Week 14: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Kyle Lawton
2024-10-24
# 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.
five stocks: “SPY”, “EFA”, “IJS”, “EEM”, “AGG” from 2012-12-31 to 2017-12-31
1 Import stock prices
symbols <- c("SPY", "EFA", "IJS", "EEM", "AGG")
prices <- tq_get(x = symbols,
get = "stock.prices",
from = "2012-12-31",
to = "2017-12-31")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
Refresh your memory on covariance with this video. Click this link Refresh your memory on matrix multiplication. Click this link
# 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## AGG EEM EFA IJS SPY
## 2013-01-31 -0.0062308443 -0.0029355732 0.0366062100 0.052132980 4.992279e-02
## 2013-02-28 0.0058911577 -0.0231052304 -0.0129693860 0.016175350 1.267829e-02
## 2013-03-28 0.0009851822 -0.0102351239 0.0129693860 0.040258401 3.726803e-02
## 2013-04-30 0.0096389282 0.0120847911 0.0489676317 0.001222365 1.903035e-02
## 2013-05-31 -0.0202141224 -0.0494830211 -0.0306553323 0.041976086 2.333503e-02
## 2013-06-28 -0.0157780844 -0.0547288037 -0.0271445590 -0.001402849 -1.343423e-02
## 2013-07-31 0.0026874686 0.0131598233 0.0518603429 0.063541446 5.038565e-02
## 2013-08-30 -0.0082975347 -0.0257057373 -0.0197466411 -0.034743276 -3.045080e-02
## 2013-09-30 0.0111435965 0.0695889042 0.0753386822 0.063873816 3.115554e-02
## 2013-10-31 0.0082923089 0.0408611832 0.0320817183 0.034233927 4.526658e-02
## 2013-11-29 -0.0025100792 -0.0025941418 0.0054497013 0.041661085 2.920714e-02
## 2013-12-31 -0.0055837464 -0.0040742478 0.0215279768 0.012891800 2.559607e-02
## 2014-01-31 0.0152926458 -0.0903227476 -0.0534132249 -0.035775080 -3.588464e-02
## 2014-02-28 0.0037567551 0.0332204236 0.0595049311 0.045257251 4.451040e-02
## 2014-03-31 -0.0014815359 0.0380221208 -0.0046023347 0.013315513 8.261415e-03
## 2014-04-30 0.0081829203 0.0077726260 0.0165291395 -0.023184437 6.927372e-03
## 2014-05-30 0.0117212292 0.0290913038 0.0158286510 0.006205464 2.294128e-02
## 2014-06-30 -0.0005760335 0.0237339410 0.0091654813 0.037718486 2.043469e-02
## 2014-07-31 -0.0025114694 0.0135554632 -0.0263800046 -0.052009372 -1.352864e-02
## 2014-08-29 0.0114314922 0.0279047890 0.0018004988 0.043657738 3.870473e-02
## 2014-09-30 -0.0061686548 -0.0808567872 -0.0395985696 -0.061260224 -1.389256e-02
## 2014-10-31 0.0105851629 0.0140963391 -0.0026548113 0.068874895 2.327815e-02
## 2014-11-28 0.0065493435 -0.0155410693 0.0006254685 0.004773485 2.710122e-02
## 2014-12-31 0.0014742534 -0.0404424598 -0.0407468895 0.025295757 -2.539661e-03
## 2015-01-30 0.0203155788 -0.0068956776 0.0062265051 -0.054627821 -3.007734e-02
## 2015-02-27 -0.0089883346 0.0431361987 0.0614506173 0.056914714 5.468207e-02
## 2015-03-31 0.0037401294 -0.0150863686 -0.0143887845 0.010156536 -1.583019e-02
## 2015-04-30 -0.0032330927 0.0662815314 0.0358167334 -0.018418042 9.785604e-03
## 2015-05-29 -0.0043833779 -0.0419112429 0.0019525723 0.007509800 1.277439e-02
## 2015-06-30 -0.0108259655 -0.0297463832 -0.0316787473 0.004171596 -2.052118e-02
## 2015-07-31 0.0085847356 -0.0651783133 0.0201143281 -0.027375365 2.233771e-02
## 2015-08-31 -0.0033634784 -0.0925122105 -0.0771523273 -0.047268261 -6.288660e-02
## 2015-09-30 0.0080811643 -0.0318249209 -0.0451949791 -0.038464793 -2.584714e-02
## 2015-10-30 0.0006854062 0.0618082331 0.0640258921 0.063589710 8.163521e-02
## 2015-11-30 -0.0038977771 -0.0255603347 -0.0075557175 0.024415031 3.648019e-03
## 2015-12-31 -0.0019190332 -0.0389471703 -0.0235951109 -0.052156997 -1.743339e-02
## 2016-01-29 0.0123295118 -0.0516368254 -0.0567577314 -0.060306871 -5.106857e-02
## 2016-02-29 0.0088316604 -0.0082114554 -0.0339139897 0.020604956 -8.263938e-04
## 2016-03-31 0.0087093268 0.1218791854 0.0637456882 0.089910827 6.510015e-02
## 2016-04-29 0.0025457170 0.0040791489 0.0219750146 0.021044308 3.933565e-03
## 2016-05-31 0.0001354794 -0.0376287124 -0.0008560461 0.004396965 1.686846e-02
## 2016-06-30 0.0191671219 0.0445825396 -0.0244913662 0.008292103 3.469633e-03
## 2016-07-29 0.0054296699 0.0524420901 0.0390001108 0.049348669 3.582240e-02
## 2016-08-31 -0.0021561973 0.0087984760 0.0053268628 0.011260899 1.196493e-03
## 2016-09-30 0.0005155668 0.0248729368 0.0132790773 0.008614876 5.821667e-05
## 2016-10-31 -0.0082051349 -0.0083121300 -0.0224036687 -0.038135142 -1.748954e-02
## 2016-11-30 -0.0259893724 -0.0451619603 -0.0179744835 0.125246065 3.617647e-02
## 2016-12-30 0.0025375760 -0.0025299463 0.0267027805 0.031492431 2.006901e-02
## 2017-01-31 0.0021265676 0.0644312792 0.0323819616 -0.012144342 1.773638e-02
## 2017-02-28 0.0064376887 0.0172579011 0.0118366296 0.013429304 3.853919e-02
## 2017-03-31 -0.0005523639 0.0361891043 0.0318055557 -0.006533203 1.249307e-03
## 2017-04-28 0.0090289405 0.0168663993 0.0239523650 0.005107588 9.877308e-03
## 2017-05-31 0.0068472470 0.0280599865 0.0348101824 -0.022862564 1.401401e-02
## 2017-06-30 -0.0001823347 0.0092238728 0.0029557828 0.029151750 6.354904e-03
## 2017-07-31 0.0033342327 0.0565943318 0.0261878698 0.007481617 2.034579e-02
## 2017-08-31 0.0093691963 0.0232439732 -0.0004482236 -0.027564422 2.913378e-03
## 2017-09-29 -0.0057323844 -0.0004463953 0.0233427751 0.082321526 1.994928e-02
## 2017-10-31 0.0009780360 0.0322786679 0.0166536632 0.005915744 2.329041e-02
## 2017-11-30 -0.0014837338 -0.0038969517 0.0068701719 0.036913625 3.010820e-02
## 2017-12-29 0.0047397328 0.0369251093 0.0133983343 -0.003731246 1.205506e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398459e-05 0.0001042110 4.178165e-05 -7.811832e-05 -9.031472e-06
## EEM 1.042110e-04 0.0017547138 1.039018e-03 6.437739e-04 6.795430e-04
## EFA 4.178165e-05 0.0010390178 1.064237e-03 6.490305e-04 6.975407e-04
## IJS -7.811832e-05 0.0006437739 6.490305e-04 1.565449e-03 8.290265e-04
## SPY -9.031472e-06 0.0006795430 6.975407e-04 8.290265e-04 7.408291e-04# 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,] 0.02347492# 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## AGG EEM EFA IJS SPY
## [1,] 0.0003874177 0.009257154 0.005815631 0.00568447 0.002330249rowSums(component_contribution)## [1] 0.02347492# Component contribution in percentage
component_percentages <- (component_contribution / sd_portfolio[1,1]) %>%
round(3) %>%
as_tibble()
component_percentages## # A tibble: 1 × 5
## AGG EEM EFA IJS SPY
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.017 0.394 0.248 0.242 0.099component_percentages %>%
as_tibble() %>%
gather(key = "asset", value = "contribution")## # A tibble: 5 × 2
## asset contribution
## <chr> <dbl>
## 1 AGG 0.017
## 2 EEM 0.394
## 3 EFA 0.248
## 4 IJS 0.242
## 5 SPY 0.0994 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## AGG EEM EFA IJS SPY
## 2013-01-31 -0.0062308443 -0.0029355732 0.0366062100 0.052132980 4.992279e-02
## 2013-02-28 0.0058911577 -0.0231052304 -0.0129693860 0.016175350 1.267829e-02
## 2013-03-28 0.0009851822 -0.0102351239 0.0129693860 0.040258401 3.726803e-02
## 2013-04-30 0.0096389282 0.0120847911 0.0489676317 0.001222365 1.903035e-02
## 2013-05-31 -0.0202141224 -0.0494830211 -0.0306553323 0.041976086 2.333503e-02
## 2013-06-28 -0.0157780844 -0.0547288037 -0.0271445590 -0.001402849 -1.343423e-02
## 2013-07-31 0.0026874686 0.0131598233 0.0518603429 0.063541446 5.038565e-02
## 2013-08-30 -0.0082975347 -0.0257057373 -0.0197466411 -0.034743276 -3.045080e-02
## 2013-09-30 0.0111435965 0.0695889042 0.0753386822 0.063873816 3.115554e-02
## 2013-10-31 0.0082923089 0.0408611832 0.0320817183 0.034233927 4.526658e-02
## 2013-11-29 -0.0025100792 -0.0025941418 0.0054497013 0.041661085 2.920714e-02
## 2013-12-31 -0.0055837464 -0.0040742478 0.0215279768 0.012891800 2.559607e-02
## 2014-01-31 0.0152926458 -0.0903227476 -0.0534132249 -0.035775080 -3.588464e-02
## 2014-02-28 0.0037567551 0.0332204236 0.0595049311 0.045257251 4.451040e-02
## 2014-03-31 -0.0014815359 0.0380221208 -0.0046023347 0.013315513 8.261415e-03
## 2014-04-30 0.0081829203 0.0077726260 0.0165291395 -0.023184437 6.927372e-03
## 2014-05-30 0.0117212292 0.0290913038 0.0158286510 0.006205464 2.294128e-02
## 2014-06-30 -0.0005760335 0.0237339410 0.0091654813 0.037718486 2.043469e-02
## 2014-07-31 -0.0025114694 0.0135554632 -0.0263800046 -0.052009372 -1.352864e-02
## 2014-08-29 0.0114314922 0.0279047890 0.0018004988 0.043657738 3.870473e-02
## 2014-09-30 -0.0061686548 -0.0808567872 -0.0395985696 -0.061260224 -1.389256e-02
## 2014-10-31 0.0105851629 0.0140963391 -0.0026548113 0.068874895 2.327815e-02
## 2014-11-28 0.0065493435 -0.0155410693 0.0006254685 0.004773485 2.710122e-02
## 2014-12-31 0.0014742534 -0.0404424598 -0.0407468895 0.025295757 -2.539661e-03
## 2015-01-30 0.0203155788 -0.0068956776 0.0062265051 -0.054627821 -3.007734e-02
## 2015-02-27 -0.0089883346 0.0431361987 0.0614506173 0.056914714 5.468207e-02
## 2015-03-31 0.0037401294 -0.0150863686 -0.0143887845 0.010156536 -1.583019e-02
## 2015-04-30 -0.0032330927 0.0662815314 0.0358167334 -0.018418042 9.785604e-03
## 2015-05-29 -0.0043833779 -0.0419112429 0.0019525723 0.007509800 1.277439e-02
## 2015-06-30 -0.0108259655 -0.0297463832 -0.0316787473 0.004171596 -2.052118e-02
## 2015-07-31 0.0085847356 -0.0651783133 0.0201143281 -0.027375365 2.233771e-02
## 2015-08-31 -0.0033634784 -0.0925122105 -0.0771523273 -0.047268261 -6.288660e-02
## 2015-09-30 0.0080811643 -0.0318249209 -0.0451949791 -0.038464793 -2.584714e-02
## 2015-10-30 0.0006854062 0.0618082331 0.0640258921 0.063589710 8.163521e-02
## 2015-11-30 -0.0038977771 -0.0255603347 -0.0075557175 0.024415031 3.648019e-03
## 2015-12-31 -0.0019190332 -0.0389471703 -0.0235951109 -0.052156997 -1.743339e-02
## 2016-01-29 0.0123295118 -0.0516368254 -0.0567577314 -0.060306871 -5.106857e-02
## 2016-02-29 0.0088316604 -0.0082114554 -0.0339139897 0.020604956 -8.263938e-04
## 2016-03-31 0.0087093268 0.1218791854 0.0637456882 0.089910827 6.510015e-02
## 2016-04-29 0.0025457170 0.0040791489 0.0219750146 0.021044308 3.933565e-03
## 2016-05-31 0.0001354794 -0.0376287124 -0.0008560461 0.004396965 1.686846e-02
## 2016-06-30 0.0191671219 0.0445825396 -0.0244913662 0.008292103 3.469633e-03
## 2016-07-29 0.0054296699 0.0524420901 0.0390001108 0.049348669 3.582240e-02
## 2016-08-31 -0.0021561973 0.0087984760 0.0053268628 0.011260899 1.196493e-03
## 2016-09-30 0.0005155668 0.0248729368 0.0132790773 0.008614876 5.821667e-05
## 2016-10-31 -0.0082051349 -0.0083121300 -0.0224036687 -0.038135142 -1.748954e-02
## 2016-11-30 -0.0259893724 -0.0451619603 -0.0179744835 0.125246065 3.617647e-02
## 2016-12-30 0.0025375760 -0.0025299463 0.0267027805 0.031492431 2.006901e-02
## 2017-01-31 0.0021265676 0.0644312792 0.0323819616 -0.012144342 1.773638e-02
## 2017-02-28 0.0064376887 0.0172579011 0.0118366296 0.013429304 3.853919e-02
## 2017-03-31 -0.0005523639 0.0361891043 0.0318055557 -0.006533203 1.249307e-03
## 2017-04-28 0.0090289405 0.0168663993 0.0239523650 0.005107588 9.877308e-03
## 2017-05-31 0.0068472470 0.0280599865 0.0348101824 -0.022862564 1.401401e-02
## 2017-06-30 -0.0001823347 0.0092238728 0.0029557828 0.029151750 6.354904e-03
## 2017-07-31 0.0033342327 0.0565943318 0.0261878698 0.007481617 2.034579e-02
## 2017-08-31 0.0093691963 0.0232439732 -0.0004482236 -0.027564422 2.913378e-03
## 2017-09-29 -0.0057323844 -0.0004463953 0.0233427751 0.082321526 1.994928e-02
## 2017-10-31 0.0009780360 0.0322786679 0.0166536632 0.005915744 2.329041e-02
## 2017-11-30 -0.0014837338 -0.0038969517 0.0068701719 0.036913625 3.010820e-02
## 2017-12-29 0.0047397328 0.0369251093 0.0133983343 -0.003731246 1.205506e-02calculate_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, .2, .2, .1))## # A tibble: 1 × 5
## AGG EEM EFA IJS SPY
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.017 0.394 0.248 0.242 0.0995 Visualizing Component Contribution
plot_data <- asset_returns_wide_tbl %>%
calculate_component_contribution(w = c(.25, .25, .2, .2, .1)) %>%
# 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 = "Percent Contribution to Portfolio Volatility")
Column Chart of Compont Contribution and Weight
plot_data <- asset_returns_wide_tbl %>%
calculate_component_contribution(w = c(.25, .25, .2, .2, .1)) %>%
# Transform to long form
pivot_longer(cols = everything() ,names_to = "Asset", values_to = "Contribution") %>%
# Add weights
add_column(weight = c(.25, .25, .2, .2, .1)) %>%
# 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)) +
theme(plot.title = element_text(hjust = 0.5)) +
theme_tq() +
labs(title = "Percent Contribution to Portfolio Volatility and Weight", y = "Percent",
x = NULL)