X=read.delim(file.choose(),sep=";",header=FALSE) # Loading the data
X=diff(as.matrix(log(X)),1) # computing returns
mu=apply(X,2,mean) # Estimating expectation
sigma=cov(X) # Estimating covariance
sigma_inv=solve(sigma) # Inverting covariance
gamma=3 # Setting the risk aversion parameter
w=1/gammasigma_inv%%mu # Computing the optimal weights
w=w/sum(w) # rescaling the parameters to be make sure portfolio weight sum to 1
RP=X%*%w
P=cumprod(1+RP)
plot(log(P),type="l",ylim=c(0,25),xlab="Time",ylab="log performance")
Splitting the sample in two
index=nrow(X)/2 # defining the size of the sample used to estimated the moments
mu=apply(X[1:index,],2,mean)
sigma=cov(X[1:index,])
sigma_inv=solve(sigma)
gamma=3
w=1/gammasigma_inv%%mu
w=w/sum(w)
RP=X%*%w
P=cumprod(1+RP)
lines(log(P),type="l",col="red")
legend("topleft",c("Full sample","Half sample"),col=c(1,2),lty=1)
w_total=c()
w_sigma=c()
w_mu=c()
count=0
for (i in 1:1000)
{
u=round(runif(1,1000,nrow(X)),0)
sample=X[(u-499):(u),]
check=try(solve(var(sample)),silent=TRUE)
if (is.character(check))
{
count=count+1
}else{
mu_temp=apply(sample,2,mean)
sigma_inv_temp=solve(cov(sample))
temp=1/gammasigma_inv_temp%%mu
w_sigma=rbind(w_sigma,t(temp))
temp=1/gamma*sigma_inv%*%mu_temp
w_mu=rbind(mu_temp,t(temp))
temp=1/gamma*sigma_inv_temp%*%mu_temp
w_total=rbind(w_total,t(temp))
}
print(c(i,count/500))
}
X[mu(mu+500),]
par(mfrow=c(1,3))
boxplot((w_total[,1:20]), main="MU AND SIGMA UPDATED")
boxplot((w_mu[,1:20]), main="MU UPDATED")
boxplot((w_sigma[,1:20]), main= "SIGMA UPDATED")
F= I , lambda = 0.2, minimizing parameter
par(mfrow=c(1,1))
lambda=0.2
sigmashrinked=0.8sigma+0.2diag(452) # the identity matrix has to be length of 452 to correspond to the size
sigmashrinked
boxplot(sigmashrinked, xlim=c(0,20), ylim=c(-10,10))
####################2-2
corelation_matrix= cor(sigma) - diag(452)
ro_tot=sum(corelation_matrix)
sqr= 451*452 # divided by two means
cons_corr=ro_tot/(sqr)
ro_sig=cons_corr*sigma
mat1= (matrix(1,452,452)-diag(452))cons_corr + diag(452)
verdict=mat1%%sigma
verdict
debut=sigma*cons_corr
diagmat=diag(452)*debut
milieu=debut-diagmat
diasig=diag(452)*sigma
fin=milieu+diasig
sigmashrinked_second=0.8sigma+0.2fin
boxplot(sigmashrinked_second, xlim=c(0,20), ylim=c(-10,10))