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 -0.0062315603 -0.0029355739  0.0366063983  0.052133092  4.992318e-02
## 2013-02-28  0.0058916369 -0.0231052356 -0.0129696618  0.016175140  1.267804e-02
## 2013-03-28  0.0009841449 -0.0102347832  0.0129696618  0.040258712  3.726857e-02
## 2013-04-30  0.0096398939  0.0120845638  0.0489677181  0.001222466  1.902941e-02
## 2013-05-31 -0.0202143788 -0.0494831455 -0.0306555079  0.041976272  2.333550e-02
## 2013-06-28 -0.0157781580 -0.0547284410 -0.0271445615 -0.001403431 -1.343435e-02
## 2013-07-31  0.0026881923  0.0131595742  0.0518603476  0.063541367  5.038611e-02
## 2013-08-30 -0.0082990517 -0.0257052962 -0.0197462881 -0.034743192 -3.045148e-02
## 2013-09-30  0.0111447483  0.0695885868  0.0753384984  0.063873562  3.115611e-02
## 2013-10-31  0.0082915611  0.0408612969  0.0320817157  0.034234198  4.526679e-02
## 2013-11-29 -0.0025101304 -0.0025941415  0.0054494632  0.041661174  2.920692e-02
## 2013-12-31 -0.0055828109 -0.0040743618  0.0215283678  0.012892044  2.559607e-02
## 2014-01-31  0.0152914343 -0.0903226224 -0.0534136210 -0.035775325 -3.588433e-02
## 2014-02-28  0.0037570157  0.0332207224  0.0595053258  0.045257415  4.450989e-02
## 2014-03-31 -0.0014810877  0.0380214635 -0.0046026433  0.013315354  8.261514e-03
## 2014-04-30  0.0081829973  0.0077727436  0.0165292931 -0.023184196  6.927372e-03
## 2014-05-30  0.0117214527  0.0290914195  0.0158284250  0.006205141  2.294118e-02
## 2014-06-30 -0.0005759655  0.0237338312  0.0091654826  0.037718879  2.043469e-02
## 2014-07-31 -0.0025113815  0.0135554647 -0.0263800086 -0.052009441 -1.352873e-02
## 2014-08-29  0.0114305858  0.0279045813  0.0018007274  0.043657809  3.870501e-02
## 2014-09-30 -0.0061678745 -0.0808566996 -0.0395984874 -0.061260624 -1.389256e-02
## 2014-10-31  0.0105847412  0.0140966801 -0.0026550491  0.068875294  2.327770e-02
## 2014-11-28  0.0065489703 -0.0155411819  0.0006253893  0.004773484  2.710167e-02
## 2014-12-31  0.0014750949 -0.0404422216 -0.0407466482  0.025295676 -2.539749e-03
## 2015-01-30  0.0203150070 -0.0068958558  0.0062264224 -0.054628051 -3.007707e-02
## 2015-02-27 -0.0089879245  0.0431361387  0.0614506173  0.056914868  5.468171e-02
## 2015-03-31  0.0037399819 -0.0150860189 -0.0143886278  0.010156312 -1.583045e-02
## 2015-04-30 -0.0032326771  0.0662809635  0.0358163499 -0.018417742  9.786299e-03
## 2015-05-29 -0.0043839127 -0.0419109109  0.0019528745  0.007509724  1.277379e-02
## 2015-06-30 -0.0108251825 -0.0297464970 -0.0316788228  0.004171297 -2.052119e-02
## 2015-07-31  0.0085842148 -0.0651781257  0.0201144044 -0.027375218  2.233806e-02
## 2015-08-31 -0.0033638194 -0.0925123982 -0.0771524861 -0.047268506 -6.288668e-02
## 2015-09-30  0.0080820866 -0.0318250626 -0.0451949829 -0.038464387 -2.584714e-02
## 2015-10-30  0.0006848549  0.0618083747  0.0640261402  0.063589784  8.163496e-02
## 2015-11-30 -0.0038981627 -0.0255604713 -0.0075558793  0.024414797  3.648448e-03
## 2015-12-31 -0.0019187169 -0.0389471047 -0.0235951944 -0.052156920 -1.743357e-02
## 2016-01-29  0.0123300904 -0.0516367544 -0.0567577363 -0.060306785 -5.106875e-02
## 2016-02-29  0.0088314017 -0.0082115308 -0.0339139014  0.020605123 -8.260274e-04
## 2016-03-31  0.0087091270  0.1218792608  0.0637457739  0.089910652  6.510006e-02
## 2016-04-29  0.0025455119  0.0040790824  0.0219750127  0.021043855  3.933393e-03
## 2016-05-31  0.0001358296 -0.0376285078 -0.0008559620  0.004397416  1.686872e-02
## 2016-06-30  0.0191663357  0.0445824016 -0.0244915341  0.008292028  3.469465e-03
## 2016-07-29  0.0054301183  0.0524419648  0.0390001936  0.049348598  3.582232e-02
## 2016-08-31 -0.0021564307  0.0087986634  0.0053266155  0.011260899  1.196655e-03
## 2016-09-30  0.0005163086  0.0248731170  0.0132790795  0.008614669  5.797444e-05
## 2016-10-31 -0.0082053127 -0.0083123112 -0.0224034232 -0.038134721 -1.748905e-02
## 2016-11-30 -0.0259900463 -0.0451618296 -0.0179745666  0.125246556  3.617598e-02
## 2016-12-30  0.0025384174 -0.0025300099  0.0267031098  0.031491488  2.006901e-02
## 2017-01-31  0.0021260744  0.0644313313  0.0323817917 -0.012143598  1.773662e-02
## 2017-02-28  0.0064381902  0.0172579571  0.0118363126  0.013428622  3.853926e-02
## 2017-03-31 -0.0005533896  0.0361888681  0.0318056370 -0.006533081  1.248940e-03
## 2017-04-28  0.0090292543  0.0168666233  0.0239522178  0.005107958  9.877456e-03
## 2017-05-31  0.0068475214  0.0280596536  0.0348101901 -0.022862685  1.401430e-02
## 2017-06-30 -0.0001831195  0.0092237659  0.0029559987  0.029151746  6.354546e-03
## 2017-07-31  0.0033348083  0.0565947515  0.0261880794  0.007481494  2.034572e-02
## 2017-08-31  0.0093691635  0.0232435701 -0.0004484332 -0.027564859  2.913657e-03
## 2017-09-29 -0.0057318345 -0.0004461961  0.0233427068  0.082321848  1.994901e-02
## 2017-10-31  0.0009778384  0.0322784749  0.0166537987  0.005916087  2.329075e-02
## 2017-11-30 -0.0014839749 -0.0038969524  0.0068697044  0.036913176  3.010800e-02
## 2017-12-29  0.0047404530  0.0369253964  0.0133987346 -0.003731136  1.205512e-02

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

covariance_matrix

##               AGG          EEM          EFA           IJS           SPY
## AGG  7.398475e-05 0.0001042135 4.178435e-05 -7.811947e-05 -9.030995e-06
## EEM  1.042135e-04 0.0017547093 1.039017e-03  6.437763e-04  6.795436e-04
## EFA  4.178435e-05 0.0010390175 1.064240e-03  6.490318e-04  6.975416e-04
## IJS -7.811947e-05 0.0006437763 6.490318e-04  1.565452e-03  8.290262e-04
## SPY -9.030995e-06 0.0006795436 6.975416e-04  8.290262e-04  7.408300e-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,] 0.02347494

# 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,] 0.0003874286 0.009257147 0.005815639 0.005684475 0.00233025

rowSums(component_contribution)

## [1] 0.02347494

# 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 -0.0062315603 -0.0029355739  0.0366063983  0.052133092  4.992318e-02
## 2013-02-28  0.0058916369 -0.0231052356 -0.0129696618  0.016175140  1.267804e-02
## 2013-03-28  0.0009841449 -0.0102347832  0.0129696618  0.040258712  3.726857e-02
## 2013-04-30  0.0096398939  0.0120845638  0.0489677181  0.001222466  1.902941e-02
## 2013-05-31 -0.0202143788 -0.0494831455 -0.0306555079  0.041976272  2.333550e-02
## 2013-06-28 -0.0157781580 -0.0547284410 -0.0271445615 -0.001403431 -1.343435e-02
## 2013-07-31  0.0026881923  0.0131595742  0.0518603476  0.063541367  5.038611e-02
## 2013-08-30 -0.0082990517 -0.0257052962 -0.0197462881 -0.034743192 -3.045148e-02
## 2013-09-30  0.0111447483  0.0695885868  0.0753384984  0.063873562  3.115611e-02
## 2013-10-31  0.0082915611  0.0408612969  0.0320817157  0.034234198  4.526679e-02
## 2013-11-29 -0.0025101304 -0.0025941415  0.0054494632  0.041661174  2.920692e-02
## 2013-12-31 -0.0055828109 -0.0040743618  0.0215283678  0.012892044  2.559607e-02
## 2014-01-31  0.0152914343 -0.0903226224 -0.0534136210 -0.035775325 -3.588433e-02
## 2014-02-28  0.0037570157  0.0332207224  0.0595053258  0.045257415  4.450989e-02
## 2014-03-31 -0.0014810877  0.0380214635 -0.0046026433  0.013315354  8.261514e-03
## 2014-04-30  0.0081829973  0.0077727436  0.0165292931 -0.023184196  6.927372e-03
## 2014-05-30  0.0117214527  0.0290914195  0.0158284250  0.006205141  2.294118e-02
## 2014-06-30 -0.0005759655  0.0237338312  0.0091654826  0.037718879  2.043469e-02
## 2014-07-31 -0.0025113815  0.0135554647 -0.0263800086 -0.052009441 -1.352873e-02
## 2014-08-29  0.0114305858  0.0279045813  0.0018007274  0.043657809  3.870501e-02
## 2014-09-30 -0.0061678745 -0.0808566996 -0.0395984874 -0.061260624 -1.389256e-02
## 2014-10-31  0.0105847412  0.0140966801 -0.0026550491  0.068875294  2.327770e-02
## 2014-11-28  0.0065489703 -0.0155411819  0.0006253893  0.004773484  2.710167e-02
## 2014-12-31  0.0014750949 -0.0404422216 -0.0407466482  0.025295676 -2.539749e-03
## 2015-01-30  0.0203150070 -0.0068958558  0.0062264224 -0.054628051 -3.007707e-02
## 2015-02-27 -0.0089879245  0.0431361387  0.0614506173  0.056914868  5.468171e-02
## 2015-03-31  0.0037399819 -0.0150860189 -0.0143886278  0.010156312 -1.583045e-02
## 2015-04-30 -0.0032326771  0.0662809635  0.0358163499 -0.018417742  9.786299e-03
## 2015-05-29 -0.0043839127 -0.0419109109  0.0019528745  0.007509724  1.277379e-02
## 2015-06-30 -0.0108251825 -0.0297464970 -0.0316788228  0.004171297 -2.052119e-02
## 2015-07-31  0.0085842148 -0.0651781257  0.0201144044 -0.027375218  2.233806e-02
## 2015-08-31 -0.0033638194 -0.0925123982 -0.0771524861 -0.047268506 -6.288668e-02
## 2015-09-30  0.0080820866 -0.0318250626 -0.0451949829 -0.038464387 -2.584714e-02
## 2015-10-30  0.0006848549  0.0618083747  0.0640261402  0.063589784  8.163496e-02
## 2015-11-30 -0.0038981627 -0.0255604713 -0.0075558793  0.024414797  3.648448e-03
## 2015-12-31 -0.0019187169 -0.0389471047 -0.0235951944 -0.052156920 -1.743357e-02
## 2016-01-29  0.0123300904 -0.0516367544 -0.0567577363 -0.060306785 -5.106875e-02
## 2016-02-29  0.0088314017 -0.0082115308 -0.0339139014  0.020605123 -8.260274e-04
## 2016-03-31  0.0087091270  0.1218792608  0.0637457739  0.089910652  6.510006e-02
## 2016-04-29  0.0025455119  0.0040790824  0.0219750127  0.021043855  3.933393e-03
## 2016-05-31  0.0001358296 -0.0376285078 -0.0008559620  0.004397416  1.686872e-02
## 2016-06-30  0.0191663357  0.0445824016 -0.0244915341  0.008292028  3.469465e-03
## 2016-07-29  0.0054301183  0.0524419648  0.0390001936  0.049348598  3.582232e-02
## 2016-08-31 -0.0021564307  0.0087986634  0.0053266155  0.011260899  1.196655e-03
## 2016-09-30  0.0005163086  0.0248731170  0.0132790795  0.008614669  5.797444e-05
## 2016-10-31 -0.0082053127 -0.0083123112 -0.0224034232 -0.038134721 -1.748905e-02
## 2016-11-30 -0.0259900463 -0.0451618296 -0.0179745666  0.125246556  3.617598e-02
## 2016-12-30  0.0025384174 -0.0025300099  0.0267031098  0.031491488  2.006901e-02
## 2017-01-31  0.0021260744  0.0644313313  0.0323817917 -0.012143598  1.773662e-02
## 2017-02-28  0.0064381902  0.0172579571  0.0118363126  0.013428622  3.853926e-02
## 2017-03-31 -0.0005533896  0.0361888681  0.0318056370 -0.006533081  1.248940e-03
## 2017-04-28  0.0090292543  0.0168666233  0.0239522178  0.005107958  9.877456e-03
## 2017-05-31  0.0068475214  0.0280596536  0.0348101901 -0.022862685  1.401430e-02
## 2017-06-30 -0.0001831195  0.0092237659  0.0029559987  0.029151746  6.354546e-03
## 2017-07-31  0.0033348083  0.0565947515  0.0261880794  0.007481494  2.034572e-02
## 2017-08-31  0.0093691635  0.0232435701 -0.0004484332 -0.027564859  2.913657e-03
## 2017-09-29 -0.0057318345 -0.0004461961  0.0233427068  0.082321848  1.994901e-02
## 2017-10-31  0.0009778384  0.0322784749  0.0166537987  0.005916087  2.329075e-02
## 2017-11-30 -0.0014839749 -0.0038969524  0.0068697044  0.036913176  3.010800e-02
## 2017-12-29  0.0047404530  0.0369253964  0.0133987346 -0.003731136  1.205512e-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)