Value at risk in R

I will estimate market risk with VaR model with R. I used Dell stock price.

Data and packages

library(quantmod)
library(dygraphs)
library(tseries)
library(tidyverse)

getSymbols(Symbols = "DELL",from='2016-08-17',auto.assign = T)

## [1] "DELL"

tail(DELL)

##            DELL.Open DELL.High DELL.Low DELL.Close DELL.Volume DELL.Adjusted
## 2020-02-07     52.50     52.50    51.00      51.62     4722800         51.62
## 2020-02-10     51.00     52.17    50.56      52.11     2700000         52.11
## 2020-02-11     52.10     53.10    52.00      52.26     4402400         52.26
## 2020-02-12     52.73     53.52    52.58      53.30     3484100         53.30
## 2020-02-13     51.95     52.83    51.43      52.55     3426500         52.55
## 2020-02-14     52.95     53.55    52.63      52.88     2107600         52.88

str(DELL)

## An 'xts' object on 2016-08-17/2020-02-14 containing:
##   Data: num [1:880, 1:6] 24.1 24.4 23.6 23.8 24.2 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr [1:6] "DELL.Open" "DELL.High" "DELL.Low" "DELL.Close" ...
##   Indexed by objects of class: [Date] TZ: UTC
##   xts Attributes:  
## List of 2
##  $ src    : chr "yahoo"
##  $ updated: POSIXct[1:1], format: "2020-02-15 10:55:11"

chartSeries(DELL, TA=NULL)

barChart(DELL)

Check normality

dygraph(DELL$DELL.Close,main = 'Time series of DELL stock price'
        ,ylab = 'Currency in USD')

P<-DELL$DELL.Close
ra <- (P-lag(P))/lag(P)
rg <- log(P/lag(P))

ra = na.omit(ra)
rg = na.omit(rg)

returns<-data.frame(ra$DELL.Close,rg$DELL.Close)
head(returns)

##              DELL.Close DELL.Close.1
## 2016-08-18 -0.005813976 -0.005830943
## 2016-08-19  0.017543800  0.017391684
## 2016-08-22  0.003448339  0.003442407
## 2016-08-23  0.030927780  0.030459154
## 2016-08-24  0.013333377  0.013245270
## 2016-08-25 -0.004166672 -0.004175376

colnames(returns)<-c('ra','rg')

head(returns)

##                      ra           rg
## 2016-08-18 -0.005813976 -0.005830943
## 2016-08-19  0.017543800  0.017391684
## 2016-08-22  0.003448339  0.003442407
## 2016-08-23  0.030927780  0.030459154
## 2016-08-24  0.013333377  0.013245270
## 2016-08-25 -0.004166672 -0.004175376

g_returns<-gather(returns,key='method',value = 'return')
head(g_returns)

##   method       return
## 1     ra -0.005813976
## 2     ra  0.017543800
## 3     ra  0.003448339
## 4     ra  0.030927780
## 5     ra  0.013333377
## 6     ra -0.004166672

ggplot(data=returns,aes(ra))+
  geom_histogram(bins = 18)+
  xlab('Dell')

ggplot(data=g_returns,aes(x=return,color=method))+
  geom_density()

ggplot(data=g_returns,aes(x=method,y=return,fill=method))+
  geom_boxplot()

jarque.bera.test(ra)

## 
##  Jarque Bera Test
## 
## data:  ra
## X-squared = 17967, df = 2, p-value < 2.2e-16

jarque.bera.test(rg)

## 
##  Jarque Bera Test
## 
## data:  rg
## X-squared = 34260, df = 2, p-value < 2.2e-16

Arithmetic return

mu_a<-mean(ra)
sd_a<-sd(ra)
z_a<-qnorm(.05)

(VaR <- mu_a + z_a * sd_a)

## [1] -0.03076105

dygraph(ra,main='Aritmatic return and VaR',xlab = 'Date'
        ,ylab='Return') %>% dyLimit(VaR, color = "red")

Geometric return

mu_g <- mean(rg)
sd_g <- sd(rg)
z_g <- qnorm(.05)

(VaR<-mu_g + z_g*sd_g)

## [1] -0.0316285

dygraph(ra,main='Geometer return and VaR',xlab = 'Date'
        ,ylab='Return') %>% dyLimit(VaR, color = "red")  

Source:

• VaR-Wikipedia
• Technical Analysis with R
• Jarque bera test
• Normality assumption