# Load packages
# Core
library(tidyverse)
library(tidyquant)
library(readr)
# Time series
library(lubridate)
library(tibbletime)
# modeling
library(broom)
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
# 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 -0.0062315601 -0.0029352045 0.0366063344 0.052133270 4.992271e-02
## 2013-02-28 0.0058918505 -0.0231058279 -0.0129697347 0.016175587 1.267838e-02
## 2013-03-28 0.0009844370 -0.0102345667 0.0129697347 0.040258131 3.726824e-02
## 2013-04-30 0.0096390815 0.0120846536 0.0489676230 0.001222011 1.902973e-02
## 2013-05-31 -0.0202138805 -0.0494834296 -0.0306555699 0.041976703 2.333507e-02
## 2013-06-28 -0.0157782669 -0.0547283273 -0.0271442971 -0.001402992 -1.343410e-02
## 2013-07-31 0.0026878497 0.0131599380 0.0518600140 0.063541395 5.038592e-02
## 2013-08-30 -0.0082978190 -0.0257059377 -0.0197461242 -0.034743555 -3.045123e-02
## 2013-09-30 0.0111435229 0.0695891622 0.0753385829 0.063873984 3.115606e-02
## 2013-10-31 0.0082920800 0.0408611599 0.0320815455 0.034233886 4.526656e-02
## 2013-11-29 -0.0025094682 -0.0025940732 0.0054499160 0.041661123 2.920726e-02
## 2013-12-31 -0.0055834339 -0.0040744164 0.0215277756 0.012892123 2.559571e-02
## 2014-01-31 0.0152922551 -0.0903225241 -0.0534132019 -0.035775378 -3.588444e-02
## 2014-02-28 0.0037558268 0.0332203074 0.0595048974 0.045257424 4.451011e-02
## 2014-03-31 -0.0014808867 0.0380219842 -0.0046023324 0.013315318 8.261597e-03
## 2014-04-30 0.0081831047 0.0077726777 0.0165294367 -0.023184382 6.927468e-03
## 2014-05-30 0.0117214635 0.0290909599 0.0158283493 0.006205467 2.294127e-02
## 2014-06-30 -0.0005762206 0.0237339583 0.0091652849 0.037718724 2.043436e-02
## 2014-07-31 -0.0025115963 0.0135555756 -0.0263797279 -0.052009541 -1.352832e-02
## 2014-08-29 0.0114306241 0.0279047915 0.0018004559 0.043657969 3.870454e-02
## 2014-09-30 -0.0061675319 -0.0808566890 -0.0395983763 -0.061260635 -1.389263e-02
## 2014-10-31 0.0105849725 0.0140964530 -0.0026549510 0.068875095 2.327834e-02
## 2014-11-28 0.0065487042 -0.0155412045 0.0006251760 0.004773544 2.710112e-02
## 2014-12-31 0.0014750008 -0.0404422091 -0.0407465280 0.025295823 -2.539852e-03
## 2015-01-30 0.0203152454 -0.0068957476 0.0062263384 -0.054628062 -3.007703e-02
## 2015-02-27 -0.0089879601 0.0431361342 0.0614506078 0.056914681 5.468186e-02
## 2015-03-31 0.0037399743 -0.0150862381 -0.0143886921 0.010156474 -1.583005e-02
## 2015-04-30 -0.0032328722 0.0662812579 0.0358165742 -0.018417694 9.785643e-03
## 2015-05-29 -0.0043836322 -0.0419108998 0.0019526727 0.007509740 1.277433e-02
## 2015-06-30 -0.0108257314 -0.0297466579 -0.0316789392 0.004171529 -2.052134e-02
## 2015-07-31 0.0085855320 -0.0651782975 0.0201146462 -0.027375530 2.233798e-02
## 2015-08-31 -0.0033649334 -0.0925122633 -0.0771524286 -0.047268316 -6.288677e-02
## 2015-09-30 0.0080817647 -0.0318250055 -0.0451949488 -0.038464612 -2.584693e-02
## 2015-10-30 0.0006853715 0.0618083440 0.0640258032 0.063589685 8.163503e-02
## 2015-11-30 -0.0038982071 -0.0255604653 -0.0075558000 0.024415191 3.648255e-03
## 2015-12-31 -0.0019189172 -0.0389470837 -0.0235950350 -0.052157198 -1.743337e-02
## 2016-01-29 0.0123300564 -0.0516367613 -0.0567579021 -0.060306867 -5.106897e-02
## 2016-02-29 0.0088314706 -0.0082113098 -0.0339138259 0.020605372 -8.262692e-04
## 2016-03-31 0.0087091197 0.1218789238 0.0637455915 0.089910297 6.510035e-02
## 2016-04-29 0.0025461876 0.0040792898 0.0219752075 0.021044348 3.933446e-03
## 2016-05-31 0.0001353850 -0.0376286321 -0.0008560588 0.004397040 1.686856e-02
## 2016-06-30 0.0191668104 0.0445822654 -0.0244915580 0.008292173 3.469969e-03
## 2016-07-29 0.0054296218 0.0524423478 0.0390002822 0.049348651 3.582155e-02
## 2016-08-31 -0.0021561708 0.0087985990 0.0053267594 0.011260870 1.197035e-03
## 2016-09-30 0.0005164227 0.0248727823 0.0132791871 0.008614677 5.805468e-05
## 2016-10-31 -0.0082052751 -0.0083123542 -0.0224035594 -0.038134617 -1.748925e-02
## 2016-11-30 -0.0259900274 -0.0451615642 -0.0179745296 0.125246265 3.617627e-02
## 2016-12-30 0.0025379451 -0.0025301565 0.0267028672 0.031491870 2.006885e-02
## 2017-01-31 0.0021261831 0.0644314794 0.0323817970 -0.012144336 1.773651e-02
## 2017-02-28 0.0064382076 0.0172577716 0.0118364607 0.013429243 3.853918e-02
## 2017-03-31 -0.0005535251 0.0361891145 0.0318056750 -0.006533323 1.249347e-03
## 2017-04-28 0.0090292782 0.0168663683 0.0239523104 0.005108009 9.877254e-03
## 2017-05-31 0.0068475066 0.0280599886 0.0348102689 -0.022862623 1.401419e-02
## 2017-06-30 -0.0001823073 0.0092235023 0.0029557966 0.029151717 6.354781e-03
## 2017-07-31 0.0033340485 0.0565948097 0.0261878997 0.007481543 2.034565e-02
## 2017-08-31 0.0093689703 0.0232436027 -0.0004482966 -0.027564741 2.913399e-03
## 2017-09-29 -0.0057318861 -0.0004462797 0.0233427730 0.082321622 1.994919e-02
## 2017-10-31 0.0009779271 0.0322784897 0.0166537072 0.005916104 2.329065e-02
## 2017-11-30 -0.0014840877 -0.0038968531 0.0068699364 0.036913506 3.010824e-02
## 2017-12-29 0.0047403577 0.0369254109 0.0133983026 -0.003731204 1.205496e-02
# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix
## AGG EEM EFA IJS SPY
## AGG 7.398478e-05 0.0001042097 4.178137e-05 -7.812117e-05 -9.031399e-06
## EEM 1.042097e-04 0.0017547114 1.039016e-03 6.437755e-04 6.795437e-04
## EFA 4.178137e-05 0.0010390164 1.064235e-03 6.490285e-04 6.975390e-04
## IJS -7.812117e-05 0.0006437755 6.490285e-04 1.565453e-03 8.290261e-04
## SPY -9.031399e-06 0.0006795437 6.975390e-04 8.290261e-04 7.408280e-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,] 0.0003874085 0.009257151 0.005815624 0.005684474 0.00233025
rowSums(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 0.099
component_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 0.099
4 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 0.099
5 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 0.088
asset_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 0.089
dump(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
## # … with 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."))
