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

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 -0.0062311778 -0.0029354630  0.0366063983  0.052133418  4.992310e-02
## 2013-02-28  0.0058915923 -0.0231053436 -0.0129694779  0.016175507  1.267840e-02
## 2013-03-28  0.0009847549 -0.0102350107  0.0129694779  0.040258020  3.726786e-02
## 2013-04-30  0.0096387911  0.0120849040  0.0489678045  0.001222381  1.903017e-02
## 2013-05-31 -0.0202136325 -0.0494836088 -0.0306557725  0.041976433  2.333516e-02
## 2013-06-28 -0.0157785484 -0.0547281409 -0.0271445664 -0.001403003 -1.343435e-02
## 2013-07-31  0.0026884075  0.0131592640  0.0518606176  0.063541391  5.038668e-02
## 2013-08-30 -0.0082985000 -0.0257054296 -0.0197464637 -0.034743613 -3.045244e-02
## 2013-09-30  0.0111441585  0.0695887308  0.0753385871  0.063874036  3.115667e-02
## 2013-10-31  0.0082913747  0.0408614200  0.0320814768  0.034233800  4.526645e-02
## 2013-11-29 -0.0025093823 -0.0025941418  0.0054498606  0.041661124  2.920690e-02
## 2013-12-31 -0.0055832953 -0.0040743622  0.0215281319  0.012892056  2.559620e-02
## 2014-01-31  0.0152914662 -0.0903223827 -0.0534132981 -0.035775224 -3.588433e-02
## 2014-02-28  0.0037571357  0.0332205366  0.0595049263  0.045257418  4.451010e-02
## 2014-03-31 -0.0014816571  0.0380216407 -0.0046025666  0.013315272  8.261429e-03
## 2014-04-30  0.0081830915  0.0077727427  0.0165294466 -0.023184200  6.927661e-03
## 2014-05-30  0.0117220573  0.0290911914  0.0158280491  0.006205220  2.294122e-02
## 2014-06-30 -0.0005757154  0.0237336143  0.0091655596  0.037718802  2.043440e-02
## 2014-07-31 -0.0025128264  0.0135559023 -0.0263796333 -0.052009583 -1.352881e-02
## 2014-08-29  0.0114308629  0.0279048943  0.0018007271  0.043657707  3.870509e-02
## 2014-09-30 -0.0061674913 -0.0808570067 -0.0395986396 -0.061260029 -1.389279e-02
## 2014-10-31  0.0105851858  0.0140965659 -0.0026547315  0.068874496  2.327762e-02
## 2014-11-28  0.0065487496 -0.0155412963  0.0006250717  0.004773802  2.710162e-02
## 2014-12-31  0.0014749274 -0.0404422264 -0.0407467308  0.025295892 -2.539875e-03
## 2015-01-30  0.0203147686 -0.0068954969  0.0062265872 -0.054628257 -3.007700e-02
## 2015-02-27 -0.0089881425  0.0431360138  0.0614506124  0.056914874  5.468202e-02
## 2015-03-31  0.0037409929 -0.0150864834 -0.0143889400  0.010156453 -1.583005e-02
## 2015-04-30 -0.0032334867  0.0662814223  0.0358167361 -0.018417599  9.785645e-03
## 2015-05-29 -0.0043836244 -0.0419110200  0.0019527233  0.007509579  1.277421e-02
## 2015-06-30 -0.0108257805 -0.0297468486 -0.0316788228  0.004171458 -2.052136e-02
## 2015-07-31  0.0085850777 -0.0651778992  0.0201144044 -0.027375123  2.233786e-02
## 2015-08-31 -0.0033635070 -0.0925122731 -0.0771524036 -0.047268574 -6.288684e-02
## 2015-09-30  0.0080812418 -0.0318249209 -0.0451949791 -0.038464378 -2.584681e-02
## 2015-10-30  0.0006853211  0.0618082331  0.0640259730  0.063589312  8.163501e-02
## 2015-11-30 -0.0038984014 -0.0255604713 -0.0075557984  0.024415388  3.648306e-03
## 2015-12-31 -0.0019187549 -0.0389470337 -0.0235951109 -0.052157112 -1.743356e-02
## 2016-01-29  0.0123299744 -0.0516368254 -0.0567579081 -0.060306948 -5.106835e-02
## 2016-02-29  0.0088316178 -0.0082113800 -0.0339139958  0.020605483 -8.265146e-04
## 2016-03-31  0.0087087865  0.1218787762  0.0637458709  0.089910262  6.510017e-02
## 2016-04-29  0.0025458871  0.0040794826  0.0219751824  0.021044146  3.933410e-03
## 2016-05-31  0.0001358556 -0.0376286433 -0.0008561299  0.004397100  1.686853e-02
## 2016-06-30  0.0191670016  0.0445823386 -0.0244915362  0.008292486  3.469985e-03
## 2016-07-29  0.0054291370  0.0524422848  0.0390002796  0.049347963  3.582190e-02
## 2016-08-31 -0.0021562545  0.0087985997  0.0053269447  0.011261358  1.196701e-03
## 2016-09-30  0.0005159284  0.0248728717  0.0132789127  0.008614720  5.828014e-05
## 2016-10-31 -0.0082053628 -0.0083123122 -0.0224035856 -0.038134891 -1.748908e-02
## 2016-11-30 -0.0259897704 -0.0451617714 -0.0179744820  0.125246544  3.617604e-02
## 2016-12-30  0.0025381246 -0.0025301382  0.0267027783  0.031491782  2.006896e-02
## 2017-01-31  0.0021264221  0.0644316436  0.0323818793 -0.012143782  1.773656e-02
## 2017-02-28  0.0064378151  0.0172574827  0.0118365508  0.013428484  3.853930e-02
## 2017-03-31 -0.0005522683  0.0361893362  0.0318056345 -0.006532707  1.248925e-03
## 2017-04-28  0.0090288038  0.0168660615  0.0239522905  0.005107417  9.877367e-03
## 2017-05-31  0.0068471308  0.0280602104  0.0348101850 -0.022862697  1.401422e-02
## 2017-06-30 -0.0001822873  0.0092238728  0.0029558548  0.029151949  6.354611e-03
## 2017-07-31  0.0033342493  0.0565943318  0.0261880794  0.007481562  2.034571e-02
## 2017-08-31  0.0093691464  0.0232437740 -0.0004485032 -0.027564590  2.913491e-03
## 2017-09-29 -0.0057318311 -0.0004460965  0.0233428450  0.082321441  1.994900e-02
## 2017-10-31  0.0009775887  0.0322785683  0.0166534617  0.005916043  2.329077e-02
## 2017-11-30 -0.0014838910 -0.0038969517  0.0068701733  0.036913125  3.010798e-02
## 2017-12-29  0.0047402086  0.0369251093  0.0133983369 -0.003730867  1.205551e-02

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

covariance_matrix

##               AGG          EEM          EFA           IJS           SPY
## AGG  7.398403e-05 0.0001042088 4.178258e-05 -7.811671e-05 -9.029471e-06
## EEM  1.042088e-04 0.0017547094 1.039018e-03  6.437712e-04  6.795438e-04
## EFA  4.178258e-05 0.0010390179 1.064239e-03  6.490304e-04  6.975432e-04
## IJS -7.811671e-05 0.0006437712 6.490304e-04  1.565448e-03  8.290255e-04
## SPY -9.029471e-06 0.0006795438 6.975432e-04  8.290255e-04  7.408313e-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,] 0.0003874183 0.009257134 0.005815641 0.005684466 0.002330255

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 -0.0062311778 -0.0029354630  0.0366063983  0.052133418  4.992310e-02
## 2013-02-28  0.0058915923 -0.0231053436 -0.0129694779  0.016175507  1.267840e-02
## 2013-03-28  0.0009847549 -0.0102350107  0.0129694779  0.040258020  3.726786e-02
## 2013-04-30  0.0096387911  0.0120849040  0.0489678045  0.001222381  1.903017e-02
## 2013-05-31 -0.0202136325 -0.0494836088 -0.0306557725  0.041976433  2.333516e-02
## 2013-06-28 -0.0157785484 -0.0547281409 -0.0271445664 -0.001403003 -1.343435e-02
## 2013-07-31  0.0026884075  0.0131592640  0.0518606176  0.063541391  5.038668e-02
## 2013-08-30 -0.0082985000 -0.0257054296 -0.0197464637 -0.034743613 -3.045244e-02
## 2013-09-30  0.0111441585  0.0695887308  0.0753385871  0.063874036  3.115667e-02
## 2013-10-31  0.0082913747  0.0408614200  0.0320814768  0.034233800  4.526645e-02
## 2013-11-29 -0.0025093823 -0.0025941418  0.0054498606  0.041661124  2.920690e-02
## 2013-12-31 -0.0055832953 -0.0040743622  0.0215281319  0.012892056  2.559620e-02
## 2014-01-31  0.0152914662 -0.0903223827 -0.0534132981 -0.035775224 -3.588433e-02
## 2014-02-28  0.0037571357  0.0332205366  0.0595049263  0.045257418  4.451010e-02
## 2014-03-31 -0.0014816571  0.0380216407 -0.0046025666  0.013315272  8.261429e-03
## 2014-04-30  0.0081830915  0.0077727427  0.0165294466 -0.023184200  6.927661e-03
## 2014-05-30  0.0117220573  0.0290911914  0.0158280491  0.006205220  2.294122e-02
## 2014-06-30 -0.0005757154  0.0237336143  0.0091655596  0.037718802  2.043440e-02
## 2014-07-31 -0.0025128264  0.0135559023 -0.0263796333 -0.052009583 -1.352881e-02
## 2014-08-29  0.0114308629  0.0279048943  0.0018007271  0.043657707  3.870509e-02
## 2014-09-30 -0.0061674913 -0.0808570067 -0.0395986396 -0.061260029 -1.389279e-02
## 2014-10-31  0.0105851858  0.0140965659 -0.0026547315  0.068874496  2.327762e-02
## 2014-11-28  0.0065487496 -0.0155412963  0.0006250717  0.004773802  2.710162e-02
## 2014-12-31  0.0014749274 -0.0404422264 -0.0407467308  0.025295892 -2.539875e-03
## 2015-01-30  0.0203147686 -0.0068954969  0.0062265872 -0.054628257 -3.007700e-02
## 2015-02-27 -0.0089881425  0.0431360138  0.0614506124  0.056914874  5.468202e-02
## 2015-03-31  0.0037409929 -0.0150864834 -0.0143889400  0.010156453 -1.583005e-02
## 2015-04-30 -0.0032334867  0.0662814223  0.0358167361 -0.018417599  9.785645e-03
## 2015-05-29 -0.0043836244 -0.0419110200  0.0019527233  0.007509579  1.277421e-02
## 2015-06-30 -0.0108257805 -0.0297468486 -0.0316788228  0.004171458 -2.052136e-02
## 2015-07-31  0.0085850777 -0.0651778992  0.0201144044 -0.027375123  2.233786e-02
## 2015-08-31 -0.0033635070 -0.0925122731 -0.0771524036 -0.047268574 -6.288684e-02
## 2015-09-30  0.0080812418 -0.0318249209 -0.0451949791 -0.038464378 -2.584681e-02
## 2015-10-30  0.0006853211  0.0618082331  0.0640259730  0.063589312  8.163501e-02
## 2015-11-30 -0.0038984014 -0.0255604713 -0.0075557984  0.024415388  3.648306e-03
## 2015-12-31 -0.0019187549 -0.0389470337 -0.0235951109 -0.052157112 -1.743356e-02
## 2016-01-29  0.0123299744 -0.0516368254 -0.0567579081 -0.060306948 -5.106835e-02
## 2016-02-29  0.0088316178 -0.0082113800 -0.0339139958  0.020605483 -8.265146e-04
## 2016-03-31  0.0087087865  0.1218787762  0.0637458709  0.089910262  6.510017e-02
## 2016-04-29  0.0025458871  0.0040794826  0.0219751824  0.021044146  3.933410e-03
## 2016-05-31  0.0001358556 -0.0376286433 -0.0008561299  0.004397100  1.686853e-02
## 2016-06-30  0.0191670016  0.0445823386 -0.0244915362  0.008292486  3.469985e-03
## 2016-07-29  0.0054291370  0.0524422848  0.0390002796  0.049347963  3.582190e-02
## 2016-08-31 -0.0021562545  0.0087985997  0.0053269447  0.011261358  1.196701e-03
## 2016-09-30  0.0005159284  0.0248728717  0.0132789127  0.008614720  5.828014e-05
## 2016-10-31 -0.0082053628 -0.0083123122 -0.0224035856 -0.038134891 -1.748908e-02
## 2016-11-30 -0.0259897704 -0.0451617714 -0.0179744820  0.125246544  3.617604e-02
## 2016-12-30  0.0025381246 -0.0025301382  0.0267027783  0.031491782  2.006896e-02
## 2017-01-31  0.0021264221  0.0644316436  0.0323818793 -0.012143782  1.773656e-02
## 2017-02-28  0.0064378151  0.0172574827  0.0118365508  0.013428484  3.853930e-02
## 2017-03-31 -0.0005522683  0.0361893362  0.0318056345 -0.006532707  1.248925e-03
## 2017-04-28  0.0090288038  0.0168660615  0.0239522905  0.005107417  9.877367e-03
## 2017-05-31  0.0068471308  0.0280602104  0.0348101850 -0.022862697  1.401422e-02
## 2017-06-30 -0.0001822873  0.0092238728  0.0029558548  0.029151949  6.354611e-03
## 2017-07-31  0.0033342493  0.0565943318  0.0261880794  0.007481562  2.034571e-02
## 2017-08-31  0.0093691464  0.0232437740 -0.0004485032 -0.027564590  2.913491e-03
## 2017-09-29 -0.0057318311 -0.0004460965  0.0233428450  0.082321441  1.994900e-02
## 2017-10-31  0.0009775887  0.0322785683  0.0166534617  0.005916043  2.329077e-02
## 2017-11-30 -0.0014838910 -0.0038969517  0.0068701733  0.036913125  3.010798e-02
## 2017-12-29  0.0047402086  0.0369251093  0.0133983369 -0.003730867  1.205551e-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

rowSums(component_contribution)

# Component contribution in percentage
component_percentages <- (component_contribution / sd_portfolio[1,1]) %>%
    round(3) %>%
    as_tibble()

return (component_percentages)
}

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)) %>%
  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)) %>%
  pivot_longer(cols = everything(), names_to = "Asset", values_to = "Contribution") %>%
  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)