Apply it to your data 12
Which of the assets the largest contributor to the portfolio volatility?
Anton Jellvik
2023-04-23
# 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
symbols <- c("AAPL", "MMM", "MSFT", "AMZN", "TSLA")
prices <- tq_get(x = symbols,
get = "stock.prices",
from = "2012-12-31",
to = "2022-12-31")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
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# 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 MMM MSFT TSLA
## 2013-01-31 -1.555890e-01 0.0566799640 7.966964e-02 0.027328325 0.102078031
## 2013-02-28 -2.561096e-02 -0.0046435329 3.989242e-02 0.020915312 -0.074128613
## 2013-03-28 2.850439e-03 0.0083654117 2.196836e-02 0.028720037 0.084208141
## 2013-04-30 2.710890e-04 -0.0487507638 -1.516467e-02 0.145776924 0.354111527
## 2013-05-31 2.217174e-02 0.0588686422 5.742273e-02 0.059941419 0.593716693
## 2013-06-28 -1.258955e-01 0.0310507858 -8.378334e-03 -0.010368706 0.093672182
## 2013-07-31 1.321020e-01 0.0813355112 7.128868e-02 -0.081394862 0.223739545
## 2013-08-30 8.044268e-02 -0.0695574024 -2.781830e-02 0.054854602 0.229971572
## 2013-09-30 -2.172311e-02 0.1067688764 5.005569e-02 -0.003599296 0.134706682
## 2013-10-31 9.201532e-02 0.1521839130 5.252784e-02 0.062037466 -0.189806650
## 2013-11-29 6.770783e-02 0.0781496951 6.398034e-02 0.081562362 -0.228409431
## 2013-12-31 8.862583e-03 0.0130490358 4.925005e-02 -0.019063475 0.167108548
## 2014-01-31 -1.139494e-01 -0.1059765070 -8.991294e-02 0.011429161 0.187261770
## 2014-02-28 5.591824e-02 0.0094619111 5.630829e-02 0.019814741 0.299722757
## 2014-03-31 1.975637e-02 -0.0737086127 6.879096e-03 0.067617291 -0.160783192
## 2014-04-30 9.476110e-02 -0.1007565625 2.496919e-02 -0.014498367 -0.002690159
## 2014-05-30 7.576538e-02 0.0273092148 3.068765e-02 0.020307595 -0.000577395
## 2014-06-30 2.728594e-02 0.0383835737 4.828692e-03 0.018393740 0.144457218
## 2014-07-31 2.832635e-02 -0.0369767889 -1.654205e-02 0.034412909 -0.072372711
## 2014-08-29 7.465198e-02 0.0799468534 2.777896e-02 0.057484943 0.188794049
## 2014-09-30 -1.722081e-02 -0.0502010221 -1.624293e-02 0.020264250 -0.105566506
## 2014-10-31 6.948875e-02 -0.0540982353 8.188728e-02 0.012646379 -0.004046457
## 2014-11-28 1.007311e-01 0.1031187000 4.563109e-02 0.024438812 0.011599756
## 2014-12-31 -7.460604e-02 -0.0872368443 2.608000e-02 -0.028858429 -0.094774520
## 2015-01-30 5.961131e-02 0.1330922758 -1.236996e-02 -0.139546831 -0.088365243
## 2015-02-27 9.601592e-02 0.0697991955 4.458010e-02 0.089036432 -0.001277805
## 2015-03-31 -3.187409e-02 -0.0214295288 -2.218331e-02 -0.075529620 -0.074350086
## 2015-04-30 5.769513e-03 0.1253212631 -5.328944e-02 0.179201478 0.180226844
## 2015-05-29 4.434117e-02 0.0175090073 2.335812e-02 -0.030804142 0.103899535
## 2015-06-30 -3.793796e-02 0.0112589801 -3.050858e-02 -0.059571228 0.067300966
## 2015-07-31 -3.348104e-02 0.2111621241 -1.936995e-02 0.056151196 -0.007896618
## 2015-08-31 -6.848885e-02 -0.0443525737 -5.578118e-02 -0.063951069 -0.066366266
## 2015-09-30 -2.205791e-02 -0.0019516780 -2.606465e-03 0.016860571 -0.002653542
## 2015-10-30 8.011268e-02 0.2010808557 1.033767e-01 0.173395261 -0.182659742
## 2015-11-30 -5.821392e-03 0.0602956898 2.533380e-03 0.038685904 0.106828579
## 2015-12-31 -1.167902e-01 0.0165439780 -3.867423e-02 0.020578017 0.041471546
## 2016-01-29 -7.822373e-02 -0.1410054619 2.386944e-03 -0.007054279 -0.227360646
## 2016-02-29 -1.288217e-03 -0.0605352242 4.533664e-02 -0.072344369 0.003810669
## 2016-03-31 1.197462e-01 0.0717834457 6.035869e-02 0.082036588 0.179948112
## 2016-04-29 -1.507312e-01 0.1053453885 4.490580e-03 -0.102086783 0.046721799
## 2016-05-31 6.931408e-02 0.0915002937 1.223707e-02 0.067842343 -0.075597977
## 2016-06-30 -4.359620e-02 -0.0099694796 3.960428e-02 -0.035138500 -0.050296472
## 2016-07-29 8.623522e-02 0.0586021200 1.833246e-02 0.102267968 0.100785361
## 2016-08-31 2.337665e-02 0.0135476463 1.113352e-02 0.019881054 -0.102058076
## 2016-09-30 6.344796e-02 0.0848953859 -1.693573e-02 0.002433625 -0.038366402
## 2016-10-31 4.324992e-03 -0.0583892995 -6.402805e-02 0.039487747 -0.031364578
## 2016-11-30 -2.183760e-02 -0.0509721788 4.461062e-02 0.012390911 -0.043041257
## 2016-12-30 4.684083e-02 -0.0009330597 3.899894e-02 0.030721416 0.120665160
## 2017-01-31 4.664165e-02 0.0936394046 -2.122354e-02 0.039598250 0.164624944
## 2017-02-28 1.255552e-01 0.0258446771 7.036077e-02 -0.004373343 -0.007730394
## 2017-03-31 4.754171e-02 0.0479423059 2.637319e-02 0.028960773 0.107278734
## 2017-04-28 -6.984302e-05 0.0424566809 2.324727e-02 0.038718091 0.120916240
## 2017-05-31 6.560732e-02 0.0725778079 4.912913e-02 0.025672934 0.082295867
## 2017-06-30 -5.891581e-02 -0.0271286060 1.802967e-02 -0.013115395 0.058654469
## 2017-07-31 3.218019e-02 0.0202278723 -3.430083e-02 0.053250049 -0.111459838
## 2017-08-31 1.016533e-01 -0.0072953921 2.127236e-02 0.033389089 0.095543417
## 2017-09-29 -6.213504e-02 -0.0198260414 2.694387e-02 -0.003752233 -0.042474117
## 2017-10-31 9.240386e-02 0.1395154081 9.227389e-02 0.110342313 -0.028457431
## 2017-11-30 2.007541e-02 0.0626577388 5.976449e-02 0.016841122 -0.070862536
## 2017-12-29 -1.536329e-02 -0.0062057977 -3.247853e-02 0.016145640 0.008061927
## 2018-01-31 -1.069370e-02 0.2156265512 6.230005e-02 0.104997966 0.129254601
## 2018-02-28 6.596104e-02 0.0415536373 -5.582635e-02 -0.008450622 -0.032266877
## 2018-03-29 -5.980371e-02 -0.0440034786 -7.030986e-02 -0.027022993 -0.253920406
## 2018-04-30 -1.513383e-02 0.0788802990 -1.215769e-01 0.024353128 0.099254538
## 2018-05-31 1.267418e-01 0.0397392491 2.132014e-02 0.059652055 -0.031698143
## 2018-06-29 -9.462591e-03 0.0421636779 -2.589330e-03 -0.002329705 0.186043287
## 2018-07-31 2.759906e-02 0.0446635758 7.631330e-02 0.073020979 -0.140021525
## 2018-08-31 1.826730e-01 0.1243079035 6.450937e-05 0.061088346 0.011737398
## 2018-09-28 -8.337664e-03 -0.0048359762 -9.959471e-04 0.017997770 -0.130439016
## 2018-10-31 -3.095160e-02 -0.2258870091 -1.020912e-01 -0.068387157 0.242170573
## 2018-11-30 -1.999125e-01 0.0560700362 9.556761e-02 0.041797846 0.038271593
## 2018-12-31 -1.240885e-01 -0.1180514840 -8.729117e-02 -0.087790572 -0.051761993
## 2019-01-31 5.368660e-02 0.1348080379 4.995407e-02 0.027769034 -0.080628787
## 2019-02-28 4.380316e-02 -0.0469930675 4.167471e-02 0.074511243 0.041033018
## 2019-03-29 9.260262e-02 0.0824420113 1.878857e-03 0.051409226 -0.133656450
## 2019-04-30 5.490094e-02 0.0786806236 -9.203814e-02 0.101963460 -0.159123800
## 2019-05-31 -1.326324e-01 -0.0818753437 -1.623119e-01 -0.050747040 -0.253945344
## 2019-06-28 1.226769e-01 0.0646557723 8.164481e-02 0.079843588 0.188012089
## 2019-07-31 7.361708e-02 -0.0142806642 7.929657e-03 0.017097001 0.078092368
## 2019-08-30 -1.659814e-02 -0.0496880811 -6.820927e-02 0.014924932 -0.068516906
## 2019-09-30 7.042265e-02 -0.0229951136 1.643595e-02 0.008451202 0.065449564
## 2019-10-31 1.049766e-01 0.0232034025 3.582378e-03 0.030738739 0.268061223
## 2019-11-29 7.469374e-02 0.0134958246 3.718012e-02 0.057761681 0.046592166
## 2019-12-31 9.420395e-02 0.0257863460 3.842269e-02 0.040901179 0.237359751
## 2020-01-31 5.260174e-02 0.0834803057 -1.061039e-01 0.076455997 0.441578346
## 2020-02-28 -1.218302e-01 -0.0642332025 -5.219288e-02 -0.046764868 0.026424249
## 2020-03-31 -7.231445e-02 0.0344213016 -8.915796e-02 -0.026900097 -0.242781463
## 2020-04-30 1.444240e-01 0.2381504772 1.069562e-01 0.127800391 0.400209547
## 2020-05-29 8.166673e-02 -0.0128673704 3.918810e-02 0.025074353 0.065730498
## 2020-06-30 1.374867e-01 0.1218341292 -2.880672e-03 0.104863712 0.257108653
## 2020-07-31 1.528339e-01 0.1372488981 -3.602822e-02 0.007343591 0.281420680
## 2020-08-31 1.960350e-01 0.0866005697 8.917032e-02 0.097808848 0.554719315
## 2020-09-30 -1.081715e-01 -0.0916533239 -1.757491e-02 -0.069775492 -0.149762308
## 2020-10-30 -6.188830e-02 -0.0364089200 -1.374264e-03 -0.038085982 -0.100371771
## 2020-11-30 9.120473e-02 0.0425228235 8.541936e-02 0.058326051 0.380308523
## 2020-12-31 1.084719e-01 0.0276719595 1.185548e-02 0.038264301 0.217730754
## 2021-01-29 -5.516534e-03 -0.0156985927 4.965284e-03 0.041997601 0.117343701
## 2021-02-26 -8.306871e-02 -0.0359675611 4.785130e-03 0.004109520 -0.161038203
## 2021-03-31 7.312761e-03 0.0003717143 9.590186e-02 0.014482715 -0.011269836
## 2021-04-30 7.345281e-02 0.1139202371 2.288347e-02 0.067286365 0.060292565
## 2021-05-28 -5.181659e-02 -0.0730764730 3.682067e-02 -0.007656588 -0.126372344
## 2021-06-30 9.449995e-02 0.0651836186 -2.195916e-02 0.081569662 0.083547956
## 2021-07-30 6.295836e-02 -0.0332696344 -3.479903e-03 0.050423609 0.010973846
## 2021-08-31 4.161137e-02 0.0421339383 -8.693994e-03 0.059768971 0.068224264
## 2021-09-30 -7.046188e-02 -0.0550034402 -1.044823e-01 -0.068406528 0.052632613
## 2021-10-29 5.700140e-02 0.0262547660 1.841341e-02 0.162366493 0.362230204
## 2021-11-30 9.991938e-02 0.0391473427 -4.145772e-02 -0.001283013 0.027237847
## 2021-12-31 7.160291e-02 -0.0505062023 4.366925e-02 0.017184254 -0.079968439
## 2022-01-31 -1.583675e-02 -0.1085098100 -6.759462e-02 -0.078334521 -0.120597477
## 2022-02-28 -5.558243e-02 0.0263230081 -1.008936e-01 -0.037921966 -0.073397011
## 2022-03-31 5.588263e-02 0.0596239187 1.546153e-03 0.031364707 0.213504290
## 2022-04-29 -1.021778e-01 -0.2711856809 -3.180081e-02 -0.105212880 -0.213125290
## 2022-05-31 -5.603707e-02 -0.0333130912 4.460586e-02 -0.018242486 -0.138340063
## 2022-06-30 -8.493690e-02 -0.1238178220 -1.429050e-01 -0.056909736 -0.118657123
## 2022-07-29 1.728044e-01 0.2394860603 1.015359e-01 0.089014717 0.280480148
## 2022-08-31 -3.170532e-02 -0.0625299199 -1.312113e-01 -0.068989078 -0.075250273
## 2022-09-30 -1.289443e-01 -0.1149865786 -1.180847e-01 -0.115710390 -0.038313991
## 2022-10-31 1.039558e-01 -0.0981105379 1.295984e-01 -0.003311601 -0.153346761
## 2022-11-30 -3.358521e-02 -0.0593198403 1.307113e-02 0.097329063 -0.155866119
## 2022-12-30 -1.304191e-01 -0.1391406417 -4.921897e-02 -0.061923768 -0.457813197# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AAPL AMZN MMM MSFT TSLA
## AAPL 0.006606496 0.003512598 0.002071260 0.002547258 0.005598654
## AMZN 0.003512598 0.007533033 0.001988012 0.002838125 0.005205806
## MMM 0.002071260 0.001988012 0.003406897 0.001396060 0.002129166
## MSFT 0.002547258 0.002838125 0.001396060 0.003614410 0.003744153
## TSLA 0.005598654 0.005205806 0.002129166 0.003744153 0.029457675# 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,] 0.06106988# 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 MMM MSFT TSLA
## [1,] 0.0164293 0.0173867 0.00716663 0.008917179 0.01117007rowSums(component_contribution)## [1] 0.06106988# Component contribution in percentage
component_percentages <- (component_contribution / sd_portfolio[1,1]) %>%
round(3) %>%
as_tibble()
component_percentages## # A tibble: 1 × 5
## AAPL AMZN MMM MSFT TSLA
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.269 0.285 0.117 0.146 0.183component_percentages %>%
as_tibble() %>%
gather(key = "asset", value = "contribution")## # A tibble: 5 × 2
## asset contribution
## <chr> <dbl>
## 1 AAPL 0.269
## 2 AMZN 0.285
## 3 MMM 0.117
## 4 MSFT 0.146
## 5 TSLA 0.1836 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 MMM MSFT TSLA
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.269 0.285 0.117 0.146 0.183asset_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")
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?
In my portfolio the stock with the largest contribution of volatility is AMZN. I would not say the portfolio risk is contributed in any one asset, however most of the risk is in AMZN and AAPL ut they also carry the most weight. We can see that TSLA is the carrying a lot more risk for the portfolio compared to the weight it carries.