##### Scenario-based Portfolio Optimization (scenportopt)
##### (c)2013-2014 Ronald Hochreiter <ron@hochreiter.net>
##### http://www.finance-r.com/
### Portfolio Optimization minimizing Standard Deviation
# Implementation based on [Markowitz 1952]
# minimize { t(x) * Cov(data) * x }
optimal.portfolio.markowitz <- function(model) {
### Variables: x[asset]
n_var <- model$assets
ix_x <- 1
### Objective function
Objective <- list()
Objective$quadratic <- cov(model$data)
Objective$linear <- rep(0, model$assets)
### Constraints
Constraints <- list(n=n_var, A=NULL, b=NULL, Aeq=NULL, beq=NULL)
# sum(a) { x[a] } == sum.portfolio
Constraints <- linear.constraint.eq(Constraints, c(1:model$assets), model$sum.portfolio)
# sum(a) { x[a] * mean[a] } => min.mean
if(!is.null(model$min.mean)) { Constraints <- linear.constraint.iq(Constraints, c((ix_x):(ix_x+model$assets-1)), -model$min.mean, -1*model$asset.means) }
# sum(a) { x[a] * mean[a] } == fix.mean
if(!is.null(model$fix.mean)) { Constraints <- linear.constraint.eq(Constraints, c((ix_x):(ix_x+model$assets-1)), model$fix.mean, model$asset.means) }
### Bounds
Bounds <- list()
Bounds$lower <- model$asset.bound.lower
Bounds$upper <- model$asset.bound.upper
### Solve optimization problem using modopt.quadprog
solution <- quadprog(Objective$quadratic, Objective$linear, Constraints$A, Constraints$b, Constraints$Aeq, Constraints$beq, Bounds$lower, Bounds$upper)
### Add optimal portfolio to model
portfolio <- list()
portfolio$x <- solution$x
portfolio$x <- round(portfolio$x, model$precision)
model$portfolio <- portfolio
return(model)
}
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