Apply it to your data 12
Which of the assets the largest contributor to the portfolio volatility?
Shea Clark
2024-11-20
# 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("PLTR", "IBM", "BLK", "TSM", "SLB")
prices <- tq_get(x = symbols,
get = "stock.prices",
fro = "2020-12-31",
to = "2024-12-31")
prices## # A tibble: 4,895 × 8
## symbol date open high low close volume adjusted
## <chr> <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 PLTR 2020-12-31 24.6 24.7 23.5 23.5 39922500 23.5
## 2 PLTR 2021-01-04 23.9 24.5 22.5 23.4 44970400 23.4
## 3 PLTR 2021-01-05 23.2 24.7 22.9 24.6 29050400 24.6
## 4 PLTR 2021-01-06 24.1 24.5 23.2 23.5 32732900 23.5
## 5 PLTR 2021-01-07 24.0 25.2 23.7 25 32240000 25
## 6 PLTR 2021-01-08 25.7 26.4 24.7 25.2 41313800 25.2
## 7 PLTR 2021-01-11 24.6 26.6 24.3 25.9 32609000 25.9
## 8 PLTR 2021-01-12 26.3 26.4 25.5 26.2 26887200 26.2
## 9 PLTR 2021-01-13 25.7 27.4 25.1 25.5 51216600 25.5
## 10 PLTR 2021-01-14 25.5 25.6 24.4 24.9 32908000 24.9
## # ℹ 4,885 more rows2 Convert prices to returns (monthly)
asset_returns_tbl1 <- prices %>%
group_by(symbol) %>%
tq_transmute(select = adjusted,
mutate_fun = periodReturn,
period = "monthly",
type = "log") %>%
slice(-1) %>%
ungroup() %>%
set_names(c("asset", "date", "returns"))
asset_returns_tbl1## # A tibble: 235 × 3
## asset date returns
## <chr> <date> <dbl>
## 1 BLK 2021-01-29 -0.0285
## 2 BLK 2021-02-26 -0.00969
## 3 BLK 2021-03-31 0.0881
## 4 BLK 2021-04-30 0.0831
## 5 BLK 2021-05-28 0.0681
## 6 BLK 2021-06-30 0.00230
## 7 BLK 2021-07-30 -0.00895
## 8 BLK 2021-08-31 0.0841
## 9 BLK 2021-09-30 -0.113
## 10 BLK 2021-10-29 0.118
## # ℹ 225 more rows3 Calculate Component Contribution to Portfolio Volatility
# Transform data into wide form
asset_returns_wide_tbl1 <- asset_returns_tbl1 %>%
pivot_wider(names_from = asset, values_from = returns) %>%
column_to_rownames(var = "date")
asset_returns_wide_tbl1## BLK IBM PLTR SLB TSM
## 2021-01-29 -0.028509015 -0.0552816921 0.401351960 0.017257708 0.108363943
## 2021-02-26 -0.009686429 0.0117619825 -0.386599305 0.233122559 0.035726769
## 2021-03-31 0.088051937 0.1137671276 -0.025854320 -0.026135685 -0.058990152
## 2021-04-30 0.083111012 0.0626795105 -0.010792248 -0.005162410 -0.013105554
## 2021-05-28 0.068102238 0.0241356318 -0.003913906 0.146889325 0.005296961
## 2021-06-30 0.002301702 0.0196334195 0.138529763 0.025469944 0.027406763
## 2021-07-30 -0.008954455 -0.0391632190 -0.194074791 -0.104631843 -0.029731798
## 2021-08-31 0.084138689 0.0070388758 0.193315760 -0.023354531 0.020115170
## 2021-09-30 -0.113214733 -0.0100979469 -0.091369554 0.055492625 -0.059739543
## 2021-10-29 0.117748731 -0.1048567722 0.073751289 0.084703317 0.018194396
## 2021-11-30 -0.042050053 -0.0078558090 -0.225755136 -0.113403194 0.029891743
## 2021-12-31 0.016633609 0.1322711384 -0.125744457 0.043329214 0.030744721
## 2022-01-31 -0.106652554 -0.0006736593 -0.283845347 0.265825543 0.019099881
## 2022-02-28 -0.100990094 -0.0744595352 -0.145797597 0.007450716 -0.136249489
## 2022-03-31 0.033534033 0.0594956402 0.147255287 0.051407982 -0.021223094
## 2022-04-29 -0.201550780 0.0167032705 -0.277777417 -0.057286663 -0.115041307
## 2022-05-31 0.068664139 0.0609881041 -0.180784206 0.167590006 0.025183235
## 2022-06-30 -0.086885609 0.0167843042 0.043950667 -0.250941501 -0.148110802
## 2022-07-29 0.094169016 -0.0765133006 0.132014326 0.034898354 0.079110872
## 2022-08-31 -0.004177876 -0.0055327918 -0.293172220 0.029797468 -0.059728024
## 2022-09-30 -0.184004631 -0.0780141319 0.051746601 -0.056181074 -0.189699470
## 2022-10-31 0.160233184 0.1518272805 0.078053770 0.371083017 -0.107859491
## 2022-11-30 0.103019733 0.0857743558 -0.158711687 -0.009268223 0.298749779
## 2022-12-30 -0.003476367 -0.0552955571 -0.155484891 0.039793439 -0.102282582
## 2023-01-31 0.068944888 -0.0447065750 0.192138236 0.063766498 0.219027087
## 2023-02-28 -0.096413157 -0.0289290839 0.007682489 -0.063733822 -0.062979779
## 2023-03-31 -0.022684122 0.0137487424 0.074927565 -0.080387293 0.071294391
## 2023-04-28 0.003103750 -0.0363534522 -0.086473575 0.005078753 -0.098432461
## 2023-05-31 -0.020546310 0.0306418315 0.640834694 -0.141699003 0.156587696
## 2023-06-30 0.057148491 0.0397918331 0.041284151 0.142451120 0.027538073
## 2023-07-31 0.066752495 0.0746416897 0.257888422 0.172021712 -0.017694213
## 2023-08-31 -0.053243527 0.0296550696 -0.280984162 0.010571228 -0.057924091
## 2023-09-29 -0.073064949 -0.0454925954 0.065872775 -0.007090066 -0.068775149
## 2023-10-31 -0.054367978 0.0304649446 -0.077961529 -0.046340322 -0.006812535
## 2023-11-30 0.204522197 0.1031625469 0.303601922 -0.067249125 0.119956188
## 2023-12-29 0.084192863 0.0309856669 -0.155065436 0.004816481 0.071190905
## 2024-01-31 -0.047281665 0.1159675462 -0.064965709 -0.066333713 0.082642790
## 2024-02-29 0.046714887 0.0165072159 0.443872742 -0.001946008 0.130217238
## 2024-03-28 0.033372892 0.0315460752 -0.086141799 0.125820111 0.059824153
## 2024-04-30 -0.099632857 -0.1388720955 -0.046251059 -0.143564103 0.009437064
## 2024-05-31 0.022782582 0.0137812272 -0.013287664 -0.034061404 0.095085074
## 2024-06-28 0.026183727 0.0359072787 0.155599270 0.034078006 0.143567937
## 2024-07-31 0.107301896 0.1052217496 0.059764987 0.023254452 -0.047180510
## 2024-08-30 0.028467115 0.0593949946 0.157597961 -0.093262148 0.034966481
## 2024-09-30 0.057442537 0.0896135608 0.166956373 -0.040959925 0.015092359
## 2024-10-31 0.032656998 -0.0671594001 0.110829417 -0.045850534 0.092705175
## 2024-11-20 0.043522861 0.0452608295 0.401929782 0.082822410 -0.011507082# Covariance of asset returns
covariance_matrix1 <- cov(asset_returns_wide_tbl1)
covariance_matrix1## BLK IBM PLTR SLB TSM
## BLK 0.007054669 0.0024340667 0.0057875381 0.0030473080 0.0035689581
## IBM 0.002434067 0.0041386335 0.0009140293 0.0016291069 0.0008454151
## PLTR 0.005787538 0.0009140293 0.0448425117 -0.0038790119 0.0066852947
## SLB 0.003047308 0.0016291069 -0.0038790119 0.0123606549 -0.0001585173
## TSM 0.003568958 0.0008454151 0.0066852947 -0.0001585173 0.0090913591# 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_portfolio1 <- sqrt(t(w) %*% covariance_matrix1 %*% w)
sd_portfolio1## [,1]
## [1,] 0.06849925# 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_contribution1 <- (t(w) %*% covariance_matrix1 * w) / sd_portfolio1[1,1]
component_contribution1## BLK IBM PLTR SLB TSM
## [1,] 0.01640912 0.008161928 0.0307642 0.008320035 0.004843972rowSums(component_contribution1)## [1] 0.06849925# Component contribution in percentage
component_percentages1 <- (component_contribution1 / sd_portfolio1[1,1]) %>%
round(3) %>%
as_tibble()
component_percentages1## # A tibble: 1 × 5
## BLK IBM PLTR SLB TSM
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.24 0.119 0.449 0.121 0.071component_percentages1 %>%
as_tibble() %>%
gather(key = "asset", value = "contribution")## # A tibble: 5 × 2
## asset contribution
## <chr> <dbl>
## 1 BLK 0.24
## 2 IBM 0.119
## 3 PLTR 0.449
## 4 SLB 0.121
## 5 TSM 0.071asset_returns_wide_tbl1 <- asset_returns_tbl1 %>%
pivot_wider(names_from = asset, values_from = returns) %>%
column_to_rownames(var = "date")
calculate_component_contribution1 <- function(asset_returns_wide_tbl1, w) {
covariance_matrix <- cov(asset_returns_wide_tbl1)
sd_portfolio <- sqrt(t(w) %*% covariance_matrix %*% w)
component_contribution1 <- (t(w) %*% covariance_matrix * w) / sd_portfolio[1,1]
component_percentages1 <- (component_contribution1 / sd_portfolio[1,1]) %>%
round(3) %>%
as_tibble()
return(component_percentages1)
}
asset_returns_wide_tbl1 %>% calculate_component_contribution1(w = c(0.25,0.25,0.2,0.2,0.1))## # A tibble: 1 × 5
## BLK IBM PLTR SLB TSM
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.24 0.119 0.449 0.121 0.0716 Plot: Colum Chart of Component Contribution and Weight
plot_data1 <- asset_returns_wide_tbl1 %>% calculate_component_contribution1(w = c(.25, .25, .2, .2, .1)) %>%
# Transform to long form
pivot_longer(cols = everything(), names_to = "Asset", values_to = "Contribution")
plot_data1 %>%
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")
plot_data1 <- asset_returns_wide_tbl1 %>% calculate_component_contribution1(w = c(.25, .25, .2, .2, .1)) %>%
# Transform to long form
pivot_longer(cols = everything(), names_to = "Asset", values_to = "Contribution") %>%
# Add weights
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_data1 %>%
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?
Palantir is the largest contributor to my portfolios volatility. Its contribution percentage is over 2x its weight in the portfolio. This can be attributed to it still being relatively new to the market, in a high performing sector. I dont think its fair to say the entire risk of the portfolio is attributed to Palantir, given Blackrock has a contribution percentage of roughly 25%. With that being said, Palantir accounts for 45% of my portfolios volatility while holding a 20% weight.