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 -0.0062316529 -0.0029353521  0.0366061192  0.052132991  4.992312e-02
## 2013-02-28  0.0058917296 -0.0231054516 -0.0129692952  0.016175459  1.267823e-02
## 2013-03-28  0.0009845152 -0.0102350096  0.0129692952  0.040258405  3.726797e-02
## 2013-04-30  0.0096391558  0.0120846767  0.0489676360  0.001222365  1.903024e-02
## 2013-05-31 -0.0202140100 -0.0494837332 -0.0306554241  0.041976187  2.333549e-02
## 2013-06-28 -0.0157777762 -0.0547280916 -0.0271443808 -0.001402752 -1.343469e-02
## 2013-07-31  0.0026868636  0.0131596377  0.0518601691  0.063541713  5.038611e-02
## 2013-08-30 -0.0082978160 -0.0257053613 -0.0197462012 -0.034743923 -3.045137e-02
## 2013-09-30  0.0111439877  0.0695883585  0.0753384984  0.063873480  3.115588e-02
## 2013-10-31  0.0082924081  0.0408617658  0.0320816361  0.034234119  4.526679e-02
## 2013-11-29 -0.0025097532 -0.0025944831  0.0054497805  0.041661431  2.920682e-02
## 2013-12-31 -0.0055834678 -0.0040741338  0.0215278201  0.012892044  2.559607e-02
## 2014-01-31  0.0152918969 -0.0903227476 -0.0534132291 -0.035775325 -3.588423e-02
## 2014-02-28  0.0037568278  0.0332207265  0.0595050128  0.045257415  4.450969e-02
## 2014-03-31 -0.0014818300  0.0380217013 -0.0046026443  0.013315433  8.261713e-03
## 2014-04-30  0.0081832760  0.0077728584  0.0165295253 -0.023184356  6.927275e-03
## 2014-05-30  0.0117217258  0.0290914129  0.0158283500  0.006204740  2.294147e-02
## 2014-06-30 -0.0005759654  0.0237332771  0.0091656318  0.037719284  2.043487e-02
## 2014-07-31 -0.0025114722  0.0135560106 -0.0263800066 -0.052009282 -1.352864e-02
## 2014-08-29  0.0114304934  0.0279045754  0.0018005750  0.043657571  3.870436e-02
## 2014-09-30 -0.0061675106 -0.0808566819 -0.0395985696 -0.061260302 -1.389228e-02
## 2014-10-31  0.0105842869  0.0140964517 -0.0026548907  0.068874895  2.327806e-02
## 2014-11-28  0.0065488810 -0.0155415250  0.0006255479  0.004773331  2.710104e-02
## 2014-12-31  0.0014753626 -0.0404418786 -0.0407468068  0.025295911 -2.539750e-03
## 2015-01-30  0.0203149161 -0.0068956759  0.0062264224 -0.054627821 -3.007699e-02
## 2015-02-27 -0.0089882764  0.0431359589  0.0614506173  0.056914489  5.468164e-02
## 2015-03-31  0.0037405978 -0.0150862520 -0.0143887845  0.010156612 -1.582993e-02
## 2015-04-30 -0.0032335572  0.0662813058  0.0358165822 -0.018417818  9.785778e-03
## 2015-05-29 -0.0043837380 -0.0419109062  0.0019527235  0.007509875  1.277431e-02
## 2015-06-30 -0.0108252759 -0.0297467280 -0.0316787473  0.004171446 -2.052136e-02
## 2015-07-31  0.0085844848 -0.0651783838  0.0201142517 -0.027375211  2.233797e-02
## 2015-08-31 -0.0033631079 -0.0925118170 -0.0771522510 -0.047268414 -6.288677e-02
## 2015-09-30  0.0080814642 -0.0318251976 -0.0451947203 -0.038464709 -2.584723e-02
## 2015-10-30  0.0006852079  0.0618084371  0.0640255524  0.063589548  8.163497e-02
## 2015-11-30 -0.0038985160 -0.0255606045 -0.0075556366  0.024415109  3.648790e-03
## 2015-12-31 -0.0019187171 -0.0389471757 -0.0235951109 -0.052156593 -1.743382e-02
## 2016-01-29  0.0123294778 -0.0516366086 -0.0567579081 -0.060307018 -5.106866e-02
## 2016-02-29  0.0088318423 -0.0082114548 -0.0339139044  0.020605203 -8.258442e-04
## 2016-03-31  0.0087089570  0.1218788430  0.0637457796  0.089910399  6.509987e-02
## 2016-04-29  0.0025462862  0.0040792165  0.0219750146  0.021043930  3.933564e-03
## 2016-05-31  0.0001354860 -0.0376285129 -0.0008559621  0.004397565  1.686846e-02
## 2016-06-30  0.0191668414  0.0445826057 -0.0244915362  0.008291952  3.469716e-03
## 2016-07-29  0.0054296126  0.0524420240  0.0390002796  0.049348449  3.582182e-02
## 2016-08-31 -0.0021565147  0.0087987244  0.0053269447  0.011261039  1.196817e-03
## 2016-09-30  0.0005164766  0.0248726884  0.0132789939  0.008614667  5.821668e-05
## 2016-10-31 -0.0082052273 -0.0083119468 -0.0224037499 -0.038135003 -1.748921e-02
## 2016-11-30 -0.0259897812 -0.0451620157 -0.0179744835  0.125246573  3.617638e-02
## 2016-12-30  0.0025379830 -0.0025300101  0.0267029452  0.031492108  2.006885e-02
## 2017-01-31  0.0021261608  0.0644311551  0.0323818767 -0.012144152  1.773646e-02
## 2017-02-28  0.0064380178  0.0172581973  0.0118364711  0.013428807  3.853912e-02
## 2017-03-31 -0.0005533897  0.0361890959  0.0318056345 -0.006533204  1.249380e-03
## 2017-04-28  0.0090292551  0.0168662836  0.0239522905  0.005107774  9.877380e-03
## 2017-05-31  0.0068473527  0.0280596567  0.0348101850 -0.022862689  1.401415e-02
## 2017-06-30 -0.0001823579  0.0092240905  0.0029559265  0.029151813  6.354546e-03
## 2017-07-31  0.0033344693  0.0565944338  0.0261877980  0.007481738  2.034593e-02
## 2017-08-31  0.0093693290  0.0232435724 -0.0004482935 -0.027565043  2.913239e-03
## 2017-09-29 -0.0057320847 -0.0004458973  0.0233428450  0.082322140  1.994901e-02
## 2017-10-31  0.0009778383  0.0322781792  0.0166535960  0.005915857  2.329095e-02
## 2017-11-30 -0.0014843111 -0.0038966623  0.0068701057  0.036913066  3.010806e-02
## 2017-12-29  0.0047404541  0.0369252960  0.0133982702 -0.003730915  1.205493e-02

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

covariance_matrix

##               AGG          EEM          EFA           IJS           SPY
## AGG  7.398382e-05 0.0001042076 4.177867e-05 -7.812271e-05 -9.034227e-06
## EEM  1.042076e-04 0.0017547073 1.039014e-03  6.437702e-04  6.795403e-04
## EFA  4.177867e-05 0.0010390142 1.064235e-03  6.490294e-04  6.975387e-04
## IJS -7.812271e-05 0.0006437702 6.490294e-04  1.565452e-03  8.290252e-04
## SPY -9.034227e-06 0.0006795403 6.975387e-04  8.290252e-04  7.408274e-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,] 0.02347486

# 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,] 0.0003873891 0.009257133 0.005815625 0.005684469 0.002330246

rowSums(component_contribution)

## [1] 0.02347486

# 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 -0.0062316529 -0.0029353521  0.0366061192  0.052132991  4.992312e-02
## 2013-02-28  0.0058917296 -0.0231054516 -0.0129692952  0.016175459  1.267823e-02
## 2013-03-28  0.0009845152 -0.0102350096  0.0129692952  0.040258405  3.726797e-02
## 2013-04-30  0.0096391558  0.0120846767  0.0489676360  0.001222365  1.903024e-02
## 2013-05-31 -0.0202140100 -0.0494837332 -0.0306554241  0.041976187  2.333549e-02
## 2013-06-28 -0.0157777762 -0.0547280916 -0.0271443808 -0.001402752 -1.343469e-02
## 2013-07-31  0.0026868636  0.0131596377  0.0518601691  0.063541713  5.038611e-02
## 2013-08-30 -0.0082978160 -0.0257053613 -0.0197462012 -0.034743923 -3.045137e-02
## 2013-09-30  0.0111439877  0.0695883585  0.0753384984  0.063873480  3.115588e-02
## 2013-10-31  0.0082924081  0.0408617658  0.0320816361  0.034234119  4.526679e-02
## 2013-11-29 -0.0025097532 -0.0025944831  0.0054497805  0.041661431  2.920682e-02
## 2013-12-31 -0.0055834678 -0.0040741338  0.0215278201  0.012892044  2.559607e-02
## 2014-01-31  0.0152918969 -0.0903227476 -0.0534132291 -0.035775325 -3.588423e-02
## 2014-02-28  0.0037568278  0.0332207265  0.0595050128  0.045257415  4.450969e-02
## 2014-03-31 -0.0014818300  0.0380217013 -0.0046026443  0.013315433  8.261713e-03
## 2014-04-30  0.0081832760  0.0077728584  0.0165295253 -0.023184356  6.927275e-03
## 2014-05-30  0.0117217258  0.0290914129  0.0158283500  0.006204740  2.294147e-02
## 2014-06-30 -0.0005759654  0.0237332771  0.0091656318  0.037719284  2.043487e-02
## 2014-07-31 -0.0025114722  0.0135560106 -0.0263800066 -0.052009282 -1.352864e-02
## 2014-08-29  0.0114304934  0.0279045754  0.0018005750  0.043657571  3.870436e-02
## 2014-09-30 -0.0061675106 -0.0808566819 -0.0395985696 -0.061260302 -1.389228e-02
## 2014-10-31  0.0105842869  0.0140964517 -0.0026548907  0.068874895  2.327806e-02
## 2014-11-28  0.0065488810 -0.0155415250  0.0006255479  0.004773331  2.710104e-02
## 2014-12-31  0.0014753626 -0.0404418786 -0.0407468068  0.025295911 -2.539750e-03
## 2015-01-30  0.0203149161 -0.0068956759  0.0062264224 -0.054627821 -3.007699e-02
## 2015-02-27 -0.0089882764  0.0431359589  0.0614506173  0.056914489  5.468164e-02
## 2015-03-31  0.0037405978 -0.0150862520 -0.0143887845  0.010156612 -1.582993e-02
## 2015-04-30 -0.0032335572  0.0662813058  0.0358165822 -0.018417818  9.785778e-03
## 2015-05-29 -0.0043837380 -0.0419109062  0.0019527235  0.007509875  1.277431e-02
## 2015-06-30 -0.0108252759 -0.0297467280 -0.0316787473  0.004171446 -2.052136e-02
## 2015-07-31  0.0085844848 -0.0651783838  0.0201142517 -0.027375211  2.233797e-02
## 2015-08-31 -0.0033631079 -0.0925118170 -0.0771522510 -0.047268414 -6.288677e-02
## 2015-09-30  0.0080814642 -0.0318251976 -0.0451947203 -0.038464709 -2.584723e-02
## 2015-10-30  0.0006852079  0.0618084371  0.0640255524  0.063589548  8.163497e-02
## 2015-11-30 -0.0038985160 -0.0255606045 -0.0075556366  0.024415109  3.648790e-03
## 2015-12-31 -0.0019187171 -0.0389471757 -0.0235951109 -0.052156593 -1.743382e-02
## 2016-01-29  0.0123294778 -0.0516366086 -0.0567579081 -0.060307018 -5.106866e-02
## 2016-02-29  0.0088318423 -0.0082114548 -0.0339139044  0.020605203 -8.258442e-04
## 2016-03-31  0.0087089570  0.1218788430  0.0637457796  0.089910399  6.509987e-02
## 2016-04-29  0.0025462862  0.0040792165  0.0219750146  0.021043930  3.933564e-03
## 2016-05-31  0.0001354860 -0.0376285129 -0.0008559621  0.004397565  1.686846e-02
## 2016-06-30  0.0191668414  0.0445826057 -0.0244915362  0.008291952  3.469716e-03
## 2016-07-29  0.0054296126  0.0524420240  0.0390002796  0.049348449  3.582182e-02
## 2016-08-31 -0.0021565147  0.0087987244  0.0053269447  0.011261039  1.196817e-03
## 2016-09-30  0.0005164766  0.0248726884  0.0132789939  0.008614667  5.821668e-05
## 2016-10-31 -0.0082052273 -0.0083119468 -0.0224037499 -0.038135003 -1.748921e-02
## 2016-11-30 -0.0259897812 -0.0451620157 -0.0179744835  0.125246573  3.617638e-02
## 2016-12-30  0.0025379830 -0.0025300101  0.0267029452  0.031492108  2.006885e-02
## 2017-01-31  0.0021261608  0.0644311551  0.0323818767 -0.012144152  1.773646e-02
## 2017-02-28  0.0064380178  0.0172581973  0.0118364711  0.013428807  3.853912e-02
## 2017-03-31 -0.0005533897  0.0361890959  0.0318056345 -0.006533204  1.249380e-03
## 2017-04-28  0.0090292551  0.0168662836  0.0239522905  0.005107774  9.877380e-03
## 2017-05-31  0.0068473527  0.0280596567  0.0348101850 -0.022862689  1.401415e-02
## 2017-06-30 -0.0001823579  0.0092240905  0.0029559265  0.029151813  6.354546e-03
## 2017-07-31  0.0033344693  0.0565944338  0.0261877980  0.007481738  2.034593e-02
## 2017-08-31  0.0093693290  0.0232435724 -0.0004482935 -0.027565043  2.913239e-03
## 2017-09-29 -0.0057320847 -0.0004458973  0.0233428450  0.082322140  1.994901e-02
## 2017-10-31  0.0009778383  0.0322781792  0.0166535960  0.005915857  2.329095e-02
## 2017-11-30 -0.0014843111 -0.0038966623  0.0068701057  0.036913066  3.010806e-02
## 2017-12-29  0.0047404541  0.0369252960  0.0133982702 -0.003730915  1.205493e-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)