prtf {TSEtools} | R Documentation |
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 be random asset returns and
the portfolio
weights. The expected returns are
In addition
to these risky investments, there is a risk-free asset (a bond or bank account)
available, which has return
. Denoting the weights of
for the risk-free
asset. The return of portfolio given by
where, .
Risk is measure by a deviation functional . It is a variance-covariance of asset returns. The risk-free component
ignore in the objective. So, the standard deviation of portfolio is given by
To obtain the optimum value of we solve the following model:
where, 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)