Week 14: Code along 12
CHAPTER 10 Component Contribution to Standard Deviation
Andrew Cook
2024-11-13
# 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 -0.0062317473 -0.0029353524 0.0366062134 0.052133312 4.992316e-02
## 2013-02-28 0.0058916385 -0.0231054542 -0.0129692033 0.016175454 1.267785e-02
## 2013-03-28 0.0009848859 -0.0102350107 0.0129692033 0.040257887 3.726803e-02
## 2013-04-30 0.0096391558 0.0120847911 0.0489678089 0.001222769 1.903030e-02
## 2013-05-31 -0.0202137293 -0.0494834959 -0.0306554188 0.041976082 2.333492e-02
## 2013-06-28 -0.0157782471 -0.0547283917 -0.0271446506 -0.001402946 -1.343400e-02
## 2013-07-31 0.0026873382 0.0131598859 0.0518602606 0.063541446 5.038576e-02
## 2013-08-30 -0.0082976224 -0.0257057373 -0.0197462012 -0.034743465 -3.045137e-02
## 2013-09-30 0.0111438879 0.0695889042 0.0753383340 0.063873562 3.115600e-02
## 2013-10-31 0.0082920299 0.0408609559 0.0320817209 0.034234198 4.526658e-02
## 2013-11-29 -0.0025099412 -0.0025938005 0.0054497809 0.041661010 2.920724e-02
## 2013-12-31 -0.0055836580 -0.0040741329 0.0215282869 0.012892127 2.559577e-02
## 2014-01-31 0.0152918095 -0.0903231017 -0.0534136985 -0.035774993 -3.588434e-02
## 2014-02-28 0.0037572005 0.0332207306 0.0595052487 0.045257083 4.451050e-02
## 2014-03-31 -0.0014815515 0.0380218224 -0.0046025662 0.013315355 8.261118e-03
## 2014-04-30 0.0081823532 0.0077729741 0.0165293692 -0.023184279 6.927372e-03
## 2014-05-30 0.0117225538 0.0290910723 0.0158284238 0.006205384 2.294157e-02
## 2014-06-30 -0.0005760564 0.0237337214 0.0091654077 0.037718489 2.043440e-02
## 2014-07-31 -0.0025121115 0.0135558994 -0.0263799323 -0.052009295 -1.352864e-02
## 2014-08-29 0.0114310424 0.0279043617 0.0018005750 0.043658050 3.870474e-02
## 2014-09-30 -0.0061677837 -0.0808568050 -0.0395984905 -0.061260702 -1.389256e-02
## 2014-10-31 0.0105846503 0.0140965675 -0.0026548111 0.068874984 2.327833e-02
## 2014-11-28 0.0065491489 -0.0155410693 0.0006251511 0.004773717 2.710095e-02
## 2014-12-31 0.0014748271 -0.0404422216 -0.0407467341 0.025295528 -2.539486e-03
## 2015-01-30 0.0203147467 -0.0068958558 0.0062266698 -0.054627746 -3.007725e-02
## 2015-02-27 -0.0089876631 0.0431361387 0.0614506896 0.056914639 5.468172e-02
## 2015-03-31 0.0037404215 -0.0150861354 -0.0143889389 0.010156462 -1.583011e-02
## 2015-04-30 -0.0032333810 0.0662810801 0.0358167334 -0.018417742 9.785952e-03
## 2015-05-29 -0.0043835601 -0.0419110247 0.0019526477 0.007509874 1.277439e-02
## 2015-06-30 -0.0108252720 -0.0297465004 -0.0316788228 0.004171446 -2.052170e-02
## 2015-07-31 0.0085848366 -0.0651781336 0.0201143281 -0.027375517 2.233823e-02
## 2015-08-31 -0.0033639067 -0.0925122731 -0.0771525747 -0.047268587 -6.288659e-02
## 2015-09-30 0.0080812883 -0.0318249917 -0.0451947318 -0.038464390 -2.584741e-02
## 2015-10-30 0.0006858257 0.0618083039 0.0640261348 0.063589632 8.163496e-02
## 2015-11-30 -0.0038988689 -0.0255603347 -0.0075560418 0.024415186 3.648534e-03
## 2015-12-31 -0.0019189833 -0.0389473124 -0.0235949460 -0.052156750 -1.743365e-02
## 2016-01-29 0.0123300071 -0.0516365338 -0.0567578149 -0.060307108 -5.106848e-02
## 2016-02-29 0.0088320138 -0.0082114542 -0.0339138983 0.020605459 -8.265770e-04
## 2016-03-31 0.0087083502 0.1218788343 0.0637455110 0.089910239 6.510016e-02
## 2016-04-29 0.0025463726 0.0040792162 0.0219751842 0.021044158 3.933651e-03
## 2016-05-31 0.0001360014 -0.0376285104 -0.0008560460 0.004397041 1.686863e-02
## 2016-06-30 0.0191664118 0.0445824046 -0.0244914502 0.008292327 3.469549e-03
## 2016-07-29 0.0054296126 0.0524420934 0.0390001108 0.049348308 3.582223e-02
## 2016-08-31 -0.0021564307 0.0087987250 0.0053269451 0.011260901 1.196574e-03
## 2016-09-30 0.0005159728 0.0248726900 0.0132791575 0.008615016 5.813593e-05
## 2016-10-31 -0.0082054001 -0.0083121305 -0.0224038311 -0.038134785 -1.748913e-02
## 2016-11-30 -0.0259894493 -0.0451619631 -0.0179743989 0.125246222 3.617614e-02
## 2016-12-30 0.0025381570 -0.0025298824 0.0267028606 0.031491864 2.006917e-02
## 2017-01-31 0.0021259881 0.0644314594 0.0323818767 -0.012144032 1.773638e-02
## 2017-02-28 0.0064376758 0.0172579571 0.0118365499 0.013428687 3.853934e-02
## 2017-03-31 -0.0005527023 0.0361889820 0.0318054031 -0.006532896 1.248940e-03
## 2017-04-28 0.0090293395 0.0168663974 0.0239525177 0.005107774 9.877237e-03
## 2017-05-31 0.0068472669 0.0280599834 0.0348101105 -0.022862752 1.401452e-02
## 2017-06-30 -0.0001820194 0.0092236560 0.0029559982 0.029151876 6.354475e-03
## 2017-07-31 0.0033341305 0.0565943378 0.0261877962 0.007481738 2.034579e-02
## 2017-08-31 0.0093691611 0.0232440751 -0.0004482935 -0.027564793 2.913656e-03
## 2017-09-29 -0.0057320851 -0.0004463953 0.0233427751 0.082321661 1.994901e-02
## 2017-10-31 0.0009777544 0.0322785714 0.0166535960 0.005916202 2.329061e-02
## 2017-11-30 -0.0014838909 -0.0038971458 0.0068702391 0.036913172 3.010807e-02
## 2017-12-29 0.0047399508 0.0369254932 0.0133982026 -0.003731136 1.205525e-02# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AGG EEM EFA IJS SPY
## AGG 7.398348e-05 0.0001042082 4.178171e-05 -7.811753e-05 -9.030540e-06
## EEM 1.042082e-04 0.0017547109 1.039018e-03 6.437736e-04 6.795427e-04
## EFA 4.178171e-05 0.0010390178 1.064238e-03 6.490301e-04 6.975421e-04
## IJS -7.811753e-05 0.0006437736 6.490301e-04 1.565447e-03 8.290245e-04
## SPY -9.030540e-06 0.0006795427 6.975421e-04 8.290245e-04 7.408293e-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,] 0.02347491# 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,] 0.0003874105 0.009257143 0.005815637 0.005684468 0.002330251rowSums(component_contribution)## [1] 0.02347491# 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 0.096
## 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."))