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 -0.0062310740 -0.0029357127  0.0366063164  0.052133267  4.992300e-02
## 2013-02-28  0.0058912502 -0.0231052344 -0.0129691910  0.016175114  1.267775e-02
## 2013-03-28  0.0009847449 -0.0102346459  0.0129691910  0.040258434  3.726836e-02
## 2013-04-30  0.0096394317  0.0120846578  0.0489676260  0.001222418  1.903024e-02
## 2013-05-31 -0.0202138089 -0.0494833348 -0.0306556875  0.041976099  2.333514e-02
## 2013-06-28 -0.0157781765 -0.0547287809 -0.0271439691 -0.001402802 -1.343469e-02
## 2013-07-31  0.0026882468  0.0131604990  0.0518602020  0.063541402  5.038618e-02
## 2013-08-30 -0.0082990897 -0.0257062137 -0.0197464212 -0.034743742 -3.045141e-02
## 2013-09-30  0.0111438655  0.0695888981  0.0753384346  0.063873949  3.115616e-02
## 2013-10-31  0.0082921852  0.0408611197  0.0320816599  0.034234087  4.526656e-02
## 2013-11-29 -0.0025097781 -0.0025938424  0.0054497637  0.041661213  2.920688e-02
## 2013-12-31 -0.0055833097 -0.0040743561  0.0215277677  0.012892026  2.559598e-02
## 2014-01-31  0.0152919013 -0.0903227184 -0.0534130285 -0.035775432 -3.588453e-02
## 2014-02-28  0.0037575214  0.0332207328  0.0595049235  0.045257453  4.451028e-02
## 2014-03-31 -0.0014820859  0.0380216317 -0.0046026532  0.013315471  8.261661e-03
## 2014-04-30  0.0081833182  0.0077726130  0.0165296605 -0.023184431  6.927277e-03
## 2014-05-30  0.0117213891  0.0290910768  0.0158282105  0.006205218  2.294151e-02
## 2014-06-30 -0.0005758057  0.0237340576  0.0091656468  0.037718654  2.043425e-02
## 2014-07-31 -0.0025120439  0.0135555761 -0.0263797306 -0.052009444 -1.352880e-02
## 2014-08-29  0.0114312510  0.0279044995  0.0018001624  0.043658113  3.870547e-02
## 2014-09-30 -0.0061683760 -0.0808566713 -0.0395982980 -0.061260518 -1.389275e-02
## 2014-10-31  0.0105850830  0.0140966886 -0.0026548515  0.068874813  2.327795e-02
## 2014-11-28  0.0065491449 -0.0155414412  0.0006254112  0.004773526  2.710098e-02
## 2014-12-31  0.0014748462 -0.0404420568 -0.0407467225  0.025296073 -2.539728e-03
## 2015-01-30  0.0203148716 -0.0068955729  0.0062262805 -0.054628026 -3.007696e-02
## 2015-02-27 -0.0089879820  0.0431359574  0.0614506677  0.056914605  5.468176e-02
## 2015-03-31  0.0037404688 -0.0150864206 -0.0143887929  0.010156426 -1.583018e-02
## 2015-04-30 -0.0032332924  0.0662813596  0.0358163453 -0.018417830  9.785650e-03
## 2015-05-29 -0.0043830020 -0.0419106929  0.0019528674  0.007509980  1.277483e-02
## 2015-06-30 -0.0108260488 -0.0297466985 -0.0316789227  0.004171216 -2.052168e-02
## 2015-07-31  0.0085846300 -0.0651783269  0.0201147332 -0.027375421  2.233791e-02
## 2015-08-31 -0.0033637009 -0.0925122625 -0.0771526622 -0.047268362 -6.288648e-02
## 2015-09-30  0.0080816991 -0.0318249564 -0.0451949385 -0.038464334 -2.584740e-02
## 2015-10-30  0.0006848861  0.0618082062  0.0640260006  0.063589567  8.163529e-02
## 2015-11-30 -0.0038974463 -0.0255603348 -0.0075557282  0.024414906  3.648275e-03
## 2015-12-31 -0.0019195747 -0.0389470612 -0.0235950500 -0.052156700 -1.743370e-02
## 2016-01-29  0.0123296515 -0.0516369228 -0.0567579689 -0.060306786 -5.106845e-02
## 2016-02-29  0.0088320903 -0.0082113836 -0.0339139283  0.020605158 -8.265477e-04
## 2016-03-31  0.0087085118  0.1218788136  0.0637459390  0.089910239  6.510045e-02
## 2016-04-29  0.0025463969  0.0040794464  0.0219749278  0.021044202  3.933451e-03
## 2016-05-31  0.0001355942 -0.0376283878 -0.0008560851  0.004397090  1.686826e-02
## 2016-06-30  0.0191670642  0.0445823473 -0.0244915273  0.008292694  3.469827e-03
## 2016-07-29  0.0054292049  0.0524419629  0.0390002419  0.049347969  3.582223e-02
## 2016-08-31 -0.0021560140  0.0087988536  0.0053268450  0.011261092  1.196764e-03
## 2016-09-30  0.0005157377  0.0248725375  0.0132791635  0.008614844  5.794653e-05
## 2016-10-31 -0.0082052708 -0.0083120768 -0.0224037517 -0.038134794 -1.748905e-02
## 2016-11-30 -0.0259894334 -0.0451619493 -0.0179744890  0.125246274  3.617607e-02
## 2016-12-30  0.0025384689 -0.0025299176  0.0267030747  0.031491871  2.006916e-02
## 2017-01-31  0.0021257815  0.0644317259  0.0323818267 -0.012144125  1.773648e-02
## 2017-02-28  0.0064379000  0.0172578311  0.0118363502  0.013428799  3.853900e-02
## 2017-03-31 -0.0005530252  0.0361889645  0.0318057522 -0.006532991  1.249223e-03
## 2017-04-28  0.0090293528  0.0168661738  0.0239523293  0.005107864  9.877393e-03
## 2017-05-31  0.0068475053  0.0280598995  0.0348099190 -0.022862899  1.401425e-02
## 2017-06-30 -0.0001831494  0.0092235499  0.0029561485  0.029152154  6.354802e-03
## 2017-07-31  0.0033351378  0.0565947503  0.0261878079  0.007481476  2.034577e-02
## 2017-08-31  0.0093684997  0.0232437140 -0.0004483592 -0.027564705  2.913312e-03
## 2017-09-29 -0.0057318448 -0.0004461573  0.0233427441  0.082321410  1.994920e-02
## 2017-10-31  0.0009778448  0.0322784976  0.0166537929  0.005916172  2.329086e-02
## 2017-11-30 -0.0014840257 -0.0038970184  0.0068700310  0.036913435  3.010777e-02
## 2017-12-29  0.0047403290  0.0369254195  0.0133982755 -0.003731168  1.205499e-02

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

covariance_matrix

##               AGG          EEM          EFA           IJS           SPY
## AGG  7.398453e-05 0.0001042096 4.178342e-05 -0.0000781144 -9.028641e-06
## EEM  1.042096e-04 0.0017547110 1.039017e-03  0.0006437746  6.795462e-04
## EFA  4.178342e-05 0.0010390165 1.064237e-03  0.0006490292  6.975429e-04
## IJS -7.811440e-05 0.0006437746 6.490292e-04  0.0015654485  8.290267e-04
## SPY -9.028641e-06 0.0006795462 6.975429e-04  0.0008290267  7.408316e-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,] 0.02347493

# 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,] 0.000387429 0.009257141 0.005815629 0.005684475 0.002330258

rowSums(component_contribution)

## [1] 0.02347493

# 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 -0.0062310740 -0.0029357127  0.0366063164  0.052133267  4.992300e-02
## 2013-02-28  0.0058912502 -0.0231052344 -0.0129691910  0.016175114  1.267775e-02
## 2013-03-28  0.0009847449 -0.0102346459  0.0129691910  0.040258434  3.726836e-02
## 2013-04-30  0.0096394317  0.0120846578  0.0489676260  0.001222418  1.903024e-02
## 2013-05-31 -0.0202138089 -0.0494833348 -0.0306556875  0.041976099  2.333514e-02
## 2013-06-28 -0.0157781765 -0.0547287809 -0.0271439691 -0.001402802 -1.343469e-02
## 2013-07-31  0.0026882468  0.0131604990  0.0518602020  0.063541402  5.038618e-02
## 2013-08-30 -0.0082990897 -0.0257062137 -0.0197464212 -0.034743742 -3.045141e-02
## 2013-09-30  0.0111438655  0.0695888981  0.0753384346  0.063873949  3.115616e-02
## 2013-10-31  0.0082921852  0.0408611197  0.0320816599  0.034234087  4.526656e-02
## 2013-11-29 -0.0025097781 -0.0025938424  0.0054497637  0.041661213  2.920688e-02
## 2013-12-31 -0.0055833097 -0.0040743561  0.0215277677  0.012892026  2.559598e-02
## 2014-01-31  0.0152919013 -0.0903227184 -0.0534130285 -0.035775432 -3.588453e-02
## 2014-02-28  0.0037575214  0.0332207328  0.0595049235  0.045257453  4.451028e-02
## 2014-03-31 -0.0014820859  0.0380216317 -0.0046026532  0.013315471  8.261661e-03
## 2014-04-30  0.0081833182  0.0077726130  0.0165296605 -0.023184431  6.927277e-03
## 2014-05-30  0.0117213891  0.0290910768  0.0158282105  0.006205218  2.294151e-02
## 2014-06-30 -0.0005758057  0.0237340576  0.0091656468  0.037718654  2.043425e-02
## 2014-07-31 -0.0025120439  0.0135555761 -0.0263797306 -0.052009444 -1.352880e-02
## 2014-08-29  0.0114312510  0.0279044995  0.0018001624  0.043658113  3.870547e-02
## 2014-09-30 -0.0061683760 -0.0808566713 -0.0395982980 -0.061260518 -1.389275e-02
## 2014-10-31  0.0105850830  0.0140966886 -0.0026548515  0.068874813  2.327795e-02
## 2014-11-28  0.0065491449 -0.0155414412  0.0006254112  0.004773526  2.710098e-02
## 2014-12-31  0.0014748462 -0.0404420568 -0.0407467225  0.025296073 -2.539728e-03
## 2015-01-30  0.0203148716 -0.0068955729  0.0062262805 -0.054628026 -3.007696e-02
## 2015-02-27 -0.0089879820  0.0431359574  0.0614506677  0.056914605  5.468176e-02
## 2015-03-31  0.0037404688 -0.0150864206 -0.0143887929  0.010156426 -1.583018e-02
## 2015-04-30 -0.0032332924  0.0662813596  0.0358163453 -0.018417830  9.785650e-03
## 2015-05-29 -0.0043830020 -0.0419106929  0.0019528674  0.007509980  1.277483e-02
## 2015-06-30 -0.0108260488 -0.0297466985 -0.0316789227  0.004171216 -2.052168e-02
## 2015-07-31  0.0085846300 -0.0651783269  0.0201147332 -0.027375421  2.233791e-02
## 2015-08-31 -0.0033637009 -0.0925122625 -0.0771526622 -0.047268362 -6.288648e-02
## 2015-09-30  0.0080816991 -0.0318249564 -0.0451949385 -0.038464334 -2.584740e-02
## 2015-10-30  0.0006848861  0.0618082062  0.0640260006  0.063589567  8.163529e-02
## 2015-11-30 -0.0038974463 -0.0255603348 -0.0075557282  0.024414906  3.648275e-03
## 2015-12-31 -0.0019195747 -0.0389470612 -0.0235950500 -0.052156700 -1.743370e-02
## 2016-01-29  0.0123296515 -0.0516369228 -0.0567579689 -0.060306786 -5.106845e-02
## 2016-02-29  0.0088320903 -0.0082113836 -0.0339139283  0.020605158 -8.265477e-04
## 2016-03-31  0.0087085118  0.1218788136  0.0637459390  0.089910239  6.510045e-02
## 2016-04-29  0.0025463969  0.0040794464  0.0219749278  0.021044202  3.933451e-03
## 2016-05-31  0.0001355942 -0.0376283878 -0.0008560851  0.004397090  1.686826e-02
## 2016-06-30  0.0191670642  0.0445823473 -0.0244915273  0.008292694  3.469827e-03
## 2016-07-29  0.0054292049  0.0524419629  0.0390002419  0.049347969  3.582223e-02
## 2016-08-31 -0.0021560140  0.0087988536  0.0053268450  0.011261092  1.196764e-03
## 2016-09-30  0.0005157377  0.0248725375  0.0132791635  0.008614844  5.794653e-05
## 2016-10-31 -0.0082052708 -0.0083120768 -0.0224037517 -0.038134794 -1.748905e-02
## 2016-11-30 -0.0259894334 -0.0451619493 -0.0179744890  0.125246274  3.617607e-02
## 2016-12-30  0.0025384689 -0.0025299176  0.0267030747  0.031491871  2.006916e-02
## 2017-01-31  0.0021257815  0.0644317259  0.0323818267 -0.012144125  1.773648e-02
## 2017-02-28  0.0064379000  0.0172578311  0.0118363502  0.013428799  3.853900e-02
## 2017-03-31 -0.0005530252  0.0361889645  0.0318057522 -0.006532991  1.249223e-03
## 2017-04-28  0.0090293528  0.0168661738  0.0239523293  0.005107864  9.877393e-03
## 2017-05-31  0.0068475053  0.0280598995  0.0348099190 -0.022862899  1.401425e-02
## 2017-06-30 -0.0001831494  0.0092235499  0.0029561485  0.029152154  6.354802e-03
## 2017-07-31  0.0033351378  0.0565947503  0.0261878079  0.007481476  2.034577e-02
## 2017-08-31  0.0093684997  0.0232437140 -0.0004483592 -0.027564705  2.913312e-03
## 2017-09-29 -0.0057318448 -0.0004461573  0.0233427441  0.082321410  1.994920e-02
## 2017-10-31  0.0009778448  0.0322784976  0.0166537929  0.005916172  2.329086e-02
## 2017-11-30 -0.0014840257 -0.0038970184  0.0068700310  0.036913435  3.010777e-02
## 2017-12-29  0.0047403290  0.0369254195  0.0133982755 -0.003731168  1.205499e-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 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

Column Chart of Component Contribution

plot_data <- asset_returns_wide_tbl %>%
    
    calculate_component_contribution(w = c(.25, .25, .2, .2, .1)) %>%
    
    # Transform to long form
    pivot_longer(cols = everything(), names_to = "Asset", values_to = "Contribution")

plot_data %>%
    
    ggplot(aes(x = Asset, y = Contribution)) +
    geom_col(fill = "cornflowerblue") +
    
    scale_y_continuous(labels = scales::percent_format(accuracy = 1)) +
    theme(plot.title = element_text(hjust = 0.5)) +
    
    labs(title = "Percent Contribution to Portfolio Volatility")

Column Chart of Component Contribution and Weight

plot_data <- asset_returns_wide_tbl %>%
    
    calculate_component_contribution(w = c(.25, .25, .2, .2, .1)) %>%
    
    # Transform to long form
    pivot_longer(cols = everything(), names_to = "Asset", values_to = "Contribution") %>%
    
    # Add weights
    add_column(weight = c(.25, .25, .2, .2, .1)) %>%
    
    # Transform to long
    pivot_longer(cols = c(Contribution, 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 = 0.5)) +
    theme_tq()+
    
    labs(title = "Percent Contribution to Portfolio Volatility and Weight",
         y = "Percent",
         x = NULL)

## 6 Rolling Component Contribution