Week 14: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Ethan Daly
2022-12-15
# 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 -0.0062319723 -0.0029354288 0.0366061825 0.052133370 4.992306e-02
## 2013-02-28 0.0058915055 -0.0231052881 -0.0129692108 0.016175209 1.267787e-02
## 2013-03-28 0.0009848890 -0.0102349982 0.0129692108 0.040258140 3.726858e-02
## 2013-04-30 0.0096394460 0.0120848841 0.0489679631 0.001222425 1.902936e-02
## 2013-05-31 -0.0202139253 -0.0494834238 -0.0306554141 0.041976408 2.333574e-02
## 2013-06-28 -0.0157785140 -0.0547284477 -0.0271445445 -0.001402667 -1.343421e-02
## 2013-07-31 0.0026875775 0.0131596870 0.0518601924 0.063541273 5.038575e-02
## 2013-08-30 -0.0082980237 -0.0257056867 -0.0197462111 -0.034743863 -3.045118e-02
## 2013-09-30 0.0111443896 0.0695890421 0.0753385829 0.063873973 3.115581e-02
## 2013-10-31 0.0082917000 0.0408612799 0.0320816251 0.034234283 4.526618e-02
## 2013-11-29 -0.0025101096 -0.0025939865 0.0054496187 0.041660902 2.920744e-02
## 2013-12-31 -0.0055827574 -0.0040745031 0.0215280708 0.012892154 2.559625e-02
## 2014-01-31 0.0152913763 -0.0903227464 -0.0534131976 -0.035775219 -3.588469e-02
## 2014-02-28 0.0037570080 0.0332204068 0.0595050275 0.045257247 4.451019e-02
## 2014-03-31 -0.0014819793 0.0380219888 -0.0046027569 0.013315419 8.261281e-03
## 2014-04-30 0.0081839262 0.0077729133 0.0165293451 -0.023184385 6.927881e-03
## 2014-05-30 0.0117210675 0.0290907286 0.0158285788 0.006205357 2.294100e-02
## 2014-06-30 -0.0005751849 0.0237341836 0.0091653598 0.037718442 2.043470e-02
## 2014-07-31 -0.0025125326 0.0135556565 -0.0263798612 -0.052009082 -1.352876e-02
## 2014-08-29 0.0114306574 0.0279045993 0.0018003801 0.043657717 3.870485e-02
## 2014-09-30 -0.0061670910 -0.0808567758 -0.0395983254 -0.061260333 -1.389230e-02
## 2014-10-31 0.0105846781 0.0140965399 -0.0026547927 0.068874860 2.327790e-02
## 2014-11-28 0.0065485323 -0.0155412045 0.0006253148 0.004773722 2.710110e-02
## 2014-12-31 0.0014752984 -0.0404422091 -0.0407465842 0.025295592 -2.539733e-03
## 2015-01-30 0.0203148531 -0.0068957476 0.0062261943 -0.054627666 -3.007685e-02
## 2015-02-27 -0.0089882410 0.0431361342 0.0614506693 0.056914499 5.468167e-02
## 2015-03-31 0.0037403887 -0.0150863268 -0.0143886921 0.010156214 -1.583011e-02
## 2015-04-30 -0.0032327836 0.0662813466 0.0358164986 -0.018417684 9.785723e-03
## 2015-05-29 -0.0043836686 -0.0419110152 0.0019527483 0.007510123 1.277457e-02
## 2015-06-30 -0.0108256913 -0.0297464533 -0.0316787251 0.004171268 -2.052157e-02
## 2015-07-31 0.0085849591 -0.0651781647 0.0201142986 -0.027375279 2.233794e-02
## 2015-08-31 -0.0033639428 -0.0925126244 -0.0771524393 -0.047268693 -6.288676e-02
## 2015-09-30 0.0080809617 -0.0318248663 -0.0451948693 -0.038464648 -2.584691e-02
## 2015-10-30 0.0006859612 0.0618083440 0.0640260094 0.063589971 8.163477e-02
## 2015-11-30 -0.0038983158 -0.0255604653 -0.0075557785 0.024414973 3.648385e-03
## 2015-12-31 -0.0019188536 -0.0389470837 -0.0235951980 -0.052156995 -1.743346e-02
## 2016-01-29 0.0123298354 -0.0516366096 -0.0567579904 -0.060306744 -5.106862e-02
## 2016-02-29 0.0088314456 -0.0082116909 -0.0339137376 0.020605140 -8.262157e-04
## 2016-03-31 0.0087089105 0.1218790178 0.0637456772 0.089910477 6.510009e-02
## 2016-04-29 0.0025463825 0.0040794252 0.0219750380 0.021044148 3.933541e-03
## 2016-05-31 0.0001353388 -0.0376285971 -0.0008559750 0.004397202 1.686845e-02
## 2016-06-30 0.0191665835 0.0445820965 -0.0244913860 0.008292079 3.469836e-03
## 2016-07-29 0.0054300419 0.0524424499 0.0390000275 0.049348401 3.582195e-02
## 2016-08-31 -0.0021561676 0.0087986308 0.0053270066 0.011261093 1.196769e-03
## 2016-09-30 0.0005157794 0.0248729051 0.0132789414 0.008614784 5.803735e-05
## 2016-10-31 -0.0082052033 -0.0083126009 -0.0224036442 -0.038134905 -1.748909e-02
## 2016-11-30 -0.0259896051 -0.0451616348 -0.0179743636 0.125246534 3.617629e-02
## 2016-12-30 0.0025377851 -0.0025299621 0.0267028055 0.031491822 2.006882e-02
## 2017-01-31 0.0021260130 0.0644313576 0.0323819384 -0.012143953 1.773644e-02
## 2017-02-28 0.0064383023 0.0172582227 0.0118364598 0.013428634 3.853931e-02
## 2017-03-31 -0.0005533517 0.0361887852 0.0318055200 -0.006533003 1.249175e-03
## 2017-04-28 0.0090294173 0.0168662832 0.0239523867 0.005107645 9.877296e-03
## 2017-05-31 0.0068475863 0.0280598805 0.0348102689 -0.022862787 1.401427e-02
## 2017-06-30 -0.0001829075 0.0092238050 0.0029558504 0.029151980 6.354715e-03
## 2017-07-31 0.0033348137 0.0565944936 0.0261879158 0.007481694 2.034578e-02
## 2017-08-31 0.0093688294 0.0232439862 -0.0004483665 -0.027564863 2.913398e-03
## 2017-09-29 -0.0057319510 -0.0004462544 0.0233429095 0.082321712 1.994915e-02
## 2017-10-31 0.0009779869 0.0322784833 0.0166534531 0.005916258 2.329059e-02
## 2017-11-30 -0.0014844784 -0.0038971225 0.0068701206 0.036913150 3.010794e-02
## 2017-12-29 0.0047404947 0.0369254846 0.0133983017 -0.003731268 1.205527e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398389e-05 0.0001042117 4.178484e-05 -7.811821e-05 -9.030033e-06
## EEM 1.042117e-04 0.0017547127 1.039017e-03 6.437755e-04 6.795417e-04
## EFA 4.178484e-05 0.0010390171 1.064236e-03 6.490313e-04 6.975388e-04
## IJS -7.811821e-05 0.0006437755 6.490313e-04 1.565450e-03 8.290253e-04
## SPY -9.030033e-06 0.0006795417 6.975388e-04 8.290253e-04 7.408273e-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,] 0.02347493# 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,] 0.0003874264 0.00925715 0.005815633 0.005684474 0.002330245rowSums(component_contribution)## [1] 0.02347493# 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")
# 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
## AGG EEM EFA IJS SPY
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.017 0.394 0.248 0.242 0.0995 Visualizing Component Contribution
# 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") 
6 Rolling Component Contribution
calculate_comp_contrib_by_window <- function(asset_returns_wide_tbl,
start = 1,
window = 24,
weights) {
# 1 Define start date
start_date <- rownames(asset_returns_wide_tbl)[start]
# 2 Define end date
end_date <- rownames(asset_returns_wide_tbl)[start + window]
# 3 Subset df
df_subset <- asset_returns_wide_tbl %>%
rownames_to_column(var = "date") %>%
filter(date >= start_date & date < end_date) %>%
column_to_rownames(var = "date")
# 4 Calculate component contribution
component_percentages <-df_subset %>%
calculate_component_contribution(w = weights)
# 5 Add end date to df
component_percentages %>%
mutate(date = ymd(end_date)) %>%
select(date, everything())
}