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
6 Rolling 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

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# 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 -0.0062307258 -0.0029353524  0.0366061192  0.052132873  0.0499233630
## 2013-02-28  0.0058914510 -0.0231054542 -0.0129693872  0.016175352  0.0126776058
## 2013-03-28  0.0009848857 -0.0102348964  0.0129693872  0.040258202  0.0372682190
## 2013-04-30  0.0096391540  0.0120847897  0.0489677225  0.001222567  0.0190304746
## 2013-05-31 -0.0202140063 -0.0494832528 -0.0306555997  0.041976381  0.0233350304
## 2013-06-28 -0.0157781535 -0.0547283716 -0.0271442001 -0.001403140 -0.0134342277
## 2013-07-31  0.0026874330  0.0131595099  0.0518601644  0.063541452  0.0503855427
## 2013-08-30 -0.0082979084 -0.0257057373 -0.0197462881 -0.034743279 -0.0304506932
## 2013-09-30  0.0111437955  0.0695889042  0.0753385807  0.063873645  0.0311556529
## 2013-10-31  0.0082922198  0.0408612969  0.0320816335  0.034233936  0.0452664705
## 2013-11-29 -0.0025097534 -0.0025940275  0.0054493840  0.041661260  0.0292070353
## 2013-12-31 -0.0055832793 -0.0040744757  0.0215284470  0.012892287  0.0255958743
## 2014-01-31  0.0152914300 -0.0903224971 -0.0534132939 -0.035775568 -0.0358842365
## 2014-02-28  0.0037572002  0.0332205972  0.0595048446  0.045257495  0.0445105949
## 2014-03-31 -0.0014819229  0.0380216967 -0.0046025666  0.013315353  0.0082609211
## 2014-04-30  0.0081832767  0.0077727418  0.0165295989 -0.023184276  0.0069275683
## 2014-05-30  0.0117217269  0.0290913005  0.0158282715  0.006205302  0.0229409933
## 2014-06-30 -0.0005755099  0.0237337188  0.0091654077  0.037718719  0.0204348790
## 2014-07-31 -0.0025125672  0.0135553564 -0.0263799323 -0.052009441 -0.0135288294
## 2014-08-29  0.0114306823  0.0279047949  0.0018004228  0.043657965  0.0387049257
## 2014-09-30 -0.0061670597 -0.0808568050 -0.0395982591 -0.061260614 -0.0138922824
## 2014-10-31  0.0105842879  0.0140966801 -0.0026547315  0.068874740  0.0232777867
## 2014-11-28  0.0065484350 -0.0155414106  0.0006249924  0.004773717  0.0271010460
## 2014-12-31  0.0014755417 -0.0404418739 -0.0407464862  0.025295906 -0.0025393099
## 2015-01-30  0.0203149232 -0.0068958549  0.0062263398 -0.054628046 -0.0300775258
## 2015-02-27 -0.0089879269  0.0431360188  0.0614506173  0.056914489  0.0546820799
## 2015-03-31  0.0037403343 -0.0150862520 -0.0143887845  0.010156612 -0.0158300164
## 2015-04-30 -0.0032332056  0.0662813058  0.0358164310 -0.018417742  0.0097856043
## 2015-05-29 -0.0043831180 -0.0419110200  0.0019530255  0.007509874  0.0127745632
## 2015-06-30 -0.0108260735 -0.0297464970 -0.0316790540  0.004171446 -0.0205213526
## 2015-07-31  0.0085849291 -0.0651783759  0.0201144838 -0.027375209  0.0223376295
## 2015-08-31 -0.0033638188 -0.0925120794 -0.0771524922 -0.047268733 -0.0628865129
## 2015-09-30  0.0080817320 -0.0318249895 -0.0451948142 -0.038464719 -0.0258473239
## 2015-10-30  0.0006849433  0.0618082331  0.0640261348  0.063589642  0.0816349709
## 2015-11-30 -0.0038975430 -0.0255604713 -0.0075560418  0.024415497  0.0036485340
## 2015-12-31 -0.0019196921 -0.0389471047 -0.0235951129 -0.052157146 -0.0174335669
## 2016-01-29  0.0123299205 -0.0516365300 -0.0567578247 -0.060306952 -0.0510687528
## 2016-02-29  0.0088321022 -0.0082117552 -0.0339139044  0.020605376 -0.0008260275
## 2016-03-31  0.0087090401  0.1218791941  0.0637457796  0.089910483  0.0651000610
## 2016-04-29  0.0025461133  0.0040791492  0.0219750985  0.021044156  0.0039336501
## 2016-05-31  0.0001351423 -0.0376285768 -0.0008560460  0.004397340  0.0168682928
## 2016-06-30  0.0191671801  0.0445823386 -0.0244913641  0.008292175  0.0034697168
## 2016-07-29  0.0054292759  0.0524423474  0.0390000248  0.049348085  0.0358222349
## 2016-08-31 -0.0021561789  0.0087984749  0.0053268628  0.011260971  0.0011966550
## 2016-09-30  0.0005156369  0.0248728126  0.0132791585  0.008614738  0.0000578937
## 2016-10-31 -0.0082051475 -0.0083121911 -0.0224039160 -0.038134721 -0.0174889707
## 2016-11-30 -0.0259891864 -0.0451618353 -0.0179742328  0.125246239  0.0361759841
## 2016-12-30  0.0025381561 -0.0025298821  0.0267029429  0.031491560  0.0200690924
## 2017-01-31  0.0021259009  0.0644312712  0.0323817146 -0.012143476  0.0177366154
## 2017-02-28  0.0064375882  0.0172580171  0.0118364721  0.013428623  0.0385394840
## 2017-03-31 -0.0005528741  0.0361889820  0.0318057133 -0.006532958  0.0012489397
## 2017-04-28  0.0090292543  0.0168663974  0.0239523650  0.005107897  0.0098772357
## 2017-05-31  0.0068478598  0.0280597656  0.0348101105 -0.022862812  0.0140143003
## 2017-06-30 -0.0001830348  0.0092239816  0.0029559982  0.029151752  0.0063546176
## 2017-07-31  0.0033343852  0.0565945357  0.0261879359  0.007481617  0.0203459279
## 2017-08-31  0.0093690799  0.0232435701 -0.0004485731 -0.027564673  0.0029133778
## 2017-09-29 -0.0057320030 -0.0004460965  0.0233429150  0.082321723  0.0199488714
## 2017-10-31  0.0009780905  0.0322783753  0.0166537304  0.005916202  0.0232909521
## 2017-11-30 -0.0014843112 -0.0038968556  0.0068700380  0.036913172  0.0301078707
## 2017-12-29  0.0047404545  0.0369252062  0.0133982693 -0.003731246  0.0120551244

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

covariance_matrix

##               AGG          EEM          EFA           IJS           SPY
## AGG  7.398343e-05 0.0001042083 0.0000417817 -7.811791e-05 -9.031111e-06
## EEM  1.042083e-04 0.0017547095 0.0010390153  6.437762e-04  6.795418e-04
## EFA  4.178170e-05 0.0010390153 0.0010642366  6.490313e-04  6.975402e-04
## IJS -7.811791e-05 0.0006437762 0.0006490313  1.565449e-03  8.290250e-04
## SPY -9.031111e-06 0.0006795418 0.0006975402  8.290250e-04  7.408280e-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,] 0.0003874091 0.009257139 0.00581563 0.00568448 0.002330248

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 -0.0062307258 -0.0029353524  0.0366061192  0.052132873  0.0499233630
## 2013-02-28  0.0058914510 -0.0231054542 -0.0129693872  0.016175352  0.0126776058
## 2013-03-28  0.0009848857 -0.0102348964  0.0129693872  0.040258202  0.0372682190
## 2013-04-30  0.0096391540  0.0120847897  0.0489677225  0.001222567  0.0190304746
## 2013-05-31 -0.0202140063 -0.0494832528 -0.0306555997  0.041976381  0.0233350304
## 2013-06-28 -0.0157781535 -0.0547283716 -0.0271442001 -0.001403140 -0.0134342277
## 2013-07-31  0.0026874330  0.0131595099  0.0518601644  0.063541452  0.0503855427
## 2013-08-30 -0.0082979084 -0.0257057373 -0.0197462881 -0.034743279 -0.0304506932
## 2013-09-30  0.0111437955  0.0695889042  0.0753385807  0.063873645  0.0311556529
## 2013-10-31  0.0082922198  0.0408612969  0.0320816335  0.034233936  0.0452664705
## 2013-11-29 -0.0025097534 -0.0025940275  0.0054493840  0.041661260  0.0292070353
## 2013-12-31 -0.0055832793 -0.0040744757  0.0215284470  0.012892287  0.0255958743
## 2014-01-31  0.0152914300 -0.0903224971 -0.0534132939 -0.035775568 -0.0358842365
## 2014-02-28  0.0037572002  0.0332205972  0.0595048446  0.045257495  0.0445105949
## 2014-03-31 -0.0014819229  0.0380216967 -0.0046025666  0.013315353  0.0082609211
## 2014-04-30  0.0081832767  0.0077727418  0.0165295989 -0.023184276  0.0069275683
## 2014-05-30  0.0117217269  0.0290913005  0.0158282715  0.006205302  0.0229409933
## 2014-06-30 -0.0005755099  0.0237337188  0.0091654077  0.037718719  0.0204348790
## 2014-07-31 -0.0025125672  0.0135553564 -0.0263799323 -0.052009441 -0.0135288294
## 2014-08-29  0.0114306823  0.0279047949  0.0018004228  0.043657965  0.0387049257
## 2014-09-30 -0.0061670597 -0.0808568050 -0.0395982591 -0.061260614 -0.0138922824
## 2014-10-31  0.0105842879  0.0140966801 -0.0026547315  0.068874740  0.0232777867
## 2014-11-28  0.0065484350 -0.0155414106  0.0006249924  0.004773717  0.0271010460
## 2014-12-31  0.0014755417 -0.0404418739 -0.0407464862  0.025295906 -0.0025393099
## 2015-01-30  0.0203149232 -0.0068958549  0.0062263398 -0.054628046 -0.0300775258
## 2015-02-27 -0.0089879269  0.0431360188  0.0614506173  0.056914489  0.0546820799
## 2015-03-31  0.0037403343 -0.0150862520 -0.0143887845  0.010156612 -0.0158300164
## 2015-04-30 -0.0032332056  0.0662813058  0.0358164310 -0.018417742  0.0097856043
## 2015-05-29 -0.0043831180 -0.0419110200  0.0019530255  0.007509874  0.0127745632
## 2015-06-30 -0.0108260735 -0.0297464970 -0.0316790540  0.004171446 -0.0205213526
## 2015-07-31  0.0085849291 -0.0651783759  0.0201144838 -0.027375209  0.0223376295
## 2015-08-31 -0.0033638188 -0.0925120794 -0.0771524922 -0.047268733 -0.0628865129
## 2015-09-30  0.0080817320 -0.0318249895 -0.0451948142 -0.038464719 -0.0258473239
## 2015-10-30  0.0006849433  0.0618082331  0.0640261348  0.063589642  0.0816349709
## 2015-11-30 -0.0038975430 -0.0255604713 -0.0075560418  0.024415497  0.0036485340
## 2015-12-31 -0.0019196921 -0.0389471047 -0.0235951129 -0.052157146 -0.0174335669
## 2016-01-29  0.0123299205 -0.0516365300 -0.0567578247 -0.060306952 -0.0510687528
## 2016-02-29  0.0088321022 -0.0082117552 -0.0339139044  0.020605376 -0.0008260275
## 2016-03-31  0.0087090401  0.1218791941  0.0637457796  0.089910483  0.0651000610
## 2016-04-29  0.0025461133  0.0040791492  0.0219750985  0.021044156  0.0039336501
## 2016-05-31  0.0001351423 -0.0376285768 -0.0008560460  0.004397340  0.0168682928
## 2016-06-30  0.0191671801  0.0445823386 -0.0244913641  0.008292175  0.0034697168
## 2016-07-29  0.0054292759  0.0524423474  0.0390000248  0.049348085  0.0358222349
## 2016-08-31 -0.0021561789  0.0087984749  0.0053268628  0.011260971  0.0011966550
## 2016-09-30  0.0005156369  0.0248728126  0.0132791585  0.008614738  0.0000578937
## 2016-10-31 -0.0082051475 -0.0083121911 -0.0224039160 -0.038134721 -0.0174889707
## 2016-11-30 -0.0259891864 -0.0451618353 -0.0179742328  0.125246239  0.0361759841
## 2016-12-30  0.0025381561 -0.0025298821  0.0267029429  0.031491560  0.0200690924
## 2017-01-31  0.0021259009  0.0644312712  0.0323817146 -0.012143476  0.0177366154
## 2017-02-28  0.0064375882  0.0172580171  0.0118364721  0.013428623  0.0385394840
## 2017-03-31 -0.0005528741  0.0361889820  0.0318057133 -0.006532958  0.0012489397
## 2017-04-28  0.0090292543  0.0168663974  0.0239523650  0.005107897  0.0098772357
## 2017-05-31  0.0068478598  0.0280597656  0.0348101105 -0.022862812  0.0140143003
## 2017-06-30 -0.0001830348  0.0092239816  0.0029559982  0.029151752  0.0063546176
## 2017-07-31  0.0033343852  0.0565945357  0.0261879359  0.007481617  0.0203459279
## 2017-08-31  0.0093690799  0.0232435701 -0.0004485731 -0.027564673  0.0029133778
## 2017-09-29 -0.0057320030 -0.0004460965  0.0233429150  0.082321723  0.0199488714
## 2017-10-31  0.0009780905  0.0322783753  0.0166537304  0.005916202  0.0232909521
## 2017-11-30 -0.0014843112 -0.0038968556  0.0068700380  0.036913172  0.0301078707
## 2017-12-29  0.0047404545  0.0369252062  0.0133982693 -0.003731246  0.0120551244

calulate_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 %>% calulate_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 %>%
    
    calulate_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")

6 Rolling Component Contribution

Column Chart of Component Contribution and Weight

plot_data <- asset_returns_wide_tbl %>%
    
    calulate_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)) +
    theme_tq()+
    
    labs(title = "Percent Contribution to Portfolio Volatility and Weight", 
         y = "Percent", 
         x = NULL)