theta_vcov {MarkowitzR}

Compute variance covariance of 'Unified' Second Moment

Description

Computes the variance covariance matrix of sample mean and second moment.

Usage

theta_vcov(X,vcov.func=vcov,fit.intercept=TRUE)

Arguments

X

an n \times p matrix of observed returns.

vcov.func

a function which takes an object of class lm, and computes a variance-covariance matrix. If equal to the string "normal", we assume multivariate normal returns.

fit.intercept

a boolean controlling whether we add a column of ones to the data, or fit the raw uncentered second moment. For now, must be true when assuming normal returns.

Details

Given p-vector x, the 'unified' sample is the (p+1)(p+2)/2 vector of 1, x, and \mbox{vech}(x x^{\top}) stacked on top of each other. Given n contemporaneous observations of p-vectors, stacked as rows in the n \times p matrix X, this function computes the mean and the variance-covariance matrix of the 'unified' sample.

One may use the default method for computing covariance, via the vcov function, or via a 'fancy' estimator, like sandwich:vcovHAC, sandwich:vcovHC, etc.

Value

a list containing the following components:

mu

a q = (p+1)(p+2)/2 vector of 1, then the mean, then the vech'd second moment of the sample data.

Ohat

the q \times q estimated variance covariance matrix. When fit.intercept is true, the left column and top row are all zeros.

n

the number of rows in X.

pp

the number of assets plus as.numeric(fit.intercept).

Note

Replaces similar functionality from SharpeR package, but with modified API.

Author(s)

Steven E. Pav [e-mail]

References

Pav, S. E. "Asymptotic Distribution of the Markowitz Portfolio." 2013 https://arxiv.org/abs/1312.0557

Pav, S. E. "Portfolio Inference with this One Weird Trick." R in Finance, 2014 http://past.rinfinance.com/agenda/2014/talk/StevenPav.pdf

See Also

itheta_vcov.

Examples

X <- matrix(rnorm(1000*3),ncol=3)
Sigmas <- theta_vcov(X)
Sigmas.n <- theta_vcov(X,vcov.func="normal")
Sigmas.n <- theta_vcov(X,fit.intercept=FALSE)

# make it fat tailed:
X <- matrix(rt(1000*3,df=5),ncol=3)
Sigmas <- theta_vcov(X)

if (require(sandwich)) {
 Sigmas <- theta_vcov(X,vcov.func=vcovHC)
}

# add some autocorrelation to X
Xf <- filter(X,c(0.2),"recursive")
colnames(Xf) <- colnames(X)
Sigmas <- theta_vcov(Xf)

if (require(sandwich)) {
Sigmas <- theta_vcov(Xf,vcov.func=vcovHAC)
}