Revision cba29dfbf1a823f21f866437ee96e8a2735c1708 authored by Roger Koenker on 13 February 2016, 00:52:06 UTC, committed by cran-robot on 13 February 2016, 00:52:06 UTC
1 parent a137ab8
qrisk.R
``````"qrisk" <-
function(x, alpha=c(.1,.3), w = c(.7,.3), mu = .07, R = NULL, r = NULL, lambda = 10000){
#
# find optimal Choquet-risk portfolios given:
#
#	x 	(n by p) matrix of asset returns
#	alphas	alphas defining a Choquet capacity risk function
#	w	w defining weights for Choquet capacity risk function
#	R	Matrix defining constraints on the parameters
#	r	rhs defining constraints on the parameters
#	mu	required mean rate of return
#	lambda	Lagrange multiplier for RoR constraint
#
n <- nrow(x)
p <- ncol(x)
m <- length(alpha)
if(length(w)!=m)stop("length of w doesn't match length of alpha")
xbar <- apply(x,2,mean)
y <- x[,1]
r <- c(r,lambda*(xbar[1]-mu), -lambda*(xbar[1]-mu))
X <- x[,1]-x[,-1]
R <- rbind(R,lambda*(xbar[1]-xbar[-1]), -lambda*(xbar[1]-xbar[-1]))
R <- cbind(matrix(0,nrow(R),m),R)
f <- rq.fit.hogg(X,y,taus=alpha,weights=w,R=R,r=r)
fit <- f\$coefficients
pihat <- c(1-sum(fit[-(1:m)]),fit[-(1:m)])
x <- as.matrix(x)
yhat <- x%*%pihat
etahat <- quantile(yhat,alpha)
muhat <- mean(yhat)
qrisk <- 0
for(i in 1:length(alpha))
qrisk <- qrisk + w[i]*sum(yhat[yhat<etahat[i]])/(n*alpha[i])
list(pihat = pihat, muhat = muhat, qrisk = qrisk)
}
"srisk" <-
function(x,mu=.07,lambda=100000000,alpha=.1,eps=.0001){
#
# find optimal sigma-risk (Markowitz) portfolios given:
#
#	x 	(n by p) matrix of asset returns
#	mu	required mean return
#	lambda	Lagrange multiplier for required mean return constraint
#
n <- nrow(x)
p <- ncol(x)
X <- rbind(x,apply(x,2,mean))
y <- X[,1]
y[n+1] <- lambda*(y[n+1]-mu)
X <- X[,1]-X[,-1]
X <- cbind(c(rep(1,n),0),X)
X[n+1,] <- lambda*X[n+1,]
fit <- lm(y~X-1)
pihat <- c(1-sum(fit\$coef[-1]),fit\$coef[-1])
if(abs(fit\$residual[n+1]) > eps) return("lambda too small?")
yhat <- x%*%pihat
muhat <- mean(x%*%pihat)
sigma <- sqrt(var(x%*%pihat))
list(pihat = pihat, muhat = muhat, sigma = sigma)
}
``````

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