prtf {TSEtools}

Design the Portfolio of assets

Description

Compute the efficient frontier function for some selected risk functionals in a portfolio optimization setting.

Usage

prtf (x, Rf = 0.0, sh = FALSE ,eRtn = NULL)

Arguments

x

a numeric matrix of random returns per unit of price within some holding period.

sh

a logical indicating whether shortsales on the risky securities are allowed. Default is FALSE.

Rf

the return of the risk free, i.e. has variance 0.

eRtn

a value of expected returen of portofilo. The mean of whole data defualt.

Details

Let \xi_1 , \ldots,\xi_n be random asset returns and w_1 , \ldots, w_n the portfolio weights. The expected returns are r_m = E\xi_m , m = 1, \ldots, n. In addition to these risky investments, there is a risk-free asset (a bond or bank account) available, which has return r_0. Denoting the weights of w_0 for the risk-free asset. The return of portfolio given by

R_p = w^t r

where, r = ( r_1, \ldots, r_n)^t.

Risk is measure by a deviation functional \Sigma. It is a variance-covariance of asset returns. The risk-free component w_0 ignore in the objective. So, the standard deviation of portfolio is given by \sigma_p = w^t \Sigma w.

To obtain the optimum value of w_i, i=1,\ldots, n, we solve the following model:

\min w^t \Sigma w\;\; s.t:\;\;w^t r > \mu \;\; and\;\; \sum w_i = 1.

where, \mu is a constant value. Note that, the portfolio weights may be negative (selling short is allowed).

Value

The minimum weights show with MIN which is the portfolio with the minimum volatility. Market portfolio is given by MP where, the risk free weight w_0 is zero. MP is the tangency point between the market line and efficient frountier curve. A list containing the following components:

prt

list the name of assests in the portfolio

obs.p

return and volatiliy of overall portfolio

vol

volatility of portfolio

rtn

return of portfolio

w

weigths of portfolio

References

Pflug and Romisch (2007, ISBN: 9789812707406)

See Also

portfolio.optimization, portfolio.optim

Examples

## Not run: 
x <- rnorm(500,0.05,0.02)
y <- rnorm(500,0.01,0.03)
z<-cbind(x, y)
colnames(z) <- c("prt1","prt2")

prtf (z, sh = FALSE)

## End(Not run)