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Author: Mingqipei

1-overview return data.R

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+setwd("/Users/peimingqi/Desktop/spl")
+data=read.csv("DB.csv")
+close=data$Adj.Close
+
+#calculate the return
+close_ln=log(close,base=exp(1))
+close_diff=diff(close_ln)
+
+#change the data format
+data$Date<-as.Date(data$Date)
+data_date=data$Date
+View(data_date)
+
+#draw the plot of the return data
+return=data.frame(data$Date[2:3897],close_diff)
+colnames(return)=c("date","diff")
+View(return)
+plot(return,type='l',xlab="date",ylab="return",col="dark red")
+

2-calculate theta.R

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+setwd("/Users/peimingqi/Desktop/spl")
+data=read.csv("DB.csv")
+close=data$Adj.Close
+close_ln=log(close,base=exp(1))
+close_diff=diff(close_ln)
+
+#the plot/curve of the kernel density distribution
+plot(density(close_diff))
+
+#estimate the approximate function of kernel distribution
+kernel_density<-density(close_diff)
+kernel_fun<-approxfun(kernel_density$x,kernel_density$y)
+
+#
+myfun=function(a){
+  b=kernel_fun(a)*a
+  return(b)
+}
+
+#calculate theta(alpha=0.05)
+alpha=0.05
+
+q=quantile(close_diff,probs=alpha)
+
+inte1=integrate(myfun,-0.2,q)[[1]]
+inte2=integrate(myfun,q,0.2)[[1]]
+
+theta=(alpha*q-inte1)/(2*inte2-(1-2*alpha)*q)
+theta

3-data .R

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+setwd("/Users/peimingqi/Desktop/spl")
+DB=read.csv("DB.csv")
+
+#date
+DB$Date<-as.Date(data$Date)
+dateframe=data.frame(DB$Date[2:3897])
+
+#index return
+index=DB$GSPC
+index_ln=log(index,base=exp(1))
+index_diff=diff(index_ln)
+indexframe=data.frame(index_diff)
+
+#P/EPS
+PE=DB$Close/DB$EPS
+PEframe=data.frame(PE[2:3897])
+
+#turnover rate
+turnover=DB$Volume/DB$shares
+turnoverframe=data.frame(turnover[2:3897])
+
+#circulated stock value
+csv=DB$shares*10000*DB$Close
+ln_csv=log(csv,exp(1))
+csvframe=data.frame(ln_csv[2:3897])
+
+#Y
+close=DB$Adj.Close
+close_ln=log(close,base=exp(1))
+close_diff=diff(close_ln)
+Yframe=data.frame(close_diff)
+
+#total data frame
+DBframe=data.frame(dateframe,indexframe,PEframe,turnoverframe,csvframe,Yframe)
+colnames(DBframe)=c("date","index","PE","turnover","csv","Y")
+View(DBframe)
+

4-prepare for iteration.R

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+#get the initial value of beta
+datamatrix=cbind(DBframe$index,DBframe$PE,DBframe$turnover,DBframe$csv)
+colnames(datamatrix)=c("index","PE","turnover","csv")
+
+
+Y=DBframe$Y
+
+result=lm(formula = Y ~ datamatrix)
+summary(result)
+
+#test heteroscedasticity
+par(mfrow=c(2,2)) # init 4 charts in 1 panel
+plot(result)
+library("lmtest")
+restest=bptest(result)
+
+#get the initial beta
+beta0=result$coefficients
+
+#estimate alpha in ARCH
+res = result$resid
+res2=res^2
+res=as.matrix(res2)
+
+m=length(res)
+U=res[4:m]
+v1=matrix(res[3:(m-1)],nrow=m-3)
+v2=matrix(res[2:(m-2)],nrow=m-3)
+v3=matrix(res[1:(m-3)],nrow=m-3)
+
+V=cbind(v1,v2,v3)
+
+lm2=lm(U~V)
+summary(lm2)
+
+alphat=lm2$coefficients
+
+#calculate sigma
+v4=matrix(rep(1,m-3),nrow=m-3)
+
+Vt=cbind(v4,v1,v2,v3)
+
+sigma=Vt%*%alphat
+
+#calculate omega
+et=result$resid
+et=as.vector(et)
+
+
+et2=matrix(0,nrow=3896)
+mode(et2)
+et2[which(et<0)]=1
+et2[which(et==0)]=1
+et2[which(et>0)]=0
+et2=as.vector(et2)
+
+
+thetavec=rep(theta,3896)
+thetavec=as.vector(thetavec)
+
+omega=abs(thetavec-et2)
+is.vector(omega)
+omega=omega[4:3896]
+
+
+#calculate the new beta
+Xt=cbind(1,datamatrix[4:3896,])
+j=1
+xxsummatrix=matrix(0,nrow=5,ncol = 5)
+xysummatrix=matrix(0,nrow = 5,ncol = 1)
+ynew=Y[4:3896]
+for (j in 1:3893) {
+  xxsummatrix=xxsummatrix+omega[j]/sigma[j]*crossprod(t(Xt[j,]),Xt[j,])
+  xysummatrix=xysummatrix+omega[j]/sigma[j]*crossprod(t(Xt[j,]),ynew[j])
+  }
+
+solve(xxsummatrix)
+beta1=crossprod(t(solve(xxsummatrix)),xysummatrix)
+
+
+

5-iterationfunction.R

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+
+  
+itefun=function(beta){
+
+#calculate residual
+Xt=cbind(1,datamatrix)
+n=nrow(Xt)
+et=Y-crossprod(t(Xt),beta)
+ets=et^2
+U=ets[4:n]
+v1=matrix(ets[3:(n-1)],nrow=n-3)
+v2=matrix(ets[2:(n-2)],nrow=n-3)
+v3=matrix(ets[1:(n-3)],nrow=n-3)
+V=cbind(v1,v2,v3)
+
+lm2=lm(U~V)
+summary(lm2)
+
+alphat=lm2$coefficients
+
+#calculate sigma
+v4=matrix(rep(1,n-3),nrow=n-3)
+
+Vt=cbind(v4,v1,v2,v3)
+
+sigma=Vt%*%alphat
+
+#calculate omega
+et2=matrix(0,nrow = n)
+et2[which(et<0)]=1
+et2[which(et==0)]=1
+et2[which(et>0)]=0
+et2=as.vector(et2)
+
+thetavec=rep(theta,n)
+thetavec=as.vector(thetavec)
+
+omega=abs(thetavec-et2)
+omega=omega[4:n]
+
+j=1
+xxsummatrix=matrix(0,nrow=5,ncol = 5)
+xysummatrix=matrix(0,nrow = 5,ncol = 1)
+ynew=Y[4:n]
+for (j in 1:(n-3)) {
+  xxsummatrix=xxsummatrix+omega[j]/sigma[j]*crossprod(t(Xt[j,]),Xt[j,])
+  xysummatrix=xysummatrix+omega[j]/sigma[j]*crossprod(t(Xt[j,]),ynew[j])
+}
+
+beta=crossprod(solve(xxsummatrix),xysummatrix)
+return(beta)
+}
+
+
+

6-iteration loop.R

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+#calculate the max diff of betas as the condition to end the iteration
+difference1=beta1-beta0
+difference1=abs(difference1)
+maxdifference1=max(difference1)
+
+#establish a matrix to put all the obtained betas
+betamatrix=cbind(beta0,beta1)
+
+#give the initial values in the loop
+beta=beta1
+maxdiff=1000
+
+#the iteration loop
+while(maxdiff>0.0001){
+  k=beta
+  beta=itefun(beta)
+  difference=abs(beta-k)
+  maxdiff=max(difference)
+  betamatrix=cbind(betamatrix,beta)
+}
+
+betafinal=beta 
+
+View(betafinal)
+View(betamatrix)
+

7-results.R

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+#calculate VaR
+alpha=0.05
+q=quantile(close_diff,probs=alpha)
+
+xmean=apply(Xt,2,mean)
+
+#calculatevtheta
+vtheta=xmean%*%betafinal
+
+#calculate ES
+ES=-(1+theta/((1-2*theta)*alpha))*vtheta+theta/((1-2*theta)*alpha)*mean(Y)
+
+#the final results
+datafinal=data.frame(alpha,theta,q,ES)
+colnames(datafinal)=c("alpha","theta","VaR","ES")
+View(datafinal)