# Load packages

# Core
library(tidyverse)
library(tidyquant)

Goal

Examine how each asset contributes to portfolio standard deviation. This is to ensure that our risk is not concentrated in any one asset.

1 Import stock prices

Choose your stocks from 2012-12-31 to present.

symbols <- c("TSLA", "DELL")

prices <- tq_get(x    = symbols,
                 get  = "stock.prices",
                 from = "2012-12-31",
                 to   = "2024-06-26")

2 Convert prices to returns (monthly)

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 Calculate Component Contribution to Portfolio Volatility

# 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
##                    DELL         TSLA
## 2016-09-30  0.067499656 -0.038366372
## 2016-10-31  0.026629724 -0.031364583
## 2016-11-30  0.087147009 -0.043041267
## 2016-12-30  0.025985210  0.120665178
## 2017-01-31  0.136188453  0.164624916
## 2017-02-28  0.007906191 -0.007730364
## 2017-03-31  0.009249951  0.107278727
## 2017-04-28  0.046200802  0.120916212
## 2017-05-31  0.033409647  0.082295892
## 2017-06-30 -0.127067307  0.058654468
## 2017-07-31  0.050417538 -0.111459860
## 2017-08-31  0.153461438  0.095543446
## 2017-09-29  0.029974495 -0.042474144
## 2017-10-31  0.069536859 -0.028457409
## 2017-11-30 -0.056284749 -0.070862541
## 2017-12-29  0.038118899  0.008061928
## 2018-01-31 -0.125409152  0.129254571
## 2018-02-28  0.035485625 -0.032266877
## 2018-03-29 -0.014644378 -0.253920408
## 2018-04-30 -0.019865462  0.099254576
## 2018-05-31  0.116776314 -0.031698139
## 2018-06-29  0.047454925  0.186043257
## 2018-07-31  0.089727080 -0.140021491
## 2018-08-31  0.038692604  0.011737389
## 2018-09-28  0.009829723 -0.130439038
## 2018-10-31 -0.071813611  0.242170576
## 2018-11-30  0.154387872  0.038271580
## 2018-12-31 -0.178243370 -0.051761952
## 2019-01-31 -0.005745827 -0.080628789
## 2019-02-28  0.138714467  0.041032981
## 2019-03-29  0.050137129 -0.133656413
## 2019-04-30  0.138523997 -0.159123803
## 2019-05-31 -0.123977157 -0.253945372
## 2019-06-28 -0.158919824  0.188012109
## 2019-07-31  0.128053836  0.078092373
## 2019-08-30 -0.113786220 -0.068516948
## 2019-09-30  0.006383733  0.065449565
## 2019-10-31  0.019666532  0.268061253
## 2019-11-29 -0.086856508  0.046592176
## 2019-12-31  0.058085901  0.237359743
## 2020-01-31 -0.052328424  0.441578342
## 2020-02-28 -0.186801501  0.026424253
## 2020-03-31 -0.022748102 -0.242781458
## 2020-04-30  0.076398933  0.400209535
## 2020-05-29  0.150832401  0.065730500
## 2020-06-30  0.101444729  0.257108657
## 2020-07-31  0.085265447  0.281420674
## 2020-08-31  0.099359089  0.554719320
## 2020-09-30  0.024072238 -0.149762306
## 2020-10-30 -0.116270016 -0.100371771
## 2020-11-30  0.135872540  0.380308519
## 2020-12-31  0.059883132  0.217730753
## 2021-01-29 -0.005472777  0.117343701
## 2021-02-26  0.106361505 -0.161038203
## 2021-03-31  0.083727052 -0.011269836
## 2021-04-30  0.109289127  0.060292565
## 2021-05-28  0.003147813 -0.126372343
## 2021-06-30  0.010387924  0.083547955
## 2021-07-30 -0.031078932  0.010973846
## 2021-08-31  0.008656156  0.068224268
## 2021-09-30  0.065333373  0.052632612
## 2021-10-29  0.055614047  0.362230202
## 2021-11-30  0.012875294  0.027237848
## 2021-12-31 -0.005326674 -0.079968440
## 2022-01-31  0.011329602 -0.120597475
## 2022-02-28 -0.108671411 -0.073397011
## 2022-03-31 -0.015225199  0.213504290
## 2022-04-29 -0.058475098 -0.213125289
## 2022-05-31  0.060461950 -0.138340062
## 2022-06-30 -0.077626063 -0.118657126
## 2022-07-29 -0.017479137  0.280480149
## 2022-08-31 -0.162806216 -0.075250271
## 2022-09-30 -0.113840926 -0.038313992
## 2022-10-31  0.126329306 -0.153346760
## 2022-11-30  0.153927563 -0.155866121
## 2022-12-30 -0.107620629 -0.457813194
## 2023-01-31  0.017969579  0.340915767
## 2023-02-28  0.000492308  0.171904973
## 2023-03-31 -0.010637087  0.008471140
## 2023-04-28  0.087035129 -0.233183710
## 2023-05-31  0.029900224  0.216021889
## 2023-06-30  0.188587655  0.249689452
## 2023-07-31 -0.015305626  0.021391609
## 2023-08-31  0.060847087 -0.035588260
## 2023-09-29  0.203027792 -0.030929027
## 2023-10-31 -0.023678037 -0.219831983
## 2023-11-30  0.125672859  0.178463656
## 2023-12-29  0.008269328  0.034390133
## 2024-01-31  0.084560546 -0.282704160
## 2024-02-29  0.132897861  0.075015304
## 2024-03-28  0.186871339 -0.138383423
## 2024-04-30  0.092148135  0.041724969
## 2024-05-31  0.113065022 -0.028782134
## 2024-06-25  0.005644747  0.050745660
## 2013-01-31           NA  0.102078114
## 2013-02-28           NA -0.074128640
## 2013-03-28           NA  0.084208138
## 2013-04-30           NA  0.354111531
## 2013-05-31           NA  0.593716684
## 2013-06-28           NA  0.093672163
## 2013-07-31           NA  0.223739522
## 2013-08-30           NA  0.229971642
## 2013-09-30           NA  0.134706620
## 2013-10-31           NA -0.189806595
## 2013-11-29           NA -0.228409405
## 2013-12-31           NA  0.167108541
## 2014-01-31           NA  0.187261714
## 2014-02-28           NA  0.299722785
## 2014-03-31           NA -0.160783242
## 2014-04-30           NA -0.002690122
## 2014-05-30           NA -0.000577422
## 2014-06-30           NA  0.144457224
## 2014-07-31           NA -0.072372676
## 2014-08-29           NA  0.188794007
## 2014-09-30           NA -0.105566477
## 2014-10-31           NA -0.004046477
## 2014-11-28           NA  0.011599801
## 2014-12-31           NA -0.094774519
## 2015-01-30           NA -0.088365289
## 2015-02-27           NA -0.001277808
## 2015-03-31           NA -0.074350051
## 2015-04-30           NA  0.180226808
## 2015-05-29           NA  0.103899574
## 2015-06-30           NA  0.067300935
## 2015-07-31           NA -0.007896616
## 2015-08-31           NA -0.066366250
## 2015-09-30           NA -0.002653519
## 2015-10-30           NA -0.182659777
## 2015-11-30           NA  0.106828586
## 2015-12-31           NA  0.041471519
## 2016-01-29           NA -0.227360626
## 2016-02-29           NA  0.003810669
## 2016-03-31           NA  0.179948109
## 2016-04-29           NA  0.046721797
## 2016-05-31           NA -0.075597968
## 2016-06-30           NA -0.050296440
## 2016-07-29           NA  0.100785334
## 2016-08-31           NA -0.102058091
# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)

covariance_matrix
##      DELL       TSLA
## DELL   NA         NA
## TSLA   NA 0.02919988
# 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(.5, .5)

sd_portfolio <- sqrt(t(w) %*% covariance_matrix %*% w)
sd_portfolio
##      [,1]
## [1,]   NA
# 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
##      DELL TSLA
## [1,]   NA   NA
rowSums(component_contribution)
## [1] NA
# Component contribution in percentage
component_percentages <- (component_contribution / sd_portfolio[1,1]) %>%
    round(3) %>%
    as_tibble()

component_percentages
## # A tibble: 1 × 2
##    DELL  TSLA
##   <dbl> <dbl>
## 1    NA    NA
component_percentages %>%

    as_tibble() %>%
    gather(key = "asset", value = "contribution")
## # A tibble: 2 × 2
##   asset contribution
##   <chr>        <dbl>
## 1 DELL            NA
## 2 TSLA            NA
# 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
##                    DELL         TSLA
## 2016-09-30  0.067499656 -0.038366372
## 2016-10-31  0.026629724 -0.031364583
## 2016-11-30  0.087147009 -0.043041267
## 2016-12-30  0.025985210  0.120665178
## 2017-01-31  0.136188453  0.164624916
## 2017-02-28  0.007906191 -0.007730364
## 2017-03-31  0.009249951  0.107278727
## 2017-04-28  0.046200802  0.120916212
## 2017-05-31  0.033409647  0.082295892
## 2017-06-30 -0.127067307  0.058654468
## 2017-07-31  0.050417538 -0.111459860
## 2017-08-31  0.153461438  0.095543446
## 2017-09-29  0.029974495 -0.042474144
## 2017-10-31  0.069536859 -0.028457409
## 2017-11-30 -0.056284749 -0.070862541
## 2017-12-29  0.038118899  0.008061928
## 2018-01-31 -0.125409152  0.129254571
## 2018-02-28  0.035485625 -0.032266877
## 2018-03-29 -0.014644378 -0.253920408
## 2018-04-30 -0.019865462  0.099254576
## 2018-05-31  0.116776314 -0.031698139
## 2018-06-29  0.047454925  0.186043257
## 2018-07-31  0.089727080 -0.140021491
## 2018-08-31  0.038692604  0.011737389
## 2018-09-28  0.009829723 -0.130439038
## 2018-10-31 -0.071813611  0.242170576
## 2018-11-30  0.154387872  0.038271580
## 2018-12-31 -0.178243370 -0.051761952
## 2019-01-31 -0.005745827 -0.080628789
## 2019-02-28  0.138714467  0.041032981
## 2019-03-29  0.050137129 -0.133656413
## 2019-04-30  0.138523997 -0.159123803
## 2019-05-31 -0.123977157 -0.253945372
## 2019-06-28 -0.158919824  0.188012109
## 2019-07-31  0.128053836  0.078092373
## 2019-08-30 -0.113786220 -0.068516948
## 2019-09-30  0.006383733  0.065449565
## 2019-10-31  0.019666532  0.268061253
## 2019-11-29 -0.086856508  0.046592176
## 2019-12-31  0.058085901  0.237359743
## 2020-01-31 -0.052328424  0.441578342
## 2020-02-28 -0.186801501  0.026424253
## 2020-03-31 -0.022748102 -0.242781458
## 2020-04-30  0.076398933  0.400209535
## 2020-05-29  0.150832401  0.065730500
## 2020-06-30  0.101444729  0.257108657
## 2020-07-31  0.085265447  0.281420674
## 2020-08-31  0.099359089  0.554719320
## 2020-09-30  0.024072238 -0.149762306
## 2020-10-30 -0.116270016 -0.100371771
## 2020-11-30  0.135872540  0.380308519
## 2020-12-31  0.059883132  0.217730753
## 2021-01-29 -0.005472777  0.117343701
## 2021-02-26  0.106361505 -0.161038203
## 2021-03-31  0.083727052 -0.011269836
## 2021-04-30  0.109289127  0.060292565
## 2021-05-28  0.003147813 -0.126372343
## 2021-06-30  0.010387924  0.083547955
## 2021-07-30 -0.031078932  0.010973846
## 2021-08-31  0.008656156  0.068224268
## 2021-09-30  0.065333373  0.052632612
## 2021-10-29  0.055614047  0.362230202
## 2021-11-30  0.012875294  0.027237848
## 2021-12-31 -0.005326674 -0.079968440
## 2022-01-31  0.011329602 -0.120597475
## 2022-02-28 -0.108671411 -0.073397011
## 2022-03-31 -0.015225199  0.213504290
## 2022-04-29 -0.058475098 -0.213125289
## 2022-05-31  0.060461950 -0.138340062
## 2022-06-30 -0.077626063 -0.118657126
## 2022-07-29 -0.017479137  0.280480149
## 2022-08-31 -0.162806216 -0.075250271
## 2022-09-30 -0.113840926 -0.038313992
## 2022-10-31  0.126329306 -0.153346760
## 2022-11-30  0.153927563 -0.155866121
## 2022-12-30 -0.107620629 -0.457813194
## 2023-01-31  0.017969579  0.340915767
## 2023-02-28  0.000492308  0.171904973
## 2023-03-31 -0.010637087  0.008471140
## 2023-04-28  0.087035129 -0.233183710
## 2023-05-31  0.029900224  0.216021889
## 2023-06-30  0.188587655  0.249689452
## 2023-07-31 -0.015305626  0.021391609
## 2023-08-31  0.060847087 -0.035588260
## 2023-09-29  0.203027792 -0.030929027
## 2023-10-31 -0.023678037 -0.219831983
## 2023-11-30  0.125672859  0.178463656
## 2023-12-29  0.008269328  0.034390133
## 2024-01-31  0.084560546 -0.282704160
## 2024-02-29  0.132897861  0.075015304
## 2024-03-28  0.186871339 -0.138383423
## 2024-04-30  0.092148135  0.041724969
## 2024-05-31  0.113065022 -0.028782134
## 2024-06-25  0.005644747  0.050745660
## 2013-01-31           NA  0.102078114
## 2013-02-28           NA -0.074128640
## 2013-03-28           NA  0.084208138
## 2013-04-30           NA  0.354111531
## 2013-05-31           NA  0.593716684
## 2013-06-28           NA  0.093672163
## 2013-07-31           NA  0.223739522
## 2013-08-30           NA  0.229971642
## 2013-09-30           NA  0.134706620
## 2013-10-31           NA -0.189806595
## 2013-11-29           NA -0.228409405
## 2013-12-31           NA  0.167108541
## 2014-01-31           NA  0.187261714
## 2014-02-28           NA  0.299722785
## 2014-03-31           NA -0.160783242
## 2014-04-30           NA -0.002690122
## 2014-05-30           NA -0.000577422
## 2014-06-30           NA  0.144457224
## 2014-07-31           NA -0.072372676
## 2014-08-29           NA  0.188794007
## 2014-09-30           NA -0.105566477
## 2014-10-31           NA -0.004046477
## 2014-11-28           NA  0.011599801
## 2014-12-31           NA -0.094774519
## 2015-01-30           NA -0.088365289
## 2015-02-27           NA -0.001277808
## 2015-03-31           NA -0.074350051
## 2015-04-30           NA  0.180226808
## 2015-05-29           NA  0.103899574
## 2015-06-30           NA  0.067300935
## 2015-07-31           NA -0.007896616
## 2015-08-31           NA -0.066366250
## 2015-09-30           NA -0.002653519
## 2015-10-30           NA -0.182659777
## 2015-11-30           NA  0.106828586
## 2015-12-31           NA  0.041471519
## 2016-01-29           NA -0.227360626
## 2016-02-29           NA  0.003810669
## 2016-03-31           NA  0.179948109
## 2016-04-29           NA  0.046721797
## 2016-05-31           NA -0.075597968
## 2016-06-30           NA -0.050296440
## 2016-07-29           NA  0.100785334
## 2016-08-31           NA -0.102058091
calculate_component_contribution <- function(.data, w) {
    
    # Covariance of asset returns
    covariance_matrix <- cov(asset_returns_wide_tbl)
    
    # 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(.5, .5))
## # A tibble: 1 × 2
##    DELL  TSLA
##   <dbl> <dbl>
## 1    NA    NA

6 Plot: Colum Chart of Component Contribution and Weight

plot_data <- asset_returns_wide_tbl %>% 
    calculate_component_contribution(w = c(.5, .5)) %>%
    
    # Transform to long from
    pivot_longer(cols = everything() ,names_to = "Asset", values_to = "Contribution") %>%
    
    # Add weights
    add_column(weight = c(.5, .5)) %>%

    # Transfrom 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)

Which of the assets in your portfolio the largest contributor to the portfolio volatility? Do you think your portfolio risk is concentrated in any one asset?

It seems that Tesla and Dell contribute equally to the portfolio volatility. It is not concentrated with one asset.