Comment coder selon O

########### EXO 1 ###########

#1

sharpe<-function(S,Sf){
(mean(S)-mean(Sf))/sd(S)
}

#2

covars<-function(x){
cov<-matrix(NA,dim(x)[2],dim(x)[2])
Y<-matrix(NA,dim(x)[1],1)
Z<-matrix(NA,dim(x)[1],1)
for(i in 1:dim(x)[2]){
for(j in 1:dim(x)[2]){
for(k in 1:dim(x)[1]){
Y[k]<-x[k,i]-mean(x[,i])
Z[k]<-x[k,j]-mean(x[,j])
cov[i,j]<-sum(Y*Z)/(dim(x)[1]-1)
}
}
}
return(cov)
}
f<-matrix(seq(1,9),3,3)
f
covars(f)
cov(f)

covar<-function(r){
(r-colMeans(r))%*%t(r-colMeans(r))/(dim(r)[1]-1)
}

#3

portret<-function(matw,matr){
t(matw)%*%matr
}

portretbis<-function(vw,vr){
sum(vw*vr)
}

portsig<-function(matw,r){
sqrt((t(matw)%*%covars(r))%*%matw)
}


#4
install.packages("tseries")
library("tseries")
?get.hist.quote
getdata<-function(x){
get.hist.quote(x,quote="Close",start="2000-09-01",end="2014-04-01",compression="m")
}
getdata(FCHI)

#5

Code.R<-{
FF<-read.csv(file=file.choose(),header=TRUE)
MKt<-as.matrix(FF[,2])
SMB<-as.matrix(FF[,3])
P<-sharpe(MKt,SMB)
print("Le ratio de Sharpe est:",sep="")
print(P)
}


########### EXO 2 ###########

#1
library("zoo")
library("tseries")
bmw<-getdata("BMW.DE")
telefonica<-getdata("TEF.MC")
oreal<-getdata("OR.PA")
unilever<-getdata("UNA.AS")
unicredit<-getdata("UCG.MI")
eurostoxx<-getdata("^STOXX50E")

getwd()


#2
typeof(bmw)
class(bmw)

stocks<-cbind(bmw,telefonica,oreal,unilever,unicredit,eurostoxx)
dim(stocks)
class(stocks)
colnames(stocks)<-c("bmw","telefonica","oreal","unilever","unicredit")
print(paste("Le nombre de NA est:",sum(apply(stocks,2,is.na)),"NA"))


stocks<-na.locf(stocks)
head(stocks)

stocks<-stocks[which(index(stocks)=="2006-06-01"):nrow(stocks),]
nrow(stocks)

#3
rstocks<-diff(log(stocks))

nrow(rstocks)
head(rstocks)
tail(rstocks)

install.packages("Quandl")
library("Quandl")
RF<-Quandl("BOF/QS_M_IEUTIO1M", collapse="monthly", trim_start="1999-01-01", trim_end="2015-03-02")
#RF<-RF[order(RF[,1]),]
#RF<-as.zoo(RF,order.by=RF[,1])


RF<-RF[,2]/100
dim(RF)
typeof(RF)
class(RF)
head(RF,1)

rstocks<-rstocks[-1,]
dim(rstocks)


prime_actif<-rstocks-RF[,2]
head(prime_actif,3)

dim(prime_actif)
dim(prime_mkt)

capm1<-lm(prime_actif[,1]~prime_actif[,6])
capm2<-lm(prime_actif[,2]~prime_actif[,6])
capm3<-lm(prime_actif[,3]~prime_actif[,6])
capm4<-lm(prime_actif[,4]~prime_actif[,6])
capm5<-lm(prime_actif[,5]~prime_actif[,6])

capm1
capm2
capm3
capm4
capm5

summary(capm1)


colnames(prime_actif)<-c("bmw","telefonica","oreal","unilever","unicredit","eurstoxx")
head(prime_actif,2)
dim(prime_actif)



#4
setwd("C:/Users/Ouadiä/Documents/Cours/Master 2 GRA/Semestre 4/Methodes Numeriques J")
FF<-read.csv(file="FF.csv")
#FF[,2]<-as.numeric(FF[,2])/100
#FF[,3]<-as.numeric(FF[,3])/100
#FF[,4]<-as.numeric(FF[,4])/100
head(FF)
dim(FF)
FF<-as.zoo(FF[,2:4],order.by=FF[,1])/100
class(FF)
FF<-FF[which(index(FF)=="2006-07-01"):nrow(FF),]
dim(FF)


prime_actif<-prime_actif[which(1:index(prime_actif)=="2010-12-01"),]

dim(prime_actif)

fama<-lm(prime_actif[,1]~FF)

#5

Rcapm1<-cbind(summary(capm1)$coefficients,summary(capm1)$r.squared)
Rfama1<-cbind(summary(fama)$coefficients,summary(fama)$r.squared)

summary(capm1)

########### EXO 3 ###########

#1

CAC<-as.matrix(getdata("^FCHI"))
LCAC<-as.matrix(diff(log(CAC)))
library("stats")
library("urca")

acf(CAC)
pacf(CAC)

acf(LCAC)
pacf(LCAC)
?ur.df
summary(ur.df(CAC, type ="trend", lags = 1, selectlags = c("Fixed", "AIC", "BIC")))
summary(ur.df(CAC, type ="drift", lags = 1, selectlags = c("Fixed", "AIC", "BIC")))
summary(ur.df(CAC, type ="none", lags = 1, selectlags = c("Fixed", "AIC", "BIC")))

summary(ur.df(CAC))
summary(ur.df(LCAC))

AR<-arima(LCAC,c(1,0,0))
AR
MA<-arima(LCAC,c(0,0,1))
MA
ARMA<-arima(LCAC,c(1,0,1))
ARMA
ARMA22<-arima(LCAC,c(2,0,2))
ARMA12<-arima(LCAC,c(1,0,2))
ARMA21<-arima(LCAC,c(2,0,1))

install.packages("fGarch")
library("fGarch")
library("vars")
?VAR
?arch.test
?VARselect
?arma

########### EXO 4 ###########

#1

head(rstocks)

covars<-function(x){
Y<-matrix(NA,dim(x)[2],1)
Z<-matrix(NA,dim(x)[2],1)
cov<-matrix(NA,dim(x)[2],dim(x)[2])
for(i in 1:dim(x)[2]){
for(j in 1:dim(x)[2]){
for(k in 1:dim(x)[1]){
Y[k]<-x[k,i]-mean(x[,i])
Z[k]<-x[k,j]-mean(x[,j])
cov[i,j]<-sum(Y*Z)/(dim(x)[1]-1)
}
}
}
return(cov) }
rstock<-cbind(rstocks[,1],rstocks[,2],rstocks[,3],rstocks[,4],rstocks[,5])
colnames(rstock)<-c("bmw","telefonica","oreal","unilever","unicredit")
head(rstock)

rstock1<-na.locf(rstock,na.rm =TRUE,fromLast=TRUE)
head(rstock1)

sup_na<-function(x){
for(j in 1:dim(x)[2]){
for(i in dim(x)[1]:1){
if (is.na(x[i,j])){x[i,j]<-x[i+1,j]}
}
}
return(x)
}

rstock2<-sup_na(rstock)
head(rstock2)
tail(rstock)

covars(rstock1)

S<-cov(rstock2)

#2
library("quadprog")
?solve.QP
Dmat<-S
dvec<-as.matrix(colMeans(rstock2))
amat<-rbind(rep(1,5),diag(5))
Amat<-t(amat)
bvec<-c(1,rep(0,5))
results<-solve.QP(Dmat,dvec,Amat,bvec,meq=1,factorized=FALSE)

results$solution

portret(results$solution,dvec)

lambda<-c(seq(-100,-1),seq(1,100))
solution<-matrix(NA,5,length(lambda))

for (j in 1:length(lambda)){
solution[,j]<-solve.QP(Dmat, dvec/lambda[j], Amat, bvec, meq=1, factorized=FALSE)$solution
}

solution

rp<-matrix(NA,1,length(lambda))
for(i in 1:length(lambda)){
rp[i]<-portret(solution[,i],dvec)
}
rp

vp<-matrix(NA,1,length(lambda))
for(i in 1:length(lambda)){
vp[i]<-portsig(solution[,i],S)
}
vp

plot(vp,rp)