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 -0.0062311938 -0.0029356149  0.0366062071  0.052132890  4.992312e-02
## 2013-02-28  0.0058911491 -0.0231052718 -0.0129692988  0.016175296  1.267823e-02
## 2013-03-28  0.0009846267 -0.0102349807  0.0129692988  0.040258214  3.726804e-02
## 2013-04-30  0.0096394590  0.0120845659  0.0489679629  0.001222503  1.903027e-02
## 2013-05-31 -0.0202137559 -0.0494833281 -0.0306557129  0.041976150  2.333483e-02
## 2013-06-28 -0.0157784203 -0.0547283624 -0.0271442996 -0.001402875 -1.343410e-02
## 2013-07-31  0.0026879274  0.0131597634  0.0518602591  0.063541614  5.038575e-02
## 2013-08-30 -0.0082981024 -0.0257056700 -0.0197465446 -0.034743794 -3.045118e-02
## 2013-09-30  0.0111437569  0.0695889000  0.0753385995  0.063873903  3.115581e-02
## 2013-10-31  0.0082919677  0.0408614731  0.0320816661  0.034233899  4.526690e-02
## 2013-11-29 -0.0025098434 -0.0025942668  0.0054497972  0.041661323  2.920683e-02
## 2013-12-31 -0.0055833727 -0.0040744756  0.0215279453  0.012891974  2.559586e-02
## 2014-01-31  0.0152916452 -0.0903224525 -0.0534132453 -0.035775315 -3.588430e-02
## 2014-02-28  0.0037573509  0.0332204476  0.0595049838  0.045257432  4.451039e-02
## 2014-03-31 -0.0014815444  0.0380218609 -0.0046024237  0.013315164  8.261372e-03
## 2014-04-30  0.0081827068  0.0077727660  0.0165293809 -0.023184109  6.927500e-03
## 2014-05-30  0.0117219368  0.0290909984  0.0158283807  0.006205324  2.294118e-02
## 2014-06-30 -0.0005757119  0.0237339392  0.0091655176  0.037718692  2.043452e-02
## 2014-07-31 -0.0025121844  0.0135557339 -0.0263799557 -0.052009333 -1.352858e-02
## 2014-08-29  0.0114310779  0.0279045096  0.0018005836  0.043657633  3.870484e-02
## 2014-09-30 -0.0061681053 -0.0808568044 -0.0395986345 -0.061260472 -1.389256e-02
## 2014-10-31  0.0105853577  0.0140966491 -0.0026546487  0.068874806  2.327807e-02
## 2014-11-28  0.0065486076 -0.0155414839  0.0006251483  0.004774007  2.710101e-02
## 2014-12-31  0.0014745513 -0.0404419447 -0.0407467496  0.025295475 -2.539391e-03
## 2015-01-30  0.0203157653 -0.0068958195  0.0062266515 -0.054627727 -3.007737e-02
## 2015-02-27 -0.0089882366  0.0431361518  0.0614504471  0.056914519  5.468185e-02
## 2015-03-31  0.0037401380 -0.0150863650 -0.0143885547  0.010156103 -1.583028e-02
## 2015-04-30 -0.0032333579  0.0662812915  0.0358163054 -0.018417512  9.785978e-03
## 2015-05-29 -0.0043836810 -0.0419110348  0.0019528441  0.007510072  1.277407e-02
## 2015-06-30 -0.0108250229 -0.0297465862 -0.0316789216  0.004171341 -2.052115e-02
## 2015-07-31  0.0085842899 -0.0651780054  0.0201145590 -0.027375405  2.233794e-02
## 2015-08-31 -0.0033637686 -0.0925125820 -0.0771524288 -0.047268445 -6.288667e-02
## 2015-09-30  0.0080819523 -0.0318247067 -0.0451950749 -0.038464611 -2.584727e-02
## 2015-10-30  0.0006850480  0.0618083092  0.0640260980  0.063589665  8.163521e-02
## 2015-11-30 -0.0038983052 -0.0255606226 -0.0075558630  0.024415189  3.648134e-03
## 2015-12-31 -0.0019186899 -0.0389470367 -0.0235949324 -0.052157053 -1.743346e-02
## 2016-01-29  0.0123295753 -0.0516366466 -0.0567579292 -0.060306943 -5.106853e-02
## 2016-02-29  0.0088320249 -0.0082114300 -0.0339139210  0.020605353 -8.261283e-04
## 2016-03-31  0.0087085888  0.1218788614  0.0637456380  0.089910556  6.509991e-02
## 2016-04-29  0.0025460543  0.0040793342  0.0219751258  0.021044115  3.933460e-03
## 2016-05-31  0.0001355821 -0.0376285480 -0.0008561489  0.004397040  1.686870e-02
## 2016-06-30  0.0191668948  0.0445823791 -0.0244914495  0.008292351  3.469841e-03
## 2016-07-29  0.0054293384  0.0524423965  0.0390002318  0.049348444  3.582171e-02
## 2016-08-31 -0.0021557030  0.0087987423  0.0053268061  0.011260998  1.197078e-03
## 2016-09-30  0.0005155519  0.0248726899  0.0132792447  0.008614733  5.796024e-05
## 2016-10-31 -0.0082048919 -0.0083126000 -0.0224036216 -0.038134756 -1.748909e-02
## 2016-11-30 -0.0259896866 -0.0451615541 -0.0179744997  0.125246265  3.617591e-02
## 2016-12-30  0.0025377956 -0.0025300701  0.0267028663  0.031492019  2.006913e-02
## 2017-01-31  0.0021260874  0.0644312746  0.0323817590 -0.012144235  1.773659e-02
## 2017-02-28  0.0064378146  0.0172581706  0.0118365242  0.013428817  3.853930e-02
## 2017-03-31 -0.0005524628  0.0361890071  0.0318056037 -0.006533221  1.249100e-03
## 2017-04-28  0.0090290975  0.0168659566  0.0239522302  0.005108111  9.877365e-03
## 2017-05-31  0.0068472617  0.0280601914  0.0348102875 -0.022862715  1.401392e-02
## 2017-06-30 -0.0001825845  0.0092236754  0.0029558483  0.029151873  6.354856e-03
## 2017-07-31  0.0033347298  0.0565944551  0.0261879254  0.007481106  2.034571e-02
## 2017-08-31  0.0093693012  0.0232439220 -0.0004482983 -0.027564554  2.913602e-03
## 2017-09-29 -0.0057328166 -0.0004461971  0.0233427221  0.082321936  1.994909e-02
## 2017-10-31  0.0009779872  0.0322782484  0.0166538934  0.005915878  2.329066e-02
## 2017-11-30 -0.0014839301 -0.0038969126  0.0068697764  0.036913503  3.010794e-02
## 2017-12-29  0.0047405756  0.0369254493  0.0133983353 -0.003731344  1.205502e-02

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

covariance_matrix

##               AGG          EEM          EFA           IJS           SPY
## AGG  7.398457e-05 0.0001042109 4.178171e-05 -7.811982e-05 -9.032008e-06
## EEM  1.042109e-04 0.0017547095 1.039017e-03  6.437747e-04  6.795427e-04
## EFA  4.178171e-05 0.0010390166 1.064238e-03  6.490309e-04  6.975400e-04
## IJS -7.811982e-05 0.0006437747 6.490309e-04  1.565450e-03  8.290244e-04
## SPY -9.032008e-06 0.0006795427 6.975400e-04  8.290244e-04  7.408275e-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,] 0.0003874141 0.009257145 0.005815633 0.005684472 0.002330247

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 -0.0062311938 -0.0029356149  0.0366062071  0.052132890  4.992312e-02
## 2013-02-28  0.0058911491 -0.0231052718 -0.0129692988  0.016175296  1.267823e-02
## 2013-03-28  0.0009846267 -0.0102349807  0.0129692988  0.040258214  3.726804e-02
## 2013-04-30  0.0096394590  0.0120845659  0.0489679629  0.001222503  1.903027e-02
## 2013-05-31 -0.0202137559 -0.0494833281 -0.0306557129  0.041976150  2.333483e-02
## 2013-06-28 -0.0157784203 -0.0547283624 -0.0271442996 -0.001402875 -1.343410e-02
## 2013-07-31  0.0026879274  0.0131597634  0.0518602591  0.063541614  5.038575e-02
## 2013-08-30 -0.0082981024 -0.0257056700 -0.0197465446 -0.034743794 -3.045118e-02
## 2013-09-30  0.0111437569  0.0695889000  0.0753385995  0.063873903  3.115581e-02
## 2013-10-31  0.0082919677  0.0408614731  0.0320816661  0.034233899  4.526690e-02
## 2013-11-29 -0.0025098434 -0.0025942668  0.0054497972  0.041661323  2.920683e-02
## 2013-12-31 -0.0055833727 -0.0040744756  0.0215279453  0.012891974  2.559586e-02
## 2014-01-31  0.0152916452 -0.0903224525 -0.0534132453 -0.035775315 -3.588430e-02
## 2014-02-28  0.0037573509  0.0332204476  0.0595049838  0.045257432  4.451039e-02
## 2014-03-31 -0.0014815444  0.0380218609 -0.0046024237  0.013315164  8.261372e-03
## 2014-04-30  0.0081827068  0.0077727660  0.0165293809 -0.023184109  6.927500e-03
## 2014-05-30  0.0117219368  0.0290909984  0.0158283807  0.006205324  2.294118e-02
## 2014-06-30 -0.0005757119  0.0237339392  0.0091655176  0.037718692  2.043452e-02
## 2014-07-31 -0.0025121844  0.0135557339 -0.0263799557 -0.052009333 -1.352858e-02
## 2014-08-29  0.0114310779  0.0279045096  0.0018005836  0.043657633  3.870484e-02
## 2014-09-30 -0.0061681053 -0.0808568044 -0.0395986345 -0.061260472 -1.389256e-02
## 2014-10-31  0.0105853577  0.0140966491 -0.0026546487  0.068874806  2.327807e-02
## 2014-11-28  0.0065486076 -0.0155414839  0.0006251483  0.004774007  2.710101e-02
## 2014-12-31  0.0014745513 -0.0404419447 -0.0407467496  0.025295475 -2.539391e-03
## 2015-01-30  0.0203157653 -0.0068958195  0.0062266515 -0.054627727 -3.007737e-02
## 2015-02-27 -0.0089882366  0.0431361518  0.0614504471  0.056914519  5.468185e-02
## 2015-03-31  0.0037401380 -0.0150863650 -0.0143885547  0.010156103 -1.583028e-02
## 2015-04-30 -0.0032333579  0.0662812915  0.0358163054 -0.018417512  9.785978e-03
## 2015-05-29 -0.0043836810 -0.0419110348  0.0019528441  0.007510072  1.277407e-02
## 2015-06-30 -0.0108250229 -0.0297465862 -0.0316789216  0.004171341 -2.052115e-02
## 2015-07-31  0.0085842899 -0.0651780054  0.0201145590 -0.027375405  2.233794e-02
## 2015-08-31 -0.0033637686 -0.0925125820 -0.0771524288 -0.047268445 -6.288667e-02
## 2015-09-30  0.0080819523 -0.0318247067 -0.0451950749 -0.038464611 -2.584727e-02
## 2015-10-30  0.0006850480  0.0618083092  0.0640260980  0.063589665  8.163521e-02
## 2015-11-30 -0.0038983052 -0.0255606226 -0.0075558630  0.024415189  3.648134e-03
## 2015-12-31 -0.0019186899 -0.0389470367 -0.0235949324 -0.052157053 -1.743346e-02
## 2016-01-29  0.0123295753 -0.0516366466 -0.0567579292 -0.060306943 -5.106853e-02
## 2016-02-29  0.0088320249 -0.0082114300 -0.0339139210  0.020605353 -8.261283e-04
## 2016-03-31  0.0087085888  0.1218788614  0.0637456380  0.089910556  6.509991e-02
## 2016-04-29  0.0025460543  0.0040793342  0.0219751258  0.021044115  3.933460e-03
## 2016-05-31  0.0001355821 -0.0376285480 -0.0008561489  0.004397040  1.686870e-02
## 2016-06-30  0.0191668948  0.0445823791 -0.0244914495  0.008292351  3.469841e-03
## 2016-07-29  0.0054293384  0.0524423965  0.0390002318  0.049348444  3.582171e-02
## 2016-08-31 -0.0021557030  0.0087987423  0.0053268061  0.011260998  1.197078e-03
## 2016-09-30  0.0005155519  0.0248726899  0.0132792447  0.008614733  5.796024e-05
## 2016-10-31 -0.0082048919 -0.0083126000 -0.0224036216 -0.038134756 -1.748909e-02
## 2016-11-30 -0.0259896866 -0.0451615541 -0.0179744997  0.125246265  3.617591e-02
## 2016-12-30  0.0025377956 -0.0025300701  0.0267028663  0.031492019  2.006913e-02
## 2017-01-31  0.0021260874  0.0644312746  0.0323817590 -0.012144235  1.773659e-02
## 2017-02-28  0.0064378146  0.0172581706  0.0118365242  0.013428817  3.853930e-02
## 2017-03-31 -0.0005524628  0.0361890071  0.0318056037 -0.006533221  1.249100e-03
## 2017-04-28  0.0090290975  0.0168659566  0.0239522302  0.005108111  9.877365e-03
## 2017-05-31  0.0068472617  0.0280601914  0.0348102875 -0.022862715  1.401392e-02
## 2017-06-30 -0.0001825845  0.0092236754  0.0029558483  0.029151873  6.354856e-03
## 2017-07-31  0.0033347298  0.0565944551  0.0261879254  0.007481106  2.034571e-02
## 2017-08-31  0.0093693012  0.0232439220 -0.0004482983 -0.027564554  2.913602e-03
## 2017-09-29 -0.0057328166 -0.0004461971  0.0233427221  0.082321936  1.994909e-02
## 2017-10-31  0.0009779872  0.0322782484  0.0166538934  0.005915878  2.329066e-02
## 2017-11-30 -0.0014839301 -0.0038969126  0.0068697764  0.036913503  3.010794e-02
## 2017-12-29  0.0047405756  0.0369254493  0.0133983353 -0.003731344  1.205502e-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(0.25, 0.25, 0.2, 0.2, 0.1)) %>%
    
    # 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 ## 6 Rolling Component Contribution

plot_data <- asset_returns_wide_tbl %>%  

    calculate_component_contribution(w = c(0.25, 0.25, 0.2, 0.2, 0.1)) %>%
    
    # Transform to long form
    pivot_longer(cols = everything(), names_to = "Asset", values_to = "Contribution") %>% 

    # Add weights
    add_column(weight = c(0.25, 0.25, 0.2, 0.2, 0.1)) %>%
    
    # 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)