This function solves a weighted quantile regression problem to find the
optimal portfolio weights minimizing a Choquet risk criterion described
in Bassett, Koenker, and Kordas (2002).
Usage
qrisk(x, alpha = c(0.1, 0.3), w = c(0.7, 0.3), mu = 0.07,
R = NULL, r = NULL, lambda = 10000)
Arguments
x
n by q matrix of historical or simulated asset returns
alpha
vector of alphas receiving positive weights in the Choquet criterion
w
weights associated with alpha in the Choquet criterion
mu
targeted rate of return for the portfolio
R
matrix of constraints on the parameters of the quantile regression, see below
r
rhs vector of the constraints described by R
lambda
Lagrange multiplier associated with the constraints
Details
The function calls rq.fit.hogg which in turn calls the constrained Frisch
Newton algorithm. The constraints Rb=r are intended to apply only to the slope
parameters, not the intercept parameters. The user is completely responsible to
specify constraints that are consistent, ie that have at least one feasible point.
See examples for imposing non-negative portfolio weights.
Value
pihat
the optimal portfolio weights
muhat
the in-sample mean return of the optimal portfolio
qrisk
the in-sample Choquet risk of the optimal portfolio