# Load packages
# Core
library(tidyverse)
library(tidyquant)Examine how each asset contributes to portfolio standard deviation. This is to ensure that our risk is not concentrated in any one asset.
Choose your stocks from 2012-12-31 to present.
symbols <- c("WMT", "AMZN", "NVDA")
prices <- tq_get(x = symbols,
get = "stock.prices",
from = "2012-12-31",
to = "2017-12-31")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"))# 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 NVDA WMT
## 2013-01-31 0.0566799395 0.000000000 0.0248964315
## 2013-02-28 -0.0046435024 0.038222015 0.0117958128
## 2013-03-28 0.0083654162 0.013338604 0.0620732354
## 2013-04-30 -0.0487507497 0.070706278 0.0378937634
## 2013-05-31 0.0588686246 0.054651957 -0.0317800543
## 2013-06-28 0.0310507506 -0.030167461 -0.0046876694
## 2013-07-31 0.0813355350 0.028092049 0.0452744790
## 2013-08-30 -0.0695574090 0.026270421 -0.0596997341
## 2013-09-30 0.1067688897 0.053460402 0.0133389516
## 2013-10-31 0.1521839116 -0.024066669 0.0370287871
## 2013-11-29 0.0781496860 0.032034741 0.0540190125
## 2013-12-31 0.0130490386 0.026567318 -0.0232520181
## 2014-01-31 -0.1059765119 -0.020177128 -0.0523039222
## 2014-02-28 0.0094619003 0.162107514 0.0002679891
## 2014-03-31 -0.0737086161 -0.025904134 0.0293257924
## 2014-04-30 -0.1007565303 0.030788520 0.0420203246
## 2014-05-30 0.0273091844 0.032886692 -0.0314095369
## 2014-06-30 0.0383836202 -0.024508387 -0.0223926882
## 2014-07-31 -0.0369768154 -0.057729681 -0.0200476968
## 2014-08-29 0.0799468404 0.110059765 0.0323258235
## 2014-09-30 -0.0502010184 -0.052782437 0.0127660375
## 2014-10-31 -0.0540982347 0.057398974 -0.0026192017
## 2014-11-28 0.1031187277 0.074852154 0.1378165409
## 2014-12-31 -0.0872368614 -0.044863456 -0.0135740758
## 2015-01-30 0.1330922557 -0.043319011 -0.0105350977
## 2015-02-27 0.0697992426 0.142698893 -0.0124328182
## 2015-03-31 -0.0214295755 -0.052582273 -0.0142313433
## 2015-04-30 0.1253212736 0.058908754 -0.0524137242
## 2015-05-29 0.0175090293 0.001460205 -0.0433511649
## 2015-06-30 0.0112589814 -0.095717334 -0.0460136566
## 2015-07-31 0.2111621090 -0.007987990 0.0146949011
## 2015-08-31 -0.0443525782 0.123595673 -0.0993584482
## 2015-09-30 -0.0019516837 0.092150819 0.0016976106
## 2015-10-30 0.2010808743 0.140555197 -0.1246694015
## 2015-11-30 0.0602956777 0.115405147 0.0275687794
## 2015-12-31 0.0165440008 0.038347176 0.0492993646
## 2016-01-29 -0.1410054620 -0.118048446 0.0793142861
## 2016-02-29 -0.0605352209 0.071923706 -0.0003011690
## 2016-03-31 0.0717834363 0.127654936 0.0392702193
## 2016-04-29 0.1053453760 -0.002810493 -0.0239368486
## 2016-05-31 0.0915002899 0.276388360 0.0641208339
## 2016-06-30 -0.0099694639 0.006187796 0.0311567384
## 2016-07-29 0.0586021229 0.194443967 -0.0006850858
## 2016-08-31 0.0135476418 0.073469214 -0.0143679118
## 2016-09-30 0.0848953908 0.110693557 0.0094735839
## 2016-10-31 -0.0583893058 0.037804815 -0.0295505885
## 2016-11-30 -0.0509721927 0.260525496 0.0058385850
## 2016-12-30 -0.0009330556 0.146435792 -0.0116435350
## 2017-01-31 0.0936394059 0.022601817 -0.0350399061
## 2017-02-28 0.0258446800 -0.071874725 0.0608892318
## 2017-03-31 0.0479423007 0.070843562 0.0234087512
## 2017-04-28 0.0424566944 -0.043434021 0.0421087123
## 2017-05-31 0.0725778018 0.326022176 0.0511561816
## 2017-06-30 -0.0271286156 0.001453786 -0.0378575044
## 2017-07-31 0.0202278808 0.117044873 0.0553876853
## 2017-08-31 -0.0072953953 0.042639524 -0.0180254918
## 2017-09-29 -0.0198260355 0.053601089 0.0008961955
## 2017-10-31 0.1395154056 0.145700814 0.1109630081
## 2017-11-30 0.0626577318 -0.029245216 0.1076140277
## 2017-12-29 -0.0062057845 -0.036583511 0.0207685655# Covariance of asset returns
covariance_matrix <- cov(asset_returns_wide_tbl)
covariance_matrix## AMZN NVDA WMT
## AMZN 0.005466022 0.0015926684 0.0003511340
## NVDA 0.001592668 0.0077584837 0.0002178246
## WMT 0.000351134 0.0002178246 0.0022213952# 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(0.3, 0.3, 0.4)
sd_portfolio <- sqrt(t(w) %*% covariance_matrix %*% w)
sd_portfolio## [,1]
## [1,] 0.04437183# 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## AMZN NVDA WMT
## [1,] 0.01526685 0.01955616 0.009548812rowSums(component_contribution)## [1] 0.04437183# Component contribution in percentage
component_percentages <- (component_contribution / sd_portfolio[1,1]) %>%
round(3) %>%
as_tibble()
component_percentages## # A tibble: 1 × 3
## AMZN NVDA WMT
## <dbl> <dbl> <dbl>
## 1 0.344 0.441 0.215component_percentages %>%
as_tibble() %>%
gather(key = "asset", value = "contribution")## # A tibble: 3 × 2
## asset contribution
## <chr> <dbl>
## 1 AMZN 0.344
## 2 NVDA 0.441
## 3 WMT 0.215NVDA had the highest volatility within my portfolio. It also had a relatively high wieght in the portfolio. I would lower the risk by spreading out the wight a bit more, or add more stocks with more diversity in my portfolio.