Week 14: Code along 12

Goal
1 Import stock prices
2 Convert prices to returns
3 Component Contribution Step-by-Step
4 Component Contribution with a Custom Function
5 Visualizing Component Contribution

# 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 -0.0062315597 -0.0029355739  0.0366063075  0.052133425  4.992330e-02
## 2013-02-28  0.0058912656 -0.0231051224 -0.0129692952  0.016175454  1.267792e-02
## 2013-03-28  0.0009849785 -0.0102351250  0.0129692952  0.040257887  3.726827e-02
## 2013-04-30  0.0096389715  0.0120851313  0.0489676360  0.001222668  1.902988e-02
## 2013-05-31 -0.0202134504 -0.0494834844 -0.0306555133  0.041976280  2.333515e-02
## 2013-06-28 -0.0157788145 -0.0547283783 -0.0271443833 -0.001403140 -1.343411e-02
## 2013-07-31  0.0026881925  0.0131592640  0.0518605214  0.063541452  5.038621e-02
## 2013-08-30 -0.0082983833 -0.0257054930 -0.0197464620 -0.034743374 -3.045147e-02
## 2013-09-30  0.0111444584  0.0695891495  0.0753384984  0.063873651  3.115610e-02
## 2013-10-31  0.0082914650  0.0408609511  0.0320817953  0.034233939  4.526646e-02
## 2013-11-29 -0.0025098479 -0.0025939141  0.0054495420  0.041661263  2.920672e-02
## 2013-12-31 -0.0055829028 -0.0040743618  0.0215278218  0.012892288  2.559638e-02
## 2014-01-31  0.0152919871 -0.0903225597 -0.0534131516 -0.035775655 -3.588484e-02
## 2014-02-28  0.0037569195  0.0332204781  0.0595049358  0.045257743  4.451060e-02
## 2014-03-31 -0.0014819224  0.0380217618 -0.0046023351  0.013315115  8.261119e-03
## 2014-04-30  0.0081826288  0.0077728584  0.0165294453 -0.023184522  6.927373e-03
## 2014-05-30  0.0117217301  0.0290913005  0.0158283476  0.006205787  2.294138e-02
## 2014-06-30 -0.0005750546  0.0237338286  0.0091651849  0.037718483  2.043469e-02
## 2014-07-31 -0.0025122014  0.0135553549 -0.0263795571 -0.052009450 -1.352883e-02
## 2014-08-29  0.0114305858  0.0279044760  0.0018002703  0.043657972  3.870474e-02
## 2014-09-30 -0.0061671477 -0.0808564801 -0.0395983383 -0.061260624 -1.389192e-02
## 2014-10-31  0.0105846436  0.0140966785 -0.0026548111  0.068874906  2.327787e-02
## 2014-11-28  0.0065485197 -0.0155416376  0.0006253098  0.004773717  2.710086e-02
## 2014-12-31  0.0014746488 -0.0404419977 -0.0407468101  0.025295981 -2.539398e-03
## 2015-01-30  0.0203153619 -0.0068957367  0.0062265051 -0.054627963 -3.007716e-02
## 2015-02-27 -0.0089883646  0.0431361387  0.0614506173  0.056914480  5.468180e-02
## 2015-03-31  0.0037402468 -0.0150861354 -0.0143887061  0.010156314 -1.583036e-02
## 2015-04-30 -0.0032332062  0.0662811892  0.0358165038 -0.018417745  9.786126e-03
## 2015-05-29 -0.0043828532 -0.0419109062  0.0019527235  0.007509875  1.277396e-02
## 2015-06-30 -0.0108255356 -0.0297464936 -0.0316787473  0.004171596 -2.052101e-02
## 2015-07-31  0.0085843915 -0.0651783054  0.0201144807 -0.027375363  2.233780e-02
## 2015-08-31 -0.0033641746 -0.0925123356 -0.0771523151 -0.047268579 -6.288686e-02
## 2015-09-30  0.0080815575 -0.0318249917 -0.0451951440 -0.038464635 -2.584724e-02
## 2015-10-30  0.0006858259  0.0618082373  0.0640259730  0.063589715  8.163524e-02
## 2015-11-30 -0.0038986042 -0.0255604047 -0.0075559615  0.024415033  3.648362e-03
## 2015-12-31 -0.0019182733 -0.0389469627 -0.0235950314 -0.052156758 -1.743357e-02
## 2016-01-29  0.0123298231 -0.0516367468 -0.0567576480 -0.060306947 -5.106857e-02
## 2016-02-29  0.0088314878 -0.0082116050 -0.0339140811  0.020605291 -8.264855e-04
## 2016-03-31  0.0087083502  0.1218790519  0.0637458653  0.089910330  6.510016e-02
## 2016-04-29  0.0025468022  0.0040791494  0.0219750966  0.021044159  3.933651e-03
## 2016-05-31  0.0001353141 -0.0376285104 -0.0008561299  0.004397116  1.686838e-02
## 2016-06-30  0.0191665853  0.0445824046 -0.0244915362  0.008292252  3.469968e-03
## 2016-07-29  0.0054293616  0.0524421561  0.0390001969  0.049348594  3.582191e-02
## 2016-08-31 -0.0021555914  0.0087984760  0.0053268628  0.011260829  1.196736e-03
## 2016-09-30  0.0005152169  0.0248729368  0.0132793210  0.008614807  5.805519e-05
## 2016-10-31 -0.0082050636 -0.0083121911 -0.0224038293 -0.038134859 -1.748913e-02
## 2016-11-30 -0.0259894471 -0.0451618353 -0.0179743129  0.125246493  3.617615e-02
## 2016-12-30  0.0025380701 -0.0025299462  0.0267027738  0.031491798  2.006901e-02
## 2017-01-31  0.0021259016  0.0644312752  0.0323818741 -0.012144031  1.773654e-02
## 2017-02-28  0.0064380200  0.0172579591  0.0118363126  0.013428747  3.853927e-02
## 2017-03-31 -0.0005524442  0.0361888723  0.0318057133 -0.006532834  1.249307e-03
## 2017-04-28  0.0090286533  0.0168666252  0.0239520670  0.005107834  9.877235e-03
## 2017-05-31  0.0068476066  0.0280597656  0.0348103366 -0.022862872  1.401416e-02
## 2017-06-30 -0.0001826117  0.0092238738  0.0029559985  0.029152056  6.354689e-03
## 2017-07-31  0.0033345536  0.0565946436  0.0261877980  0.007481129  2.034579e-02
## 2017-08-31  0.0093689104  0.0232436697 -0.0004482935 -0.027564427  2.913587e-03
## 2017-09-29 -0.0057318345 -0.0004462957  0.0233427767  0.082321368  1.994914e-02
## 2017-10-31  0.0009780063  0.0322785714  0.0166536644  0.005916203  2.329054e-02
## 2017-11-30 -0.0014843110 -0.0038969521  0.0068701724  0.036913291  3.010800e-02
## 2017-12-29  0.0047402027  0.0369252062  0.0133981377 -0.003731357  1.205519e-02

# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)

covariance_matrix

##               AGG          EEM          EFA           IJS           SPY
## AGG  7.398307e-05 0.0001042085 4.178275e-05 -0.0000781186 -9.031238e-06
## EEM  1.042085e-04 0.0017547090 1.039016e-03  0.0006437740  6.795433e-04
## EFA  4.178275e-05 0.0010390158 1.064236e-03  0.0006490304  6.975416e-04
## IJS -7.811860e-05 0.0006437740 6.490304e-04  0.0015654507  8.290268e-04
## SPY -9.031238e-06 0.0006795433 6.975416e-04  0.0008290268  7.408305e-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,] 0.0003874094 0.009257136 0.005815632 0.005684476 0.002330253

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")

asset_returns_wide_tbl

##                      AGG           EEM           EFA          IJS           SPY
## 2013-01-31 -0.0062315597 -0.0029355739  0.0366063075  0.052133425  4.992330e-02
## 2013-02-28  0.0058912656 -0.0231051224 -0.0129692952  0.016175454  1.267792e-02
## 2013-03-28  0.0009849785 -0.0102351250  0.0129692952  0.040257887  3.726827e-02
## 2013-04-30  0.0096389715  0.0120851313  0.0489676360  0.001222668  1.902988e-02
## 2013-05-31 -0.0202134504 -0.0494834844 -0.0306555133  0.041976280  2.333515e-02
## 2013-06-28 -0.0157788145 -0.0547283783 -0.0271443833 -0.001403140 -1.343411e-02
## 2013-07-31  0.0026881925  0.0131592640  0.0518605214  0.063541452  5.038621e-02
## 2013-08-30 -0.0082983833 -0.0257054930 -0.0197464620 -0.034743374 -3.045147e-02
## 2013-09-30  0.0111444584  0.0695891495  0.0753384984  0.063873651  3.115610e-02
## 2013-10-31  0.0082914650  0.0408609511  0.0320817953  0.034233939  4.526646e-02
## 2013-11-29 -0.0025098479 -0.0025939141  0.0054495420  0.041661263  2.920672e-02
## 2013-12-31 -0.0055829028 -0.0040743618  0.0215278218  0.012892288  2.559638e-02
## 2014-01-31  0.0152919871 -0.0903225597 -0.0534131516 -0.035775655 -3.588484e-02
## 2014-02-28  0.0037569195  0.0332204781  0.0595049358  0.045257743  4.451060e-02
## 2014-03-31 -0.0014819224  0.0380217618 -0.0046023351  0.013315115  8.261119e-03
## 2014-04-30  0.0081826288  0.0077728584  0.0165294453 -0.023184522  6.927373e-03
## 2014-05-30  0.0117217301  0.0290913005  0.0158283476  0.006205787  2.294138e-02
## 2014-06-30 -0.0005750546  0.0237338286  0.0091651849  0.037718483  2.043469e-02
## 2014-07-31 -0.0025122014  0.0135553549 -0.0263795571 -0.052009450 -1.352883e-02
## 2014-08-29  0.0114305858  0.0279044760  0.0018002703  0.043657972  3.870474e-02
## 2014-09-30 -0.0061671477 -0.0808564801 -0.0395983383 -0.061260624 -1.389192e-02
## 2014-10-31  0.0105846436  0.0140966785 -0.0026548111  0.068874906  2.327787e-02
## 2014-11-28  0.0065485197 -0.0155416376  0.0006253098  0.004773717  2.710086e-02
## 2014-12-31  0.0014746488 -0.0404419977 -0.0407468101  0.025295981 -2.539398e-03
## 2015-01-30  0.0203153619 -0.0068957367  0.0062265051 -0.054627963 -3.007716e-02
## 2015-02-27 -0.0089883646  0.0431361387  0.0614506173  0.056914480  5.468180e-02
## 2015-03-31  0.0037402468 -0.0150861354 -0.0143887061  0.010156314 -1.583036e-02
## 2015-04-30 -0.0032332062  0.0662811892  0.0358165038 -0.018417745  9.786126e-03
## 2015-05-29 -0.0043828532 -0.0419109062  0.0019527235  0.007509875  1.277396e-02
## 2015-06-30 -0.0108255356 -0.0297464936 -0.0316787473  0.004171596 -2.052101e-02
## 2015-07-31  0.0085843915 -0.0651783054  0.0201144807 -0.027375363  2.233780e-02
## 2015-08-31 -0.0033641746 -0.0925123356 -0.0771523151 -0.047268579 -6.288686e-02
## 2015-09-30  0.0080815575 -0.0318249917 -0.0451951440 -0.038464635 -2.584724e-02
## 2015-10-30  0.0006858259  0.0618082373  0.0640259730  0.063589715  8.163524e-02
## 2015-11-30 -0.0038986042 -0.0255604047 -0.0075559615  0.024415033  3.648362e-03
## 2015-12-31 -0.0019182733 -0.0389469627 -0.0235950314 -0.052156758 -1.743357e-02
## 2016-01-29  0.0123298231 -0.0516367468 -0.0567576480 -0.060306947 -5.106857e-02
## 2016-02-29  0.0088314878 -0.0082116050 -0.0339140811  0.020605291 -8.264855e-04
## 2016-03-31  0.0087083502  0.1218790519  0.0637458653  0.089910330  6.510016e-02
## 2016-04-29  0.0025468022  0.0040791494  0.0219750966  0.021044159  3.933651e-03
## 2016-05-31  0.0001353141 -0.0376285104 -0.0008561299  0.004397116  1.686838e-02
## 2016-06-30  0.0191665853  0.0445824046 -0.0244915362  0.008292252  3.469968e-03
## 2016-07-29  0.0054293616  0.0524421561  0.0390001969  0.049348594  3.582191e-02
## 2016-08-31 -0.0021555914  0.0087984760  0.0053268628  0.011260829  1.196736e-03
## 2016-09-30  0.0005152169  0.0248729368  0.0132793210  0.008614807  5.805519e-05
## 2016-10-31 -0.0082050636 -0.0083121911 -0.0224038293 -0.038134859 -1.748913e-02
## 2016-11-30 -0.0259894471 -0.0451618353 -0.0179743129  0.125246493  3.617615e-02
## 2016-12-30  0.0025380701 -0.0025299462  0.0267027738  0.031491798  2.006901e-02
## 2017-01-31  0.0021259016  0.0644312752  0.0323818741 -0.012144031  1.773654e-02
## 2017-02-28  0.0064380200  0.0172579591  0.0118363126  0.013428747  3.853927e-02
## 2017-03-31 -0.0005524442  0.0361888723  0.0318057133 -0.006532834  1.249307e-03
## 2017-04-28  0.0090286533  0.0168666252  0.0239520670  0.005107834  9.877235e-03
## 2017-05-31  0.0068476066  0.0280597656  0.0348103366 -0.022862872  1.401416e-02
## 2017-06-30 -0.0001826117  0.0092238738  0.0029559985  0.029152056  6.354689e-03
## 2017-07-31  0.0033345536  0.0565946436  0.0261877980  0.007481129  2.034579e-02
## 2017-08-31  0.0093689104  0.0232436697 -0.0004482935 -0.027564427  2.913587e-03
## 2017-09-29 -0.0057318345 -0.0004462957  0.0233427767  0.082321368  1.994914e-02
## 2017-10-31  0.0009780063  0.0322785714  0.0166536644  0.005916203  2.329054e-02
## 2017-11-30 -0.0014843110 -0.0038969521  0.0068701724  0.036913291  3.010800e-02
## 2017-12-29  0.0047402027  0.0369252062  0.0133981377 -0.003731357  1.205519e-02

calculate_component_contribution <- function(.data, w) {
    
    # Covariance of asset returns
    covariance_matrix <- cov(.data)

    

# Standard deviation of portfolio
# Summarizes how much each asset's returns vary with those of other assets within the portfolio into a single number

    sd_portfolio <- sqrt(t(w) %*% covariance_matrix %*% w)
 

# 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


# Component contribution in percentage
    component_percentages <- (component_contribution / sd_portfolio[1,1]) %>%
    round(3) %>%
    as_tibble()

    component_percentages %>%

    as_tibble() %>%
    gather(key = "asset", value = "contribution")
    
    return(component_percentages)
}

asset_returns_wide_tbl %>% calculate_component_contribution(w = c(.25,.25,.20,.20,.10))

## # 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

column chart of component contribution

plot_data <- asset_returns_wide_tbl %>% calculate_component_contribution(w = c(.25,.25,.20,.20,.10)) %>%
    
    # transform to long form
    pivot_longer(cols = everything(), names_to = "Asset", values_to = "Contributions")

plot_data %>%
    
    ggplot(aes(x = Asset, y = Contributions)) +
    geom_col(fill = "steelblue") +
    
    scale_y_continuous(labels = scales::percent_format(accuracy = 1)) +
    theme(plot.title = element_text(hjust = .5)) +
    labs(title = "Percent Contribution to Portfolio Standerd Deveiation")

column chart of component contribution and weight

plot_data <- asset_returns_wide_tbl %>% calculate_component_contribution(w = c(.25,.25,.20,.20,.10)) %>%
    
    # transform to long form
    pivot_longer(cols = everything(), names_to = "Asset", values_to = "Contributions") %>%
    
    # add wights
    add_column(weight = c(.25,.25,.20,.20,.10)) %>%
    
    # transform to long
    pivot_longer(cols = c(Contributions, weight), names_to = "type", values_to = "value")



plot_data %>%
    
    ggplot(aes(x = Asset, y = value, fill = type)) +
    geom_col(position = "dodge") +
    
    scale_y_continuous(labels = scales::percent_format(accuracy = 1)) +
    scale_fill_tq() +
    theme(plot.title = element_text(hjust = .5)) +
    theme_tq() +
    labs(title = "Percent Contribution to Portfolio volitlity and weight", 
         y = "Percent",
         x = NULL)