[Returnanalytics-commits] r2100 - pkg/MPO/R

[noreply at r-forge.r-project.org]

Author: jamesleehobbs
Date: 2012-07-04 01:05:39 +0200 (Wed, 04 Jul 2012)
New Revision: 2100

Added:
   pkg/MPO/R/TurnoverOpt.R
Log:
- Turnover constrained portfolio optimization

Added: pkg/MPO/R/TurnoverOpt.R
===================================================================
--- pkg/MPO/R/TurnoverOpt.R	                        (rev 0)
+++ pkg/MPO/R/TurnoverOpt.R	2012-07-03 23:05:39 UTC (rev 2100)
@@ -0,0 +1,64 @@
+library(xts)
+library(quadprog)
+library(corpcor)
+
+#todo: documentation with Roxygen2 and updating package dependecies
+
+TurnoverOpt <- function(returns,mu.target,w.initial,turnover){
+  nassets <- ncol(returns)
+  #using 3 sets of variabes...w.initial, w.buy, and w.sell
+  returns <- cbind(returns,returns,returns)
+  #The covariance matrix will be 3Nx3N rather than NxN
+  cov.mat <- cov(returns)
+  Dmat <- 2*cov.mat
+  #Make covariance positive definite
+  #This should barely change the covariance matrix, as
+  #the last few eigen values are very small negative numbers
+  Dmat <- make.positive.definite(Dmat)
+  mu <- apply(returns,2,mean)
+  dvec <- rep(0,nassets*3) #no linear part in this problem
+  
+  #left hand side of constraints
+  constraint.sum <- c(rep(1,2*nassets),rep(1,nassets))
+  constraint.mu.target <- mu
+  constraint.weights.initial <- rbind(diag(nassets),matrix(0,ncol=nassets,nrow=nassets*2))
+  #Make both w_buy and w_sell negative, and check that it is > the negative turnover
+  constraint.turnover <- c(rep(0,nassets),rep(-1,nassets),rep(1,nassets))
+  constraint.weights.positive <- 
+    rbind(matrix(0,ncol=2*nassets,nrow=nassets),diag(2*nassets))
+  temp.index <- (nassets*3-nassets+1):(nassets*3)
+  #need to flip sign for w_sell
+  constraint.weights.positive[temp.index,]<- 
+    constraint.weights.positive[temp.index,]*-1
+  #put left hand side of constraints into constraint matrix
+  Amat <- cbind(constraint.sum, constraint.mu.target, constraint.weights.initial,
+               constraint.turnover, constraint.weights.positive)
+  #right hand side of constraints in this vector
+  bvec <- c(1,mu.target,w.initial,-turnover,rep(0,2*nassets))
+
+  #Note that the first 5 constraints are equality constraints
+  #The rest are >= constraints, so if you want <= you have to flip
+  #signs as done above
+  solution <- solve.QP(Dmat,dvec,Amat,bvec,meq=(2+nassets))
+  
+  port.var <- solution$value
+  w.buy <- solution$solution[(nassets+1):(2*nassets)]
+  w.sell <- solution$solution[(2*nassets+1):(3*nassets)]
+  w.total <- w.initial + w.buy + w.sell
+  achieved.turnover <- sum(abs(w.buy),abs(w.sell))
+  
+  list(w.initial = w.initial, w.buy = w.buy,w.sell=w.sell, 
+       w.total=w.total,achieved.turnover = achieved.turnover, port.var=port.var)
+} 
+
+##example
+p = TurnoverOpt(large.cap.returns,mu.target=0.01,w.initial=rep(1/100,100),turnover=1)
+p
+sum(p$w.total)
+sum(p$w.initial)
+sum(p$w.buy)
+sum(p$w.sell)
+
+wt<-p$w.total
+wt%*%cov(returns)%*%wt
+