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 -0.0062312606 -0.002935486  0.0366060287  0.052132817  4.992308e-02
## 2013-02-28  0.0058915318 -0.023105002 -0.0129691922  0.016175755  1.267794e-02
## 2013-03-28  0.0009843653 -0.010235113  0.0129691922  0.040257696  3.726806e-02
## 2013-04-30  0.0096393343  0.012084777  0.0489678978  0.001222316  1.903036e-02
## 2013-05-31 -0.0202143774 -0.049483463 -0.0306554981  0.041976504  2.333503e-02
## 2013-06-28 -0.0157778893 -0.054728215 -0.0271445255 -0.001402802 -1.343435e-02
## 2013-07-31  0.0026877619  0.013159669  0.0518601219  0.063541488  5.038618e-02
## 2013-08-30 -0.0082982137 -0.025705836 -0.0197461523 -0.034743163 -3.045175e-02
## 2013-09-30  0.0111437645  0.069588968  0.0753385194  0.063873096  3.115662e-02
## 2013-10-31  0.0082921828  0.040861180  0.0320815751  0.034234090  4.526623e-02
## 2013-11-29 -0.0025104504 -0.002594076  0.0054497637  0.041661216  2.920710e-02
## 2013-12-31 -0.0055825383 -0.004074240  0.0215280075  0.012892027  2.559588e-02
## 2014-01-31  0.0152916098 -0.090322665 -0.0534133526 -0.035775520 -3.588485e-02
## 2014-02-28  0.0037568570  0.033220362  0.0595053257  0.045257298  4.451080e-02
## 2014-03-31 -0.0014808518  0.038021947 -0.0046027316  0.013315796  8.261759e-03
## 2014-04-30  0.0081822763  0.007772733  0.0165293425 -0.023184513  6.927276e-03
## 2014-05-30  0.0117216729  0.029091077  0.0158283663  0.006205381  2.294102e-02
## 2014-06-30 -0.0005757126  0.023733945  0.0091654929  0.037718651  2.043473e-02
## 2014-07-31 -0.0025123242  0.013555689 -0.0263798899 -0.052009275 -1.352870e-02
## 2014-08-29  0.0114310695  0.027904608  0.0018005552  0.043657707  3.870464e-02
## 2014-09-30 -0.0061676354 -0.080856897 -0.0395985366 -0.061260360 -1.389239e-02
## 2014-10-31  0.0105853559  0.014096575 -0.0026547698  0.068874813  2.327787e-02
## 2014-11-28  0.0065483191 -0.015541210  0.0006251658  0.004773682  2.710134e-02
## 2014-12-31  0.0014750290 -0.040442057 -0.0407466475  0.025295765 -2.539905e-03
## 2015-01-30  0.0203153204 -0.006895881  0.0062263662 -0.054627793 -3.007705e-02
## 2015-02-27 -0.0089886101  0.043136147  0.0614506727  0.056914449  5.468211e-02
## 2015-03-31  0.0037399307 -0.015086123 -0.0143885516  0.010156502 -1.583053e-02
## 2015-04-30 -0.0032321232  0.066281292  0.0358164176 -0.018417523  9.786001e-03
## 2015-05-29 -0.0043839964 -0.041910922  0.0019525558  0.007509826  1.277413e-02
## 2015-06-30 -0.0108251405 -0.029746702 -0.0316786040  0.004171139 -2.052125e-02
## 2015-07-31  0.0085838110 -0.065178078  0.0201144923 -0.027375419  2.233809e-02
## 2015-08-31 -0.0033631564 -0.092512532 -0.0771526622 -0.047268276 -6.288675e-02
## 2015-09-30  0.0080816088 -0.031824888 -0.0451947606 -0.038464412 -2.584703e-02
## 2015-10-30  0.0006852472  0.061808142  0.0640258227  0.063589561  8.163484e-02
## 2015-11-30 -0.0038980795 -0.025560058 -0.0075558963  0.024414982  3.648621e-03
## 2015-12-31 -0.0019187584 -0.038947274 -0.0235949679 -0.052157019 -1.743352e-02
## 2016-01-29  0.0123297356 -0.051636620 -0.0567578828 -0.060306535 -5.106844e-02
## 2016-02-29  0.0088319078 -0.008211691 -0.0339136456  0.020605156 -8.264550e-04
## 2016-03-31  0.0087081563  0.121879165  0.0637455679  0.089910076  6.509956e-02
## 2016-04-29  0.0025462211  0.004079036  0.0219750163  0.021044203  3.933884e-03
## 2016-05-31  0.0001360336 -0.037628322 -0.0008561716  0.004397318  1.686868e-02
## 2016-06-30  0.0191666282  0.044582079 -0.0244914407  0.008292392  3.469825e-03
## 2016-07-29  0.0054298918  0.052442366  0.0390002419  0.049348406  3.582173e-02
## 2016-08-31 -0.0021571298  0.008798534  0.0053269298  0.011260876  1.197008e-03
## 2016-09-30  0.0005165109  0.024872917  0.0132789949  0.008614633  5.810952e-05
## 2016-10-31 -0.0082052694 -0.008312139 -0.0224035823 -0.038134799 -1.748938e-02
## 2016-11-30 -0.0259895177 -0.045162143 -0.0179744003  0.125246356  3.617608e-02
## 2016-12-30  0.0025381141 -0.002529786  0.0267027305  0.031491749  2.006908e-02
## 2017-01-31  0.0021259590  0.064431479  0.0323820788 -0.012144064  1.773648e-02
## 2017-02-28  0.0064378127  0.017257775  0.0118364304  0.013428739  3.853923e-02
## 2017-03-31 -0.0005531133  0.036188800  0.0318058258 -0.006532617  1.249445e-03
## 2017-04-28  0.0090293551  0.016866527  0.0239521701  0.005108050  9.877170e-03
## 2017-05-31  0.0068481995  0.028060014  0.0348102132 -0.022862890  1.401439e-02
## 2017-06-30 -0.0001836687  0.009223882  0.0029557035  0.029151647  6.354442e-03
## 2017-07-31  0.0033343616  0.056594313  0.0261878819  0.007481170  2.034570e-02
## 2017-08-31  0.0093696189  0.023243921 -0.0004482871 -0.027564338  2.913594e-03
## 2017-09-29 -0.0057322731 -0.000446055  0.0233428128  0.082321706  1.994900e-02
## 2017-10-31  0.0009780167  0.032278293  0.0166538599  0.005915824  2.329086e-02
## 2017-11-30 -0.0014842837 -0.003897118  0.0068698920  0.036913551  3.010797e-02
## 2017-12-29  0.0047411006  0.036925615  0.0133981388 -0.003731056  1.205493e-02

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

covariance_matrix

##               AGG          EEM          EFA           IJS           SPY
## AGG  7.398398e-05 0.0001042106 4.178069e-05 -7.812158e-05 -9.033210e-06
## EEM  1.042106e-04 0.0017547112 1.039017e-03  6.437719e-04  6.795438e-04
## EFA  4.178069e-05 0.0010390173 1.064236e-03  6.490270e-04  6.975422e-04
## IJS -7.812158e-05 0.0006437719 6.490270e-04  1.565443e-03  8.290227e-04
## SPY -9.033210e-06 0.0006795438 6.975422e-04  8.290227e-04  7.408293e-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,] 0.02347489

# 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,] 0.0003874048 0.009257155 0.005815631 0.005684448 0.00233025

rowSums(component_contribution)

## [1] 0.02347489

# 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 -0.0062312606 -0.002935486  0.0366060287  0.052132817  4.992308e-02
## 2013-02-28  0.0058915318 -0.023105002 -0.0129691922  0.016175755  1.267794e-02
## 2013-03-28  0.0009843653 -0.010235113  0.0129691922  0.040257696  3.726806e-02
## 2013-04-30  0.0096393343  0.012084777  0.0489678978  0.001222316  1.903036e-02
## 2013-05-31 -0.0202143774 -0.049483463 -0.0306554981  0.041976504  2.333503e-02
## 2013-06-28 -0.0157778893 -0.054728215 -0.0271445255 -0.001402802 -1.343435e-02
## 2013-07-31  0.0026877619  0.013159669  0.0518601219  0.063541488  5.038618e-02
## 2013-08-30 -0.0082982137 -0.025705836 -0.0197461523 -0.034743163 -3.045175e-02
## 2013-09-30  0.0111437645  0.069588968  0.0753385194  0.063873096  3.115662e-02
## 2013-10-31  0.0082921828  0.040861180  0.0320815751  0.034234090  4.526623e-02
## 2013-11-29 -0.0025104504 -0.002594076  0.0054497637  0.041661216  2.920710e-02
## 2013-12-31 -0.0055825383 -0.004074240  0.0215280075  0.012892027  2.559588e-02
## 2014-01-31  0.0152916098 -0.090322665 -0.0534133526 -0.035775520 -3.588485e-02
## 2014-02-28  0.0037568570  0.033220362  0.0595053257  0.045257298  4.451080e-02
## 2014-03-31 -0.0014808518  0.038021947 -0.0046027316  0.013315796  8.261759e-03
## 2014-04-30  0.0081822763  0.007772733  0.0165293425 -0.023184513  6.927276e-03
## 2014-05-30  0.0117216729  0.029091077  0.0158283663  0.006205381  2.294102e-02
## 2014-06-30 -0.0005757126  0.023733945  0.0091654929  0.037718651  2.043473e-02
## 2014-07-31 -0.0025123242  0.013555689 -0.0263798899 -0.052009275 -1.352870e-02
## 2014-08-29  0.0114310695  0.027904608  0.0018005552  0.043657707  3.870464e-02
## 2014-09-30 -0.0061676354 -0.080856897 -0.0395985366 -0.061260360 -1.389239e-02
## 2014-10-31  0.0105853559  0.014096575 -0.0026547698  0.068874813  2.327787e-02
## 2014-11-28  0.0065483191 -0.015541210  0.0006251658  0.004773682  2.710134e-02
## 2014-12-31  0.0014750290 -0.040442057 -0.0407466475  0.025295765 -2.539905e-03
## 2015-01-30  0.0203153204 -0.006895881  0.0062263662 -0.054627793 -3.007705e-02
## 2015-02-27 -0.0089886101  0.043136147  0.0614506727  0.056914449  5.468211e-02
## 2015-03-31  0.0037399307 -0.015086123 -0.0143885516  0.010156502 -1.583053e-02
## 2015-04-30 -0.0032321232  0.066281292  0.0358164176 -0.018417523  9.786001e-03
## 2015-05-29 -0.0043839964 -0.041910922  0.0019525558  0.007509826  1.277413e-02
## 2015-06-30 -0.0108251405 -0.029746702 -0.0316786040  0.004171139 -2.052125e-02
## 2015-07-31  0.0085838110 -0.065178078  0.0201144923 -0.027375419  2.233809e-02
## 2015-08-31 -0.0033631564 -0.092512532 -0.0771526622 -0.047268276 -6.288675e-02
## 2015-09-30  0.0080816088 -0.031824888 -0.0451947606 -0.038464412 -2.584703e-02
## 2015-10-30  0.0006852472  0.061808142  0.0640258227  0.063589561  8.163484e-02
## 2015-11-30 -0.0038980795 -0.025560058 -0.0075558963  0.024414982  3.648621e-03
## 2015-12-31 -0.0019187584 -0.038947274 -0.0235949679 -0.052157019 -1.743352e-02
## 2016-01-29  0.0123297356 -0.051636620 -0.0567578828 -0.060306535 -5.106844e-02
## 2016-02-29  0.0088319078 -0.008211691 -0.0339136456  0.020605156 -8.264550e-04
## 2016-03-31  0.0087081563  0.121879165  0.0637455679  0.089910076  6.509956e-02
## 2016-04-29  0.0025462211  0.004079036  0.0219750163  0.021044203  3.933884e-03
## 2016-05-31  0.0001360336 -0.037628322 -0.0008561716  0.004397318  1.686868e-02
## 2016-06-30  0.0191666282  0.044582079 -0.0244914407  0.008292392  3.469825e-03
## 2016-07-29  0.0054298918  0.052442366  0.0390002419  0.049348406  3.582173e-02
## 2016-08-31 -0.0021571298  0.008798534  0.0053269298  0.011260876  1.197008e-03
## 2016-09-30  0.0005165109  0.024872917  0.0132789949  0.008614633  5.810952e-05
## 2016-10-31 -0.0082052694 -0.008312139 -0.0224035823 -0.038134799 -1.748938e-02
## 2016-11-30 -0.0259895177 -0.045162143 -0.0179744003  0.125246356  3.617608e-02
## 2016-12-30  0.0025381141 -0.002529786  0.0267027305  0.031491749  2.006908e-02
## 2017-01-31  0.0021259590  0.064431479  0.0323820788 -0.012144064  1.773648e-02
## 2017-02-28  0.0064378127  0.017257775  0.0118364304  0.013428739  3.853923e-02
## 2017-03-31 -0.0005531133  0.036188800  0.0318058258 -0.006532617  1.249445e-03
## 2017-04-28  0.0090293551  0.016866527  0.0239521701  0.005108050  9.877170e-03
## 2017-05-31  0.0068481995  0.028060014  0.0348102132 -0.022862890  1.401439e-02
## 2017-06-30 -0.0001836687  0.009223882  0.0029557035  0.029151647  6.354442e-03
## 2017-07-31  0.0033343616  0.056594313  0.0261878819  0.007481170  2.034570e-02
## 2017-08-31  0.0093696189  0.023243921 -0.0004482871 -0.027564338  2.913594e-03
## 2017-09-29 -0.0057322731 -0.000446055  0.0233428128  0.082321706  1.994900e-02
## 2017-10-31  0.0009780167  0.032278293  0.0166538599  0.005915824  2.329086e-02
## 2017-11-30 -0.0014842837 -0.003897118  0.0068698920  0.036913551  3.010797e-02
## 2017-12-29  0.0047411006  0.036925615  0.0133981388 -0.003731056  1.205493e-02

calculate_component_contribution <- function(.data, w) {
    
        # Covariance of asset returns
    covariance_matrix <- cov(asset_returns_wide_tbl)
    
    covariance_matrix
    
    # 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()
    
    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 Volatility")

6 Rolling Component Contribution

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