Apply it to your data 12
Which of the assets the largest contributor to the portfolio volatility?
Daniel Lee
2022-09-19
# 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("AAPL", "TSLA", "NFLX", "MTN", "DIS")
prices <- tq_get(x = symbols,
get = "stock.prices",
from = "2012-12-31",
to = "2017-12-31")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
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 DIS MTN NFLX TSLA
## 2013-01-31 -1.555891e-01 0.078945094 -0.0231914024 0.579217807 0.102078114
## 2013-02-28 -2.561105e-02 0.013091502 0.0442294560 0.129468379 -0.074128640
## 2013-03-28 2.850624e-03 0.039685566 0.1239322285 0.006360071 0.084208138
## 2013-04-30 2.709976e-04 0.101055605 -0.0329500633 0.132375020 0.354111531
## 2013-05-31 2.217154e-02 0.003811843 0.0603318920 0.046038179 0.593716684
## 2013-06-28 -1.258953e-01 0.001109062 -0.0370412628 -0.069356059 0.093672163
## 2013-07-31 1.321024e-01 0.023475366 0.0850319034 0.146848883 0.223739522
## 2013-08-30 8.044254e-02 -0.060905136 0.0151137144 0.149523815 0.229971642
## 2013-09-30 -2.172347e-02 0.058427054 0.0200908497 0.085363345 0.134706620
## 2013-10-31 9.201551e-02 0.061636415 0.0183266282 0.042020452 -0.189806595
## 2013-11-29 6.770812e-02 0.028033537 0.0730629544 0.126045633 -0.228409405
## 2013-12-31 8.861991e-03 0.092072694 -0.0046403281 0.006458091 0.167108541
## 2014-01-31 -1.139491e-01 -0.050880032 -0.0988386256 0.105976906 0.187261714
## 2014-02-28 5.591811e-02 0.106997957 0.0313450594 0.084967340 0.299722785
## 2014-03-31 1.975620e-02 -0.009199478 -0.0028627076 -0.235772622 -0.160783242
## 2014-04-30 9.476165e-02 -0.009159041 -0.0067657191 -0.089040653 -0.002690122
## 2014-05-30 7.576512e-02 0.057193768 0.0066225316 0.260398864 -0.000577422
## 2014-06-30 2.728610e-02 0.020383646 0.1075734512 0.053062785 0.144457224
## 2014-07-31 2.832618e-02 0.001631442 -0.0220078162 -0.041427371 -0.072372676
## 2014-08-29 7.465142e-02 0.045524507 0.0514985456 0.122147235 0.188794007
## 2014-09-30 -1.722036e-02 -0.009502045 0.0875148306 -0.056990921 -0.105566477
## 2014-10-31 6.948910e-02 0.026053279 0.0002985813 -0.138642147 -0.004046477
## 2014-11-28 1.007307e-01 0.012290242 0.0147125548 -0.125081717 0.011599801
## 2014-12-31 -7.460624e-02 0.030626958 0.0436540666 -0.014472733 -0.094774519
## 2015-01-30 5.961168e-02 -0.034894293 -0.0376811900 0.257187512 -0.088365289
## 2015-02-27 9.601598e-02 0.134740118 0.0005694778 0.072268016 -0.001277808
## 2015-03-31 -3.187422e-02 0.007752275 0.1699390703 -0.130782770 -0.074350051
## 2015-04-30 5.769499e-03 0.035863625 -0.0415593983 0.289324652 0.180226808
## 2015-05-29 4.434114e-02 0.015062664 0.0446488922 0.114579343 0.103899574
## 2015-06-30 -3.793775e-02 0.033587315 0.0569931238 0.051346180 0.067300935
## 2015-07-31 -3.348127e-02 0.055865224 0.0044769491 0.197231490 -0.007896616
## 2015-08-31 -6.848893e-02 -0.163696083 -0.0163605940 0.006278919 -0.066366250
## 2015-09-30 -2.205787e-02 0.003135937 -0.0303892148 -0.107942853 -0.002653519
## 2015-10-30 8.011265e-02 0.106983486 0.0927709050 0.048393445 -0.182659777
## 2015-11-30 -5.821045e-03 -0.002376611 0.0547907525 0.129220160 0.106828586
## 2015-12-31 -1.167905e-01 -0.070426735 0.0644606346 -0.075337490 0.041471519
## 2016-01-29 -7.822342e-02 -0.092250625 -0.0236382687 -0.219478322 -0.227360626
## 2016-02-29 -1.288781e-03 -0.003135750 0.0190966123 0.016950552 0.003810669
## 2016-03-31 1.197465e-01 0.038910639 0.0546073623 0.090226765 0.179948109
## 2016-04-29 -1.507310e-01 0.039003856 -0.0308370256 -0.127082275 0.046721797
## 2016-05-31 6.931406e-02 -0.039910421 0.0123425492 0.130402555 -0.075597968
## 2016-06-30 -4.359626e-02 -0.014210656 0.0575818928 -0.114425083 -0.050296440
## 2016-07-29 8.623492e-02 -0.012063820 0.0344154685 -0.002517413 0.100785334
## 2016-08-31 2.337669e-02 -0.015650850 0.1019784044 0.065736402 -0.102058091
## 2016-09-30 6.344814e-02 -0.017083396 -0.0098316059 0.011224670 -0.038366372
## 2016-10-31 4.325004e-03 -0.001832389 0.0213717941 0.236709154 -0.031364583
## 2016-11-30 -2.183735e-02 0.067070606 -0.0065443358 -0.065099283 -0.043041267
## 2016-12-30 4.684050e-02 0.057850180 0.0231785803 0.056493450 0.120665178
## 2017-01-31 4.664184e-02 0.059867826 0.0614884654 0.128033698 0.164624916
## 2017-02-28 1.255552e-01 -0.005073886 0.0546746513 0.010041084 -0.007730364
## 2017-03-31 4.754155e-02 0.029534977 0.0631143913 0.039185483 0.107278727
## 2017-04-28 -6.977477e-05 0.019302742 0.0295739231 0.029267777 0.120916212
## 2017-05-31 6.560712e-02 -0.068560337 0.0789601038 0.068984176 0.082295892
## 2017-06-30 -5.891564e-02 -0.015780709 -0.0481438181 -0.087485372 0.058654468
## 2017-07-31 3.218013e-02 0.041460580 0.0383518237 0.195442599 -0.111459860
## 2017-08-31 1.016538e-01 -0.082745077 0.0784063125 -0.039009333 0.095543446
## 2017-09-29 -6.213524e-02 -0.026331693 0.0007453901 0.037301404 -0.042474144
## 2017-10-31 9.240363e-02 -0.007740246 0.0088134666 0.079877197 -0.028457409
## 2017-11-30 2.007537e-02 0.069217923 -0.0169983605 -0.046100666 -0.070862541
## 2017-12-29 -1.536293e-02 0.033351507 -0.0531045780 0.023081621 0.008061928covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AAPL DIS MTN NFLX TSLA
## AAPL 0.0048301421 5.731109e-04 1.066260e-03 0.0006512360 4.838981e-04
## DIS 0.0005731109 2.786560e-03 8.463594e-05 0.0019003249 1.349726e-03
## MTN 0.0010662599 8.463594e-05 2.427738e-03 -0.0003491204 -3.105253e-05
## NFLX 0.0006512360 1.900325e-03 -3.491204e-04 0.0177864943 4.989080e-03
## TSLA 0.0004838981 1.349726e-03 -3.105253e-05 0.0049890797 2.095735e-02w <- c(0.25, 0.25, 0.2, 0.2, 0.1)
sd_portfolio <- sqrt(t(w) %*% covariance_matrix %*% w)
sd_portfolio## [,1]
## [1,] 0.04688437component_contribution <- (t(w) %*% covariance_matrix * w) / sd_portfolio[1,1]
component_contribution## AAPL DIS MTN NFLX TSLA
## [1,] 0.009292555 0.007315244 0.00298753 0.01972629 0.007562748rowSums(component_contribution)## [1] 0.04688437component_percentages <- (component_contribution / sd_portfolio[1,1]) %>%
round(3) %>%
as_tibble()
component_percentages## # A tibble: 1 × 5
## AAPL DIS MTN NFLX TSLA
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.198 0.156 0.064 0.421 0.161component_percentages %>%
as_tibble() %>%
gather(key = "asset", value = "contribution")## # A tibble: 5 × 2
## asset contribution
## <chr> <dbl>
## 1 AAPL 0.198
## 2 DIS 0.156
## 3 MTN 0.064
## 4 NFLX 0.421
## 5 TSLA 0.161# 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 DIS MTN NFLX TSLA
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.198 0.156 0.064 0.421 0.1616 Plot: Colum Chart of Component Contribution and Weight
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 to the portfolios volatility is Netflix as it is at almost 45%. I think that this is where alot of my portfolios risk is concentrated. This could be because of the times looked at as I think this would look very diffrent with more current data considering tesla is in my portfolio.
# 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 Volatility",
y = "percent",
x = "asset") 