# 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 -0.0062307623 -0.0029356245 0.0366060144 0.052133270 4.992310e-02
## 2013-02-28 0.0058909604 -0.0231052881 -0.0129691407 0.016175479 1.267819e-02
## 2013-03-28 0.0009849670 -0.0102348823 0.0129691407 0.040257954 3.726772e-02
## 2013-04-30 0.0096394227 0.0120847681 0.0489678724 0.001222476 1.903020e-02
## 2013-05-31 -0.0202139531 -0.0494834238 -0.0306554809 0.041976250 2.333507e-02
## 2013-06-28 -0.0157787222 -0.0547283206 -0.0271443862 -0.001402448 -1.343376e-02
## 2013-07-31 0.0026882154 0.0131597481 0.0518601009 0.063541122 5.038568e-02
## 2013-08-30 -0.0082980901 -0.0257055209 -0.0197462111 -0.034743628 -3.045122e-02
## 2013-09-30 0.0111441460 0.0695886881 0.0753385007 0.063873965 3.115583e-02
## 2013-10-31 0.0082914569 0.0408611647 0.0320817670 0.034233976 4.526688e-02
## 2013-11-29 -0.0025098306 -0.0025939579 0.0054494799 0.041660956 2.920646e-02
## 2013-12-31 -0.0055825309 -0.0040744164 0.0215281500 0.012892228 2.559650e-02
## 2014-01-31 0.0152908231 -0.0903225876 -0.0534134224 -0.035775465 -3.588473e-02
## 2014-02-28 0.0037571563 0.0332203709 0.0595052522 0.045257349 4.451050e-02
## 2014-03-31 -0.0014813249 0.0380218659 -0.0046024668 0.013315604 8.261115e-03
## 2014-04-30 0.0081828412 0.0077726786 0.0165292071 -0.023184194 6.927657e-03
## 2014-05-30 0.0117218062 0.0290913053 0.0158284266 0.006205219 2.294127e-02
## 2014-06-30 -0.0005756089 0.0237339251 0.0091653598 0.037718645 2.043472e-02
## 2014-07-31 -0.0025119466 0.0135555730 -0.0263799374 -0.052009462 -1.352887e-02
## 2014-08-29 0.0114307101 0.0279045993 0.0018006655 0.043658049 3.870463e-02
## 2014-09-30 -0.0061678681 -0.0808568916 -0.0395984554 -0.061260481 -1.389218e-02
## 2014-10-31 0.0105842002 0.0140965415 -0.0026548718 0.068874783 2.327789e-02
## 2014-11-28 0.0065492195 -0.0155412062 0.0006253941 0.004773702 2.710121e-02
## 2014-12-31 0.0014752450 -0.0404424252 -0.0407469113 0.025295667 -2.539852e-03
## 2015-01-30 0.0203150047 -0.0068950811 0.0062264420 -0.054627742 -3.007703e-02
## 2015-02-27 -0.0089877203 0.0431357998 0.0614508044 0.056914571 5.468203e-02
## 2015-03-31 0.0037399849 -0.0150863268 -0.0143886902 0.010156416 -1.583047e-02
## 2015-04-30 -0.0032334528 0.0662813466 0.0358165883 -0.018417983 9.786062e-03
## 2015-05-29 -0.0043833152 -0.0419108998 0.0019524651 0.007509799 1.277409e-02
## 2015-06-30 -0.0108258112 -0.0297466579 -0.0316788826 0.004171683 -2.052117e-02
## 2015-07-31 0.0085848613 -0.0651782024 0.0201144364 -0.027375314 2.233806e-02
## 2015-08-31 -0.0033633317 -0.0925123584 -0.0771525278 -0.047268367 -6.288676e-02
## 2015-09-30 0.0080813420 -0.0318250055 -0.0451946398 -0.038464691 -2.584720e-02
## 2015-10-30 0.0006848667 0.0618083440 0.0640259447 0.063589680 8.163496e-02
## 2015-11-30 -0.0038978777 -0.0255603267 -0.0075558600 0.024415032 3.648672e-03
## 2015-12-31 -0.0019189943 -0.0389472583 -0.0235950539 -0.052156893 -1.743371e-02
## 2016-01-29 0.0123298929 -0.0516366494 -0.0567577218 -0.060306852 -5.106888e-02
## 2016-02-29 0.0088316341 -0.0082115386 -0.0339139774 0.020605045 -8.262692e-04
## 2016-03-31 0.0087086377 0.1218789414 0.0637456716 0.089910461 6.510061e-02
## 2016-04-29 0.0025466696 0.0040792904 0.0219750361 0.021044135 3.933281e-03
## 2016-05-31 0.0001354598 -0.0376284972 -0.0008560588 0.004397308 1.686839e-02
## 2016-06-30 0.0191664946 0.0445826336 -0.0244913860 0.008292172 3.469889e-03
## 2016-07-29 0.0054298629 0.0524418843 0.0390001102 0.049348446 3.582164e-02
## 2016-08-31 -0.0021562543 0.0087984739 0.0053267594 0.011261014 1.196957e-03
## 2016-09-30 0.0005157024 0.0248730027 0.0132792682 0.008614676 5.813243e-05
## 2016-10-31 -0.0082050291 -0.0083122303 -0.0224036405 -0.038134908 -1.748918e-02
## 2016-11-30 -0.0259896423 -0.0451618825 -0.0179746142 0.125246616 3.617611e-02
## 2016-12-30 0.0025382796 -0.0025299621 0.0267031163 0.031491803 2.006916e-02
## 2017-01-31 0.0021259462 0.0644312358 0.0323816324 -0.012143969 1.773650e-02
## 2017-02-28 0.0064378769 0.0172581350 0.0118366182 0.013428750 3.853918e-02
## 2017-03-31 -0.0005524671 0.0361888793 0.0318054412 -0.006533023 1.249064e-03
## 2017-04-28 0.0090291028 0.0168664838 0.0239523867 0.005107583 9.877395e-03
## 2017-05-31 0.0068471877 0.0280599886 0.0348101970 -0.022862434 1.401426e-02
## 2017-06-30 -0.0001826335 0.0092236117 0.0029557968 0.029151717 6.354708e-03
## 2017-07-31 0.0033343847 0.0565945969 0.0261880937 0.007481434 2.034565e-02
## 2017-08-31 0.0093691142 0.0232438828 -0.0004483665 -0.027564568 2.913333e-03
## 2017-09-29 -0.0057323650 -0.0004462544 0.0233425840 0.082321779 1.994932e-02
## 2017-10-31 0.0009780212 0.0322782876 0.0166538437 0.005915986 2.329072e-02
## 2017-11-30 -0.0014837741 -0.0038967549 0.0068700031 0.036913192 3.010823e-02
## 2017-12-29 0.0047401173 0.0369252417 0.0133981208 -0.003731106 1.205483e-02
# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix
## AGG EEM EFA IJS SPY
## AGG 7.398284e-05 0.0001042103 4.178444e-05 -7.811798e-05 -9.030269e-06
## EEM 1.042103e-04 0.0017547095 1.039017e-03 6.437721e-04 6.795429e-04
## EFA 4.178444e-05 0.0010390166 1.064237e-03 6.490290e-04 6.975419e-04
## IJS -7.811798e-05 0.0006437721 6.490290e-04 1.565449e-03 8.290253e-04
## SPY -9.030269e-06 0.0006795429 6.975419e-04 8.290253e-04 7.408300e-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,] 0.0003874195 0.009257138 0.005815636 0.005684466 0.002330252
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."))
