127628 -0.028782134
## 2024-06-21 -0.034562904 0.080166836 0.143739179 0.027307868# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AMD MSFT NVDA TSLA
## AMD 0.023742713 0.004015212 0.01056383 0.007378926
## MSFT 0.004015212 0.003544100 0.00416640 0.003217386
## NVDA 0.010563828 0.004166400 0.01538079 0.006814540
## TSLA 0.007378926 0.003217386 0.00681454 0.029197448# 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(.30, .30, .15, .15)
sd_portfolio <- sqrt(t(w) %*% covariance_matrix %*% w)
sd_portfolio## [,1]
## [1,] 0.08226545# 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## AMD MSFT NVDA TSLA
## [1,] 0.04018257 0.01230904 0.01412811 0.01564574rowSums(component_contribution)## [1] 0.08226545# Component contribution in percentage
component_percentages <- (component_contribution / sd_portfolio[1,1]) %>%
round(3) %>%
as_tibble()
component_percentages## # A tibble: 1 × 4
## AMD MSFT NVDA TSLA
## <dbl> <dbl> <dbl> <dbl>
## 1 0.488 0.15 0.172 0.19component_percentages %>%
as_tibble() %>%
gather(key = "asset", value = "contribution")## # A tibble: 4 × 2
## asset contribution
## <chr> <dbl>
## 1 AMD 0.488
## 2 MSFT 0.15
## 3 NVDA 0.172
## 4 TSLA 0.194 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")
asset_returns_wide_tbl## AMD MSFT NVDA TSLA
## 2013-01-31 0.080042631 0.027328140 0.000000000 0.102078114
## 2013-02-28 -0.043228694 0.020914748 0.038221638 -0.074128640
## 2013-03-28 0.023810626 0.028720544 0.013338473 0.084208138
## 2013-04-30 0.100643521 0.145776685 0.070706518 0.354111531
## 2013-05-31 0.349557500 0.059941424 0.054651647 0.593716684
## 2013-06-28 0.019802609 -0.010368475 -0.030166672 0.093672163
## 2013-07-31 -0.079021973 -0.081394714 0.028091702 0.223739522
## 2013-08-30 -0.142285017 0.054854545 0.026269924 0.229971642
## 2013-09-30 0.152839195 -0.003599743 0.053460626 0.134706620
## 2013-10-31 -0.131658393 0.062037930 -0.024066347 -0.189806595
## 2013-11-29 0.086012929 0.081562332 0.032034957 -0.228409405
## 2013-12-31 0.061270767 -0.019063465 0.026566803 0.167108541
## 2014-01-31 -0.120694197 0.011429005 -0.020176837 0.187261714
## 2014-02-28 0.078471606 0.019814700 0.162107429 0.299722785
## 2014-03-31 0.077759411 0.067617272 -0.025904067 -0.160783242
## 2014-04-30 0.019753709 -0.014498323 0.030788240 -0.002690122
## 2014-05-30 -0.022250646 0.020307610 0.032886765 -0.000577422
## 2014-06-30 0.046406386 0.018393254 -0.024508429 0.144457224
## 2014-07-31 -0.069163352 0.034413273 -0.057729831 -0.072372676
## 2014-08-29 0.064378658 0.057485178 0.110060177 0.188794007
## 2014-09-30 -0.201203738 0.020264417 -0.052782660 -0.105566477
## 2014-10-31 -0.197092916 0.012645820 0.057399186 -0.004046477
## 2014-11-28 -0.003577818 0.024439082 0.074852373 0.011599801
## 2014-12-31 -0.043963081 -0.028858042 -0.044863790 -0.094774519
## 2015-01-30 -0.038172628 -0.139546984 -0.043318911 -0.088365289
## 2015-02-27 0.190716820 0.089036290 0.142699056 -0.001277808
## 2015-03-31 -0.148805873 -0.075529835 -0.052582251 -0.074350051
## 2015-04-30 -0.170452010 0.179201546 0.058908748 0.180226808
## 2015-05-29 0.008810621 -0.030803793 0.001459857 0.103899574
## 2015-06-30 0.051293347 -0.059571313 -0.095717138 0.067300935
## 2015-07-31 -0.217948801 0.056150602 -0.007988106 -0.007896616
## 2015-08-31 -0.064193162 -0.063950746 0.123595437 -0.066366250
## 2015-09-30 -0.051002506 0.016860711 0.092150870 -0.002653519
## 2015-10-30 0.209091727 0.173394894 0.140555674 -0.182659777
## 2015-11-30 0.107245540 0.038686179 0.115404956 0.106828586
## 2015-12-31 0.195650415 0.020577982 0.038347215 0.041471519
## 2016-01-29 -0.265854608 -0.007054322 -0.118048303 -0.227360626
## 2016-02-29 -0.027651504 -0.072344108 0.071923572 0.003810669
## 2016-03-31 0.286513083 0.082036541 0.127654846 0.179948109
## 2016-04-29 0.219628629 -0.102086925 -0.002810731 0.046721797
## 2016-05-31 0.252565652 0.067842329 0.276388533 -0.075597968
## 2016-06-30 0.117539811 -0.035138342 0.006187785 -0.050296440
## 2016-07-29 0.288654408 0.102267934 0.194444076 0.100785334
## 2016-08-31 0.075772552 0.019880851 0.073468916 -0.102058091
## 2016-09-30 -0.068510397 0.002433661 0.110693810 -0.038366372
## 2016-10-31 0.045269423 0.039487601 0.037805045 -0.031364583
## 2016-11-30 0.208935186 0.012390994 0.260525340 -0.043041267
## 2016-12-30 0.241162087 0.030721627 0.146435639 0.120665178
## 2017-01-31 -0.089419301 0.039598006 0.022602211 0.164624916
## 2017-02-28 0.332469208 -0.004373182 -0.071875087 -0.007730364
## 2017-03-31 0.006204787 0.028960656 0.070843835 0.107278727
## 2017-04-28 -0.089826957 0.038718291 -0.043434290 0.120916212
## 2017-05-31 -0.172743565 0.025672836 0.326022326 0.082295892
## 2017-06-30 0.109106841 -0.013115062 0.001453729 0.058654468
## 2017-07-31 0.086677465 0.053249786 0.117044802 -0.111459860
## 2017-08-31 -0.045855434 0.033388955 0.042639710 0.095543446
## 2017-09-29 -0.019418086 -0.003751961 0.053600823 -0.042474144
## 2017-10-31 -0.148545524 0.110342156 0.145700326 -0.028457409
## 2017-11-30 -0.009140779 0.016841111 -0.029244711 -0.070862541
## 2017-12-29 -0.057644734 0.016145579 -0.036583514 0.008061928
## 2018-01-31 0.290111036 0.104998052 0.239240354 0.129254571
## 2018-02-28 -0.126279741 -0.008450808 -0.014958848 -0.032266877
## 2018-03-29 -0.186458876 -0.027022804 -0.043969366 -0.253920408
## 2018-04-30 0.079353598 0.024353113 -0.029312649 0.099254576
## 2018-05-31 0.232656934 0.059652267 0.115145163 -0.031698139
## 2018-06-29 0.087800110 -0.002329768 -0.062544768 0.186043257
## 2018-07-31 0.201155761 0.073020915 0.033048653 -0.140021491
## 2018-08-31 0.317113754 0.061088402 0.137075494 0.011737389
## 2018-09-28 0.204779675 0.017997510 0.001210380 -0.130439038
## 2018-10-31 -0.528461644 -0.068387097 -0.287373431 0.242170576
## 2018-11-30 0.156736193 0.041798001 -0.253667113 0.038271580
## 2018-12-31 -0.143100857 -0.087790625 -0.202283670 -0.051761952
## 2019-01-31 0.279386699 0.027768869 0.073974250 -0.080628789
## 2019-02-28 -0.036716646 0.074511259 0.071593897 0.041032981
## 2019-03-29 0.081186244 0.051409264 0.151869779 -0.133656413
## 2019-04-30 0.079439632 0.101963388 0.007987876 -0.159123803
## 2019-05-31 -0.007994204 -0.050746912 -0.288679947 -0.253945372
## 2019-06-28 0.102547402 0.079843677 0.192591631 0.188012109
## 2019-07-31 0.002630713 0.017096995 0.026972510 0.078092373
## 2019-08-30 0.032312988 0.014924704 -0.006208304 -0.068516948
## 2019-09-30 -0.081448072 0.008451044 0.038414536 0.065449565
## 2019-10-31 0.157348653 0.030739153 0.143946986 0.268061253
## 2019-11-29 0.143100874 0.057761450 0.076031728 0.046592176
## 2019-12-31 0.158192829 0.040901384 0.082162827 0.237359743
## 2020-01-31 0.024554311 0.076455956 0.004790859 0.441578342
## 2020-02-28 -0.032874943 -0.046764912 0.133626936 0.026424253
## 2020-03-31 0.000000000 -0.026900207 -0.024248349 -0.242781458
## 2020-04-30 0.141443063 0.127800617 0.103279464 0.400209535
## 2020-05-29 0.026557731 0.025074131 0.194461918 0.065730500
## 2020-06-30 -0.022367226 0.104863934 0.068216413 0.257108657
## 2020-07-31 0.386468079 0.007343402 0.111189501 0.281420674
## 2020-08-31 0.159505216 0.097808886 0.231105475 0.554719320
## 2020-09-30 -0.102282260 -0.069775287 0.011895549 -0.149762306
## 2020-10-30 -0.085249927 -0.038086127 -0.076501232 -0.100371771
## 2020-11-30 0.207589583 0.058326085 0.066921537 0.380308519
## 2020-12-31 -0.010305505 0.038264400 -0.025900028 0.217730753
## 2021-01-29 -0.068478958 0.041997470 -0.005010623 0.117343701
## 2021-02-26 -0.013282561 0.004109382 0.054293175 -0.161038203
## 2021-03-31 -0.073771271 0.014482934 -0.026723395 -0.011269836
## 2021-04-30 0.038975739 0.067286239 0.117298031 0.060292565
## 2021-05-28 -0.019048206 -0.007656595 0.079071150 -0.126372343
## 2021-06-30 0.159523669 0.081569607 0.208332116 0.083547955
## 2021-07-30 0.122680138 0.050423677 -0.025494210 0.010973846
## 2021-08-31 0.041774537 0.059768825 0.138204256 0.068224268
## 2021-09-30 -0.073246845 -0.068406124 -0.077484855 0.052632612
## 2021-10-29 0.155648945 0.162366311 0.210396084 0.362230202
## 2021-11-30 0.275527434 -0.001283055 0.245338542 0.027237848
## 2021-12-31 -0.095815465 0.017184243 -0.105149811 -0.079968440
## 2022-01-31 -0.230729542 -0.078334353 -0.183267225 -0.120597475
## 2022-02-28 0.076555710 -0.037922248 -0.004133154 -0.073397011
## 2022-03-31 -0.120482480 0.031364756 0.112575749 0.213504290
## 2022-04-29 -0.245712033 -0.105212625 -0.386065597 -0.213125289
## 2022-05-31 0.174849100 -0.018242815 0.006716877 -0.138340062
## 2022-06-30 -0.286700804 -0.056909474 -0.208219114 -0.118657126
## 2022-07-29 0.211383814 0.089014539 0.180792144 0.280480149
## 2022-08-31 -0.107161630 -0.068989111 -0.185089196 -0.075250271
## 2022-09-30 -0.292287949 -0.115710273 -0.217576827 -0.038313992
## 2022-10-31 -0.053488672 -0.003311622 0.106044023 -0.153346760
## 2022-11-30 0.256609830 0.097329043 0.226461913 -0.155866121
## 2022-12-30 -0.181111434 -0.061923720 -0.146693749 -0.457813194
## 2023-01-31 0.148643655 0.032773642 0.290330387 0.340915767
## 2023-02-28 0.044631101 0.008977423 0.172531382 0.171904973
## 2023-03-31 0.220952299 0.144863386 0.179536580 0.008471140
## 2023-04-28 -0.092284450 0.063692768 -0.001008526 -0.233183710
## 2023-05-31 0.279677610 0.068691305 0.310008254 0.216021889
## 2023-06-30 -0.037054001 0.036330672 0.111729704 0.249689452
## 2023-07-31 0.004292397 -0.013659548 0.099530583 0.021391609
## 2023-08-31 -0.078906991 -0.022476429 0.054674115 -0.035588260
## 2023-09-29 -0.027814218 -0.037330893 -0.126218698 -0.030929027
## 2023-10-31 -0.042923335 0.068420561 -0.064546193 -0.219831983
## 2023-11-30 0.207055468 0.115954969 0.137050216 0.178463656
## 2023-12-29 0.196105829 -0.007603225 0.057262968 0.034390133
## 2024-01-31 0.128899206 0.055700698 0.217059049 -0.282704160
## 2024-02-29 0.138134928 0.041447426 0.251388505 0.075015304
## 2024-03-28 -0.064576574 0.016971445 0.132939772 -0.138383423
## 2024-04-30 -0.130678165 -0.077540252 -0.044746588 0.041724969
## 2024-05-31 0.052397554 0.065966581 0.238127628 -0.028782134
## 2024-06-21 -0.034562904 0.080166836 0.143739179 0.027307868calculate_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
# 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(.30, .30, .15, .15))## # A tibble: 1 × 4
## AMD MSFT NVDA TSLA
## <dbl> <dbl> <dbl> <dbl>
## 1 0.488 0.15 0.172 0.196 Plot: Colum Chart of Component Contribution and Weight
plot_data <- asset_returns_wide_tbl %>%
calculate_component_contribution(w = c(.30, .30, .15, .15)) %>%
# transform to long form
pivot_longer(cols = everything(), names_to = "Asset", values_to = "Contribution")
plot_data %>%
ggplot(aes(x = Asset, y = Contribution)) +
geom_col(fill = "cornflowerblue") +
scale_y_continuous(labels = scales::percent_format(accuracy = 1)) +
theme(plot.title = element_text(hjust = 0.5)) +
labs(title = "Precent Contribution to Portfolio Volatility")
plot_data <- asset_returns_wide_tbl %>%
calculate_component_contribution(w = c(.30, .30, .15, .15)) %>%
# transform to long form
pivot_longer(cols = everything(), names_to = "Asset", values_to = "Contribution") %>%
# Add weight
add_column(weight = c(.30, .30, .15, .15)) %>%
# 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 = "Precent Contribution to Portfolio Volatility and Weight",
x = "Precent",
y = NULL)
Answer
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 asset in my portfolio that is the largest contributor to portfolio volatility is AMD, as represented by the highest bar in the “Contribution” category.
Given that AMD contributes substantially more to my portfolio’s volatility than its weight, it might appear that my portfolio risk is concentrated in one single asset. This concentration might pose a danger because AMD’s performance has a significant impact on the portfolio’s overall volatility. I think It may be useful to diversify my portfolio in order to more fairly distribute risk across assets.