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 -0.0062315902 -0.0029353524  0.0366063075  0.052133306  4.992260e-02
## 2013-02-28  0.0058916248 -0.0231054542 -0.0129692033  0.016175136  1.267811e-02
## 2013-03-28  0.0009853678 -0.0102348964  0.0129692033  0.040258299  3.726828e-02
## 2013-04-30  0.0096382816  0.0120847897  0.0489678089  0.001222668  1.903006e-02
## 2013-05-31 -0.0202136606 -0.0494836088 -0.0306556861  0.041976078  2.333527e-02
## 2013-06-28 -0.0157779875 -0.0547281409 -0.0271443833 -0.001402849 -1.343423e-02
## 2013-07-31  0.0026872778  0.0131596971  0.0518602606  0.063541070  5.038588e-02
## 2013-08-30 -0.0082984937 -0.0257057991 -0.0197460238 -0.034743283 -3.045114e-02
## 2013-09-30  0.0111445556  0.0695890226  0.0753384033  0.063873827  3.115610e-02
## 2013-10-31  0.0082923089  0.0408609511  0.0320815538  0.034233762  4.526614e-02
## 2013-11-29 -0.0025100792 -0.0025939141  0.0054497805  0.041661345  2.920704e-02
## 2013-12-31 -0.0055830827 -0.0040743618  0.0215277426  0.012891963  2.559628e-02
## 2014-01-31  0.0152911415 -0.0903225597 -0.0534130698 -0.035775161 -3.588433e-02
## 2014-02-28  0.0037573164  0.0332205992  0.0595050852  0.045257251  4.450999e-02
## 2014-03-31 -0.0014819090  0.0380217573 -0.0046026436  0.013315355  8.261514e-03
## 2014-04-30  0.0081834801  0.0077726260  0.0165293705 -0.023184279  6.927469e-03
## 2014-05-30  0.0117217783  0.0290913038  0.0158285748  0.006205384  2.294118e-02
## 2014-06-30 -0.0005763988  0.0237337214  0.0091654813  0.037718489  2.043450e-02
## 2014-07-31 -0.0025119273  0.0135557911 -0.0263800808 -0.052009295 -1.352836e-02
## 2014-08-29  0.0114307718  0.0279046807  0.0018006511  0.043657972  3.870409e-02
## 2014-09-30 -0.0061672033 -0.0808567872 -0.0395985666 -0.061260375 -1.389201e-02
## 2014-10-31  0.0105852492  0.0140965643 -0.0026548111  0.068874657  2.327806e-02
## 2014-11-28  0.0065479072 -0.0155412945  0.0006253098  0.004773949  2.710131e-02
## 2014-12-31  0.0014755967 -0.0404423407 -0.0407468101  0.025295524 -2.539925e-03
## 2015-01-30  0.0203147826 -0.0068956168  0.0062263408 -0.054627975 -3.007690e-02
## 2015-02-27 -0.0089880732  0.0431360188  0.0614507043  0.056914793  5.468172e-02
## 2015-03-31  0.0037398657 -0.0150862520 -0.0143886289  0.010156387 -1.583037e-02
## 2015-04-30 -0.0032327405  0.0662813058  0.0358165794 -0.018417742  9.786386e-03
## 2015-05-29 -0.0043834671 -0.0419107925  0.0019527233  0.007509799  1.277387e-02
## 2015-06-30 -0.0108252494 -0.0297469590 -0.0316789785  0.004171297 -2.052118e-02
## 2015-07-31  0.0085842861 -0.0651778287  0.0201146365 -0.027375369  2.233763e-02
## 2015-08-31 -0.0033639246 -0.0925125293 -0.0771523975 -0.047268107 -6.288652e-02
## 2015-09-30  0.0080821415 -0.0318249231 -0.0451951478 -0.038464625 -2.584723e-02
## 2015-10-30  0.0006848747  0.0618081707  0.0640259784  0.063589543  8.163514e-02
## 2015-11-30 -0.0038980433 -0.0255603382 -0.0075558806  0.024415184  3.648362e-03
## 2015-12-31 -0.0019188555 -0.0389472468 -0.0235950314 -0.052156988 -1.743339e-02
## 2016-01-29  0.0123300394 -0.0516366123 -0.0567576480 -0.060306604 -5.106847e-02
## 2016-02-29  0.0088312199 -0.0082115308 -0.0339139897  0.020604947 -8.265769e-04
## 2016-03-31  0.0087091532  0.1218789271  0.0637457739  0.089910483  6.510032e-02
## 2016-04-29  0.0025463205  0.0040794162  0.0219749289  0.021044231  3.933222e-03
## 2016-05-31  0.0001354793 -0.0376285768 -0.0008559621  0.004396890  1.686847e-02
## 2016-06-30  0.0191666894  0.0445824706 -0.0244915362  0.008292401  3.469801e-03
## 2016-07-29  0.0054298376  0.0524419648  0.0390001969  0.049348234  3.582215e-02
## 2016-08-31 -0.0021564496  0.0087986013  0.0053268628  0.011260971  1.196736e-03
## 2016-09-30  0.0005159879  0.0248729974  0.0132791585  0.008614946  5.797445e-05
## 2016-10-31 -0.0082054711 -0.0083121906 -0.0224037499 -0.038134785 -1.748889e-02
## 2016-11-30 -0.0259894573 -0.0451618325 -0.0179744835  0.125245840  3.617622e-02
## 2016-12-30  0.0025378368 -0.0025298819  0.0267029452  0.031492245  2.006893e-02
## 2017-01-31  0.0021263936  0.0644313273  0.0323817970 -0.012143907  1.773638e-02
## 2017-02-28  0.0064374296  0.0172577789  0.0118364721  0.013428869  3.853926e-02
## 2017-03-31 -0.0005527089  0.0361892139  0.0318057896 -0.006533142  1.249233e-03
## 2017-04-28  0.0090294579  0.0168661716  0.0239522142  0.005107835  9.876945e-03
## 2017-05-31  0.0068471621  0.0280598776  0.0348101850 -0.022862749  1.401430e-02
## 2017-06-30 -0.0001824196  0.0092237659  0.0029558548  0.029151933  6.354904e-03
## 2017-07-31  0.0033344871  0.0565945476  0.0261879397  0.007481433  2.034572e-02
## 2017-08-31  0.0093691955  0.0232438736 -0.0004481536 -0.027564796  2.913448e-03
## 2017-09-29 -0.0057322996 -0.0004463954  0.0233427036  0.082321785  1.994915e-02
## 2017-10-31  0.0009777832  0.0322785746  0.0166534606  0.005915973  2.329075e-02
## 2017-11-30 -0.0014840713 -0.0038969524  0.0068701061  0.036913401  3.010806e-02
## 2017-12-29  0.0047404064  0.0369254897  0.0133982711 -0.003730914  1.205525e-02

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

covariance_matrix

##               AGG          EEM          EFA           IJS           SPY
## AGG  7.398320e-05 0.0001042115 4.178201e-05 -7.811769e-05 -9.031726e-06
## EEM  1.042115e-04 0.0017547103 1.039017e-03  6.437729e-04  6.795425e-04
## EFA  4.178201e-05 0.0010390167 1.064237e-03  6.490294e-04  6.975394e-04
## IJS -7.811769e-05 0.0006437729 6.490294e-04  1.565445e-03  8.290215e-04
## SPY -9.031726e-06 0.0006795425 6.975394e-04  8.290215e-04  7.408254e-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,] 0.0234749

# 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,] 0.0003874176 0.009257148 0.005815632 0.00568446 0.002330244

rowSums(component_contribution)

## [1] 0.0234749

# 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

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 -0.0062315902 -0.0029353524  0.0366063075  0.052133306  4.992260e-02
## 2013-02-28  0.0058916248 -0.0231054542 -0.0129692033  0.016175136  1.267811e-02
## 2013-03-28  0.0009853678 -0.0102348964  0.0129692033  0.040258299  3.726828e-02
## 2013-04-30  0.0096382816  0.0120847897  0.0489678089  0.001222668  1.903006e-02
## 2013-05-31 -0.0202136606 -0.0494836088 -0.0306556861  0.041976078  2.333527e-02
## 2013-06-28 -0.0157779875 -0.0547281409 -0.0271443833 -0.001402849 -1.343423e-02
## 2013-07-31  0.0026872778  0.0131596971  0.0518602606  0.063541070  5.038588e-02
## 2013-08-30 -0.0082984937 -0.0257057991 -0.0197460238 -0.034743283 -3.045114e-02
## 2013-09-30  0.0111445556  0.0695890226  0.0753384033  0.063873827  3.115610e-02
## 2013-10-31  0.0082923089  0.0408609511  0.0320815538  0.034233762  4.526614e-02
## 2013-11-29 -0.0025100792 -0.0025939141  0.0054497805  0.041661345  2.920704e-02
## 2013-12-31 -0.0055830827 -0.0040743618  0.0215277426  0.012891963  2.559628e-02
## 2014-01-31  0.0152911415 -0.0903225597 -0.0534130698 -0.035775161 -3.588433e-02
## 2014-02-28  0.0037573164  0.0332205992  0.0595050852  0.045257251  4.450999e-02
## 2014-03-31 -0.0014819090  0.0380217573 -0.0046026436  0.013315355  8.261514e-03
## 2014-04-30  0.0081834801  0.0077726260  0.0165293705 -0.023184279  6.927469e-03
## 2014-05-30  0.0117217783  0.0290913038  0.0158285748  0.006205384  2.294118e-02
## 2014-06-30 -0.0005763988  0.0237337214  0.0091654813  0.037718489  2.043450e-02
## 2014-07-31 -0.0025119273  0.0135557911 -0.0263800808 -0.052009295 -1.352836e-02
## 2014-08-29  0.0114307718  0.0279046807  0.0018006511  0.043657972  3.870409e-02
## 2014-09-30 -0.0061672033 -0.0808567872 -0.0395985666 -0.061260375 -1.389201e-02
## 2014-10-31  0.0105852492  0.0140965643 -0.0026548111  0.068874657  2.327806e-02
## 2014-11-28  0.0065479072 -0.0155412945  0.0006253098  0.004773949  2.710131e-02
## 2014-12-31  0.0014755967 -0.0404423407 -0.0407468101  0.025295524 -2.539925e-03
## 2015-01-30  0.0203147826 -0.0068956168  0.0062263408 -0.054627975 -3.007690e-02
## 2015-02-27 -0.0089880732  0.0431360188  0.0614507043  0.056914793  5.468172e-02
## 2015-03-31  0.0037398657 -0.0150862520 -0.0143886289  0.010156387 -1.583037e-02
## 2015-04-30 -0.0032327405  0.0662813058  0.0358165794 -0.018417742  9.786386e-03
## 2015-05-29 -0.0043834671 -0.0419107925  0.0019527233  0.007509799  1.277387e-02
## 2015-06-30 -0.0108252494 -0.0297469590 -0.0316789785  0.004171297 -2.052118e-02
## 2015-07-31  0.0085842861 -0.0651778287  0.0201146365 -0.027375369  2.233763e-02
## 2015-08-31 -0.0033639246 -0.0925125293 -0.0771523975 -0.047268107 -6.288652e-02
## 2015-09-30  0.0080821415 -0.0318249231 -0.0451951478 -0.038464625 -2.584723e-02
## 2015-10-30  0.0006848747  0.0618081707  0.0640259784  0.063589543  8.163514e-02
## 2015-11-30 -0.0038980433 -0.0255603382 -0.0075558806  0.024415184  3.648362e-03
## 2015-12-31 -0.0019188555 -0.0389472468 -0.0235950314 -0.052156988 -1.743339e-02
## 2016-01-29  0.0123300394 -0.0516366123 -0.0567576480 -0.060306604 -5.106847e-02
## 2016-02-29  0.0088312199 -0.0082115308 -0.0339139897  0.020604947 -8.265769e-04
## 2016-03-31  0.0087091532  0.1218789271  0.0637457739  0.089910483  6.510032e-02
## 2016-04-29  0.0025463205  0.0040794162  0.0219749289  0.021044231  3.933222e-03
## 2016-05-31  0.0001354793 -0.0376285768 -0.0008559621  0.004396890  1.686847e-02
## 2016-06-30  0.0191666894  0.0445824706 -0.0244915362  0.008292401  3.469801e-03
## 2016-07-29  0.0054298376  0.0524419648  0.0390001969  0.049348234  3.582215e-02
## 2016-08-31 -0.0021564496  0.0087986013  0.0053268628  0.011260971  1.196736e-03
## 2016-09-30  0.0005159879  0.0248729974  0.0132791585  0.008614946  5.797445e-05
## 2016-10-31 -0.0082054711 -0.0083121906 -0.0224037499 -0.038134785 -1.748889e-02
## 2016-11-30 -0.0259894573 -0.0451618325 -0.0179744835  0.125245840  3.617622e-02
## 2016-12-30  0.0025378368 -0.0025298819  0.0267029452  0.031492245  2.006893e-02
## 2017-01-31  0.0021263936  0.0644313273  0.0323817970 -0.012143907  1.773638e-02
## 2017-02-28  0.0064374296  0.0172577789  0.0118364721  0.013428869  3.853926e-02
## 2017-03-31 -0.0005527089  0.0361892139  0.0318057896 -0.006533142  1.249233e-03
## 2017-04-28  0.0090294579  0.0168661716  0.0239522142  0.005107835  9.876945e-03
## 2017-05-31  0.0068471621  0.0280598776  0.0348101850 -0.022862749  1.401430e-02
## 2017-06-30 -0.0001824196  0.0092237659  0.0029558548  0.029151933  6.354904e-03
## 2017-07-31  0.0033344871  0.0565945476  0.0261879397  0.007481433  2.034572e-02
## 2017-08-31  0.0093691955  0.0232438736 -0.0004481536 -0.027564796  2.913448e-03
## 2017-09-29 -0.0057322996 -0.0004463954  0.0233427036  0.082321785  1.994915e-02
## 2017-10-31  0.0009777832  0.0322785746  0.0166534606  0.005915973  2.329075e-02
## 2017-11-30 -0.0014840713 -0.0038969524  0.0068701061  0.036913401  3.010806e-02
## 2017-12-29  0.0047404064  0.0369254897  0.0133982711 -0.003730914  1.205525e-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(.25, .25, .2, .2, .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 Volatitily")

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 Weight
    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)) +
    
    labs(title = "Percent Contribution to Portfolio Volatitily and Weight", 
         y = "Percent",
         x = NULL)