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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