# 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("JPM", "NVDA", "LLY", "AMZN")

prices <- tq_get(x    = symbols,
                 get  = "stock.prices",    
                 from = "2012-12-31",
                 to   = "2017-12-31")

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
##                     AMZN          JPM           LLY         NVDA
## 2013-01-31  0.0566799395  0.074549220  8.489723e-02  0.000000000
## 2013-02-28 -0.0046435024  0.038975391  2.705470e-02  0.038222120
## 2013-03-28  0.0083654162 -0.030299147  3.822806e-02  0.013338704
## 2013-04-30 -0.0487507497  0.038370189 -2.514161e-02  0.070705992
## 2013-05-31  0.0588686246  0.107826577 -3.216736e-02  0.054652320
## 2013-06-28  0.0310507506 -0.033528817 -7.904062e-02 -0.030167547
## 2013-07-31  0.0813355350  0.061462658  7.809900e-02  0.028091869
## 2013-08-30 -0.0695574090 -0.097951633 -2.361967e-02  0.026270337
## 2013-09-30  0.1067688897  0.022697024 -2.103703e-02  0.053460574
## 2013-10-31  0.1521839116  0.004434294 -1.018444e-02 -0.024066335
## 2013-11-29  0.0781496860  0.104545027  1.783311e-02  0.032034407
## 2013-12-31  0.0130490386  0.021781467  1.541233e-02  0.026567318
## 2014-01-31 -0.1059765119 -0.048308542  5.734336e-02 -0.020177289
## 2014-02-28  0.0094619003  0.026031353  1.076842e-01  0.162107675
## 2014-03-31 -0.0737086161  0.066219889 -1.266156e-02 -0.025904134
## 2014-04-30 -0.1007565303 -0.074830584  4.068651e-03  0.030788725
## 2014-05-30  0.0273091844 -0.007351280  2.105865e-02  0.032886092
## 2014-06-30  0.0383836202  0.036226201  3.786377e-02 -0.024508194
## 2014-07-31 -0.0369768154  0.007833586 -1.801526e-02 -0.057729407
## 2014-08-29  0.0799468404  0.030398863  4.814345e-02  0.110059757
## 2014-09-30 -0.0502010184  0.013200682  2.009253e-02 -0.052782636
## 2014-10-31 -0.0540982347  0.010690903  2.256525e-02  0.057399364
## 2014-11-28  0.1031187277 -0.005304876  3.387705e-02  0.074852135
## 2014-12-31 -0.0872368614  0.039437967  1.269086e-02 -0.044863508
## 2015-01-30  0.1330922557 -0.134036825  4.270426e-02 -0.043319068
## 2015-02-27  0.0697992426  0.119456693 -1.862794e-02  0.142698427
## 2015-03-31 -0.0214295755 -0.011488106  3.473241e-02 -0.052582055
## 2015-04-30  0.1253212736  0.049912892 -1.079421e-02  0.058909095
## 2015-05-29  0.0175090293  0.039062357  1.002141e-01  0.001459648
## 2015-06-30  0.0112589814  0.029656407  5.654544e-02 -0.095717000
## 2015-07-31  0.2111621090  0.017814239  1.214299e-02 -0.007988052
## 2015-08-31 -0.0443525782 -0.066827373 -1.988810e-02  0.123595408
## 2015-09-30 -0.0019516837 -0.050062407  1.614082e-02  0.092151046
## 2015-10-30  0.2010808743  0.059589313 -2.565789e-02  0.140555210
## 2015-11-30  0.0602956777  0.037123453  1.206592e-02  0.115405310
## 2015-12-31  0.0165440008 -0.009796015  2.670038e-02  0.038347469
## 2016-01-29 -0.1410054620 -0.097446549 -6.319441e-02 -0.118048567
## 2016-02-29 -0.0605352209 -0.055282243 -8.710652e-02  0.071923611
## 2016-03-31  0.0717834363  0.050564954  1.387580e-04  0.127654918
## 2016-04-29  0.1053453760  0.072421350  4.772485e-02 -0.002810766
## 2016-05-31  0.0915002899  0.032228351  1.383101e-05  0.276388497
## 2016-06-30 -0.0099694639 -0.049142695  4.839025e-02  0.006188209
## 2016-07-29  0.0586021229  0.036778732  5.123645e-02  0.194443299
## 2016-08-31  0.0135476418  0.053713440 -5.766452e-02  0.073469232
## 2016-09-30  0.0848953908 -0.013573300  3.177272e-02  0.110693865
## 2016-10-31 -0.0583893058  0.046556604 -8.337061e-02  0.037805017
## 2016-11-30 -0.0509721927  0.146281619 -8.889141e-02  0.260525119
## 2016-12-30 -0.0009330556  0.073564251  9.148347e-02  0.146435715
## 2017-01-31  0.0936394059 -0.013906724  4.622919e-02  0.022602353
## 2017-02-28  0.0258446800  0.068385744  7.906113e-02 -0.071874984
## 2017-03-31  0.0479423007 -0.031157793  1.557712e-02  0.070843467
## 2017-04-28  0.0424566944 -0.003879638 -2.467507e-02 -0.043434206
## 2017-05-31  0.0725778018 -0.057360982 -2.437732e-02  0.326022562
## 2017-06-30 -0.0271286156  0.106698595  3.373424e-02  0.001453719
## 2017-07-31  0.0202278808  0.009852354  4.364646e-03  0.117044977
## 2017-08-31 -0.0072953953 -0.009962565 -1.035508e-02  0.042639172
## 2017-09-29 -0.0198260355  0.049581217  5.096112e-02  0.053601418
## 2017-10-31  0.1395154056  0.057849039 -4.299681e-02  0.145700504
## 2017-11-30  0.0626577318  0.038126619  3.871497e-02 -0.029245218
## 2017-12-29 -0.0062057845  0.022889717 -2.128869e-03 -0.036583515
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 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(0.25, 0.25, 0.25, 0.25))
## # A tibble: 1 × 4
##    AMZN   JPM   LLY  NVDA
##   <dbl> <dbl> <dbl> <dbl>
## 1 0.333 0.203 0.083 0.381

6 Plot: Colum Chart of Component Contribution and Weight

plot_data <- asset_returns_wide_tbl %>%
    
    calculate_component_contribution(w = c(0.25, 0.25, 0.25, 0.25)) %>%
    
    # Transform to long form 
    pivot_longer(cols = everything(), names_to = "Asset", values_to = "Contribution") %>%
    
    # Add weights
    add_column(weight = c(0.25, 0.25, 0.25, 0.25)) %>%
    
    # 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)

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?

NVDA is the largest contributor to my portfolios volatility. It takes on almost 40% of my portfolios volatility. Followed by AMZN that takes on almost 35% of the portfolios volatility. This portfolio is a diversified mix of tech, financial, healthcare, and consumer cyclical stocks, each with varying levels of volatility. The tech sector, including NVDA, tends to be more volatile, inherently carrying higher risk. NVIDIA is a high-growth company, heavily reliant on emerging trends like AI, gaming, and data centers. Growth stocks often exhibit higher price fluctuations because their valuations depend on future earnings, which are uncertain and prone to rapid shifts in sentiment. In contrast, JPM and LLY have established business models, and AMZN is considered more diversified in revenue sources, which can help reduce volatility.