Value at Risk and Expected Shortfall Calculations
Essay by Babloo Kumar • May 26, 2017 • Coursework • 1,142 Words (5 Pages) • 1,004 Views
Value At Risk and Expected Shortfall Calculations
Analytical Method
- Single Asset Portfolio
R Function for VAR-
FnVaRUSD<- function(file,p,am,n) { m<-mean(file$Return) sd<-sd(file$Return) Var<-qnorm(p,m,sd) Var<-exp(Var)-1 Var<-Var*(n^0.5)*am Var } |
Inputs to function-
file = CSV file having the daily returns(log normal return) of the asset in the following format-
[pic 1]
p = p value (1- probability that the loss will be less than the Var)
am = Amount invested in the asset
n= no of days for which VAR is to be calculated
Function Call-
FnVaRUSD (read.csv("USDINR.csv"),.05,1000,1) |
- Multi Asset Portfolio
R Function for VAR-
FNVarP<-function(z,p,n) { x<-z[(2:NROW(z)),(2:NCOL(z))] cm <- cor(x,method="spearman") a<-array(NA,dim=(c=NCOL(z)-1)) v<-matrix(a, byrow=FALSE) for(i in 1:NCOL(x)) { m<-mean(x[,i]) sd<-sd(x[,i]) Var<-qnorm(p,m,sd) Var<-exp(Var)-1 Var<-Var*z[1,i+1] v[i,1]<-Var } VARP<-(t(v)%*%cm%*%v)^0.5 VARP<-VARP*(n^0.5) VARP } |
Inputs to function-
z = CSV file having the daily returns of different assets with their Market Value in the following format-
[pic 2]
p = p value (1- probability that the loss will be less than the Var)
n= no of days for which VAR is to be calculated
Function Call-
FNVarP(read.csv("CurrencyReturns.csv"),0.1,1) |
R Function for Expected Shortfall-
FNESP<-function(z,p,n) { x<-z[(2:NROW(z)),(2:NCOL(z))] cm <- cor(x,method="spearman") a<-array(NA,dim=(c=NCOL(z)-1)) e<-matrix(a, byrow=FALSE) for(i in 1:NCOL(x)) { m<-mean(x[,i]) sd<-sd(x[,i]) Var<-qnorm(p,m,sd) es<-subset(x[,i],x[,i] es<-mean(es)*z[1,i+1] e[i,1]<-es } EXPSH<-(t(e)%*%cm%*%e)^0.5 EXPSH<-EXPSH*(n^0.5) EXPSH } |
Inputs to function-
z = CSV file having the daily returns of different assets with their Market Value in the following format-
[pic 3]
p = p value (1- probability that the loss will be less than the Var)
n= no of days for which ES is to be calculated
Function Call-
FNESP(read.csv("CurrencyReturns.csv"),0.05,1) |
Historical Method
- Single Asset Portfolio
R Function for VAR-
FnVaRUSDHis<-function(file,p,am,n) { x<- sort(file$Return, decreasing=TRUE) Var<-quantile(x,c(p)) Var<-exp(Var)-1 Var<-Var*(n^0.5)*am Var } |
Inputs to function-
file = CSV file having the daily returns of the asset in the following format-
[pic 4]
p = p value (1- probability that the loss will be less than the Var)
am = Amount invested in the asset
n= no of days for which VAR is to be calculated
Function Call-
FnVaRUSDHis (read.csv("USDINR.csv"),.05,1000,1) |
- Multi Asset Portfolio
R Function for VAR-
FNVarPHis<-function(z,p,n) { y<-z[(2:NROW(z)),(2:NCOL(z))] cm <- cor(x,method="spearman") a<-array(NA,dim=(c=NCOL(z)-1)) v<-matrix(a, byrow=FALSE) for(i in 1:NCOL(x)) { x<- sort(y[,i], decreasing=TRUE) Var<-quantile(x,c(p)) Var<-exp(Var)-1 Var<-Var*z[1,i+1] v[i,1]<-Var } VARP<-(t(v)%*%cm%*%v)^0.5 VARP<-VARP*(n^0.5) VARP } |
Inputs to function-
z = CSV file having the daily returns of different assets with their Market Value in the following format-
[pic 5]
p = p value (1- probability that the loss will be less than the Var)
n= no of days for which VAR is to be calculated
Function Call-
FNVarPHis(read.csv("CurrencyReturns.csv"),0.1,1) |
R Function for Expected Shortfall-
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