marko: Compute the assets' weights and the associated CVaR using...
In TaoussD/EbEEMGARCH: Estimating MGARCH(1,1) model equation by equation

Description Usage Arguments Value Author(s) References See Also Examples

Estimation of the assets' weights and the associated CVaR which minimize the variance

1	estim.Markowitz(n, Omega, A, B, alpha, beta, S, type, level, yield)

With usual notations of DCC Garch

`n`	Number of observations used to compute the empirical quantile
`Omega`	Estimation of Omega
`A`	Estimated parameter for A
`B`	Estimated parameter for B
`alpha`	Estimated parameter for alpha
`beta`	Estimated parameter for beta
`S`	Estimated parameter for S
`eps`	Data
`type`	type="Engle" for a Engle-DCC type="Aielli" for an Aielli-DCC
`level`	Level of the CVaR
`yield`	Data

`VaR`	CVaR of the portfolio
`weights`	Matrix of the weights (time-dependant)

D. Taouss & C. Francq

C. Francq & J.M. Zakoian, Estimating multivariate GARCH and Stochastic Correlation models equation by equation
C. Francq & J.M. Zakoian, Joint inference on market and estimation risks in dynamic portfolios

EbEEMGARCH Homepage of the documentation

#####
# Sampling some data
#####

n <- 800
Omega <- c(0.001, 0.001, 0.001)
A <-matrix(c(0.03,0.01,0.01,0.01,0.03,0.01,0.01,0.01,0.03),nrow=3)
B <- c(0.1,0.1,0.1)
S <- matrix(c(1,0.4,0.4,0.4,1,0.4,0.4,0.4,1),nrow=3)
alpha <- 0.05;
beta <- 0.97 - alpha
nu <- 14
yield <- GarchDCC.sim(n, Omega, A, B, alpha, beta, S, nu = nu, noise = "student", model = "Aielli")

#####
# Estimation of the parameters
#####

EbEE <- estimDCC.EbEE(Omega, A, B, S, alpha, beta, yield$sim, type = "Aielli")

#####
# Estimation of the weights and the CVaR
#####

Marko <- estim.Markowitz(700,EbEE$Omega,EbEE$A,EbEE$B,EbEE$alpha,EbEE$beta,EbEE$S,type="Aielli",level=0.01,yield$sim)


#####
# Compute the yield of the portfolio
#####

yield_p<-c()
for (t in 1:n) {
    yield_p<-c(yield_p,drop(t(Marko$weights[t,])%*%yield$sim[t,]))
}