Week 13: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Logan Teixeira
2024-4-24
# 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 -0.0062300938 -0.0029357305 0.0366065026 0.052133168 4.992341e-02
## 2013-02-28 0.0058907664 -0.0231051036 -0.0129694926 0.016175416 1.267768e-02
## 2013-03-28 0.0009851148 -0.0102352033 0.0129694926 0.040258177 3.726829e-02
## 2013-04-30 0.0096389753 0.0120849871 0.0489675055 0.001222177 1.903009e-02
## 2013-05-31 -0.0202142167 -0.0494837072 -0.0306553609 0.041976279 2.333517e-02
## 2013-06-28 -0.0157784232 -0.0547281714 -0.0271444130 -0.001402940 -1.343394e-02
## 2013-07-31 0.0026878205 0.0131598101 0.0518602160 0.063541538 5.038547e-02
## 2013-08-30 -0.0082981576 -0.0257053223 -0.0197462770 -0.034743504 -3.045119e-02
## 2013-09-30 0.0111441764 0.0695883669 0.0753381639 0.063873479 3.115624e-02
## 2013-10-31 0.0082918343 0.0408614131 0.0320821275 0.034234338 4.526615e-02
## 2013-11-29 -0.0025096125 -0.0025940994 0.0054496601 0.041660995 2.920715e-02
## 2013-12-31 -0.0055829992 -0.0040746633 0.0215281351 0.012892066 2.559636e-02
## 2014-01-31 0.0152914695 -0.0903223211 -0.0534133990 -0.035775106 -3.588489e-02
## 2014-02-28 0.0037570439 0.0332205818 0.0595048281 0.045257392 4.451050e-02
## 2014-03-31 -0.0014817680 0.0380219217 -0.0046024808 0.013315390 8.261430e-03
## 2014-04-30 0.0081834467 0.0077724039 0.0165293818 -0.023184463 6.927083e-03
## 2014-05-30 0.0117218149 0.0290912949 0.0158283376 0.006205346 2.294165e-02
## 2014-06-30 -0.0005759727 0.0237340283 0.0091656063 0.037718582 2.043434e-02
## 2014-07-31 -0.0025123159 0.0135555274 -0.0263799315 -0.052009190 -1.352821e-02
## 2014-08-29 0.0114302238 0.0279047730 0.0018004596 0.043657634 3.870430e-02
## 2014-09-30 -0.0061666833 -0.0808567507 -0.0395983845 -0.061260207 -1.389233e-02
## 2014-10-31 0.0105838868 0.0140966284 -0.0026549362 0.068874695 2.327780e-02
## 2014-11-28 0.0065492238 -0.0155414384 0.0006254262 0.004773850 2.710161e-02
## 2014-12-31 0.0014756395 -0.0404422001 -0.0407468067 0.025295956 -2.540010e-03
## 2015-01-30 0.0203147715 -0.0068958564 0.0062265795 -0.054628227 -3.007711e-02
## 2015-02-27 -0.0089881904 0.0431363665 0.0614504309 0.056914578 5.468219e-02
## 2015-03-31 0.0037401399 -0.0150866789 -0.0143887661 0.010156378 -1.583061e-02
## 2015-04-30 -0.0032328098 0.0662815737 0.0358166812 -0.018417663 9.786119e-03
## 2015-05-29 -0.0043830966 -0.0419108429 0.0019524810 0.007509783 1.277427e-02
## 2015-06-30 -0.0108265359 -0.0297465286 -0.0316786651 0.004171332 -2.052160e-02
## 2015-07-31 0.0085849196 -0.0651780945 0.0201144464 -0.027375236 2.233794e-02
## 2015-08-31 -0.0033636240 -0.0925125948 -0.0771524492 -0.047268658 -6.288683e-02
## 2015-09-30 0.0080815271 -0.0318249808 -0.0451948062 -0.038464409 -2.584698e-02
## 2015-10-30 0.0006847906 0.0618083630 0.0640260411 0.063589409 8.163497e-02
## 2015-11-30 -0.0038979013 -0.0255607491 -0.0075559812 0.024415600 3.648829e-03
## 2015-12-31 -0.0019191180 -0.0389467614 -0.0235950118 -0.052157047 -1.743380e-02
## 2016-01-29 0.0123301239 -0.0516367829 -0.0567577196 -0.060306953 -5.106871e-02
## 2016-02-29 0.0088317637 -0.0082116787 -0.0339142075 0.020605296 -8.263143e-04
## 2016-03-31 0.0087085611 0.1218788741 0.0637458877 0.089910381 6.510037e-02
## 2016-04-29 0.0025466986 0.0040794280 0.0219751583 0.021043992 3.933277e-03
## 2016-05-31 0.0001352027 -0.0376284773 -0.0008561257 0.004397330 1.686864e-02
## 2016-06-30 0.0191670107 0.0445823224 -0.0244915778 0.008292145 3.469836e-03
## 2016-07-29 0.0054294369 0.0524422824 0.0390003137 0.049348334 3.582186e-02
## 2016-08-31 -0.0021559617 0.0087984748 0.0053267378 0.011261095 1.197108e-03
## 2016-09-30 0.0005157743 0.0248727366 0.0132791928 0.008614788 5.777177e-05
## 2016-10-31 -0.0082052777 -0.0083121569 -0.0224036999 -0.038134766 -1.748885e-02
## 2016-11-30 -0.0259899633 -0.0451614702 -0.0179744772 0.125246283 3.617582e-02
## 2016-12-30 0.0025386270 -0.0025302619 0.0267028530 0.031491978 2.006906e-02
## 2017-01-31 0.0021255438 0.0644314499 0.0323820281 -0.012144091 1.773645e-02
## 2017-02-28 0.0064382660 0.0172577163 0.0118360937 0.013428555 3.853929e-02
## 2017-03-31 -0.0005529883 0.0361892145 0.0318059692 -0.006532714 1.249283e-03
## 2017-04-28 0.0090292034 0.0168664716 0.0239519855 0.005107854 9.876858e-03
## 2017-05-31 0.0068476097 0.0280595699 0.0348104161 -0.022862952 1.401465e-02
## 2017-06-30 -0.0001827862 0.0092240167 0.0029560667 0.029152074 6.354532e-03
## 2017-07-31 0.0033344261 0.0565944492 0.0261876760 0.007481497 2.034579e-02
## 2017-08-31 0.0093690180 0.0232438893 -0.0004482988 -0.027564642 2.913254e-03
## 2017-09-29 -0.0057320002 -0.0004463023 0.0233427714 0.082321854 1.994948e-02
## 2017-10-31 0.0009777005 0.0322785458 0.0166538169 0.005915716 2.329055e-02
## 2017-11-30 -0.0014842186 -0.0038968214 0.0068699108 0.036913382 3.010824e-02
## 2017-12-29 0.0047404432 0.0369251433 0.0133983765 -0.003731305 1.205465e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398391e-05 0.0001042068 0.0000417824 -7.812113e-05 -9.031791e-06
## EEM 1.042068e-04 0.0017547097 0.0010390170 6.437721e-04 6.795442e-04
## EFA 4.178240e-05 0.0010390170 0.0010642370 6.490282e-04 6.975422e-04
## IJS -7.812113e-05 0.0006437721 0.0006490282 1.565448e-03 8.290243e-04
## SPY -9.031791e-06 0.0006795442 0.0006975422 8.290243e-04 7.408304e-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,] 0.02347489# 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,] 0.0003874006 0.00925714 0.005815636 0.005684461 0.002330253rowSums(component_contribution)## [1] 0.02347489# 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())
}
# Check the custom function
asset_returns_wide_tbl %>% calculate_comp_contrib_by_window(start = 1, window = 24,
w = c(0.25,0.25,0.2,0.2,0.1))## # A tibble: 1 × 6
## date AGG EEM EFA IJS SPY
## <date> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2015-01-30 0.039 0.372 0.256 0.245 0.088asset_returns_wide_tbl %>% calculate_comp_contrib_by_window(start = 2, window = 24,
w = c(0.25,0.25,0.2,0.2,0.1))## # A tibble: 1 × 6
## date AGG EEM EFA IJS SPY
## <date> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2015-02-27 0.036 0.374 0.249 0.252 0.089dump(list = c("calculate_component_contribution",
"calculate_comp_contrib_by_window"),
file = "../00_scripts/calculate_comp_contrib_to_portfolio_volatility.R")# Iterate the custom function
w <- c(0.25,0.25,0.2,0.2,0.1)
window <- 24
rolling_comp_contrib_tbl <- 1:(nrow(asset_returns_wide_tbl) - window) %>%
map_df(.x = ., .f = ~calculate_comp_contrib_by_window(asset_returns_wide_tbl,
start = .x,
weights = w,
window = window))
rolling_comp_contrib_tbl## # A tibble: 36 × 6
## date AGG EEM EFA IJS SPY
## <date> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2015-01-30 0.039 0.372 0.256 0.245 0.088
## 2 2015-02-27 0.036 0.374 0.249 0.252 0.089
## 3 2015-03-31 0.027 0.37 0.255 0.255 0.092
## 4 2015-04-30 0.027 0.372 0.256 0.252 0.093
## 5 2015-05-29 0.024 0.385 0.254 0.246 0.092
## 6 2015-06-30 0.018 0.383 0.248 0.257 0.094
## 7 2015-07-31 0.014 0.375 0.253 0.261 0.097
## 8 2015-08-31 0.013 0.404 0.237 0.257 0.09
## 9 2015-09-30 0.012 0.407 0.248 0.238 0.094
## 10 2015-10-30 0.003 0.405 0.244 0.243 0.105
## # ℹ 26 more rows# Figure 10.3 Component Contribution ggplot ----
rolling_comp_contrib_tbl %>%
# Transform data to long form
pivot_longer(cols = -date, names_to = "asset", values_to = "contribution") %>%
# Plot
ggplot(aes(date, contribution, color = asset)) +
geom_line() +
scale_x_date(breaks = scales::pretty_breaks(n = 7)) +
scale_y_continuous(labels = scales::percent_format()) +
annotate(geom = "text",
x = as.Date("2016-07-01"),
y = 0.03,
color = "red", size = 5,
label = str_glue("AGG dips below zero sometimes, indicating
it reduces the portfolio volatility."))
# Figure 10.4 Stacked Component Contribution ggplot ----
rolling_comp_contrib_tbl %>%
# Transform data to long form
pivot_longer(cols = -date, names_to = "asset", values_to = "contribution") %>%
# Plot
ggplot(aes(date, contribution, fill = asset)) +
geom_area() +
scale_x_date(breaks = scales::pretty_breaks(n = 7)) +
scale_y_continuous(labels = scales::percent_format()) +
annotate(geom = "text",
x = as.Date("2016-07-01"),
y = 0.08,
color = "red", size = 5,
label = str_glue("AGG dips below zero sometimes, indicating
it reduces the portfolio volatility."))