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fPortfolio - Maximum Return Portfolio

5 messages · Yaakov Moser, Diethelm Wuertz

Original
Yaakov Moser
# 
Can anyone suggest a simple way to find the maximum return portfolio on 
an efficient frontier with fPortfolio?

Without constraints, this is simply the asset with the highest return.
However, with constraints, it needs to be solved.

The only option I have come up with so far is to use the 
portfolioFrontier function (ideally with a large number of points), and 
then take the end one.
However, this point varies depending on how many points were selected in 
the Spec...

As far as I can tell, there is no built in functionality equivalent to 
the minriskPortfolio.

Thanks

Yaakov
Diethelm Wuertz
#
Yaakov Moser wrote:
That's true.

It is quite difficult to find the end of the frontier with constraints. 
To find the endpoint of the frontier, one has to go along the frontier 
with the function portfolioFrontier which can even fail if the constraints
are to restrictive, since then no solution can be found by the solver.

Maybe a nested interval solver can help:  take the return of the minimum 
global risk portfolio, the return of the endpoint of the (unconstrained) 
frontier, and the point of the return in between. When the intermediate 
point exists go up the frontier, otherwise go down the frontier, repeat 
this until you have the desired precision. Use the R function try() to 
find out if the intermediate point fails or not.
After a few steps one should have reached the endpoint of the frontier.

Has anybody a better and/or faster (more efficient) algorithmic (maybe 
analytic) solution to find the frontier endpoint under constraints?

There may be another problem which I often observed, that the solver may 
become unstable close to the endpoint of the constrained frontier.
Has anybody a good argument why this may happen and how to circumvent this?


Diethelm
That is true, a first implemetation can be done easily along the recipe 
given above.
Diethelm Wuertz
#
Yaakov Moser wrote:
There may be a faster solution (compared to my previous email), just 
look for the portfolio with the highest risk, i.e. the lowest negative 
risk. That can be easily implemented
by reversion of the sign of the objective risk function in the portfolio 
optimization.
Yaakov Moser
# 
I tried reversing the sign by redefining a maxriskPortfolio function 
based on the minriskPortfolio as you suggested.

I changed the one line to be:

targetRisk = -ans$objective


The function ran - and found something close to the maxriskPortfolio, 
but it is not the end of the efficient frontier...

My constraints were long-only, so it should have been 100% in one asset, 
but it turned out to be 99.54% only, with the rest elsewhere.


Any suggestions?


See sample program below.


Thanks


Yaakov


library(fPortfolio)
Data=SMALLCAP.RET
Data=Data[,c(1:3)]
Spec=portfolioSpec()
constraints="long-only"
maxriskPortfolio <- function (data, spec = portfolioSpec(), constraints 
= "LongOnly")
{
    Data = portfolioData(data, spec)
    data <- getSeries(Data)
    targetRiskFun <- function(x, data, spec, constraints) {
        setTargetReturn(spec) = x[1]
        Solver = match.fun(getSolver(spec))
        ans = Solver(data, spec, constraints)
        targetRisk = -ans$objective
        attr(targetRisk, "weights") <- ans$weights
        attr(targetRisk, "status") <- ans$status
        return(targetRisk)
    }
    portfolio <- optimize(targetRiskFun, interval = range(getMu(Data)),
        data = Data, spec = spec, constraints = constraints)
    STATUS = attr(portfolio$objective, "status")
    if (STATUS != 0) {
        cat("\nExecution stopped:")
        cat("\n  The minimum risk portfolio could not be computed.")
        cat("\nPossible Reason:")
        cat("\n  Your portfolio constraints may be too restrictive.")
        cat("\nStatus Information:")
        cat("\n  status=", STATUS, " from solver ", getSolver(spec),
            ".", sep = "")
        cat("\n")
        stop(call. = FALSE, show.error.messages = "\n  returned from 
Rmetrics")
    }
    setWeights(spec) <- attr(portfolio$objective, "weights")
    setStatus(spec) <- attr(portfolio$objective, "status")
    portfolio = feasiblePortfolio(data, spec, constraints)
    portfolio at call = match.call()
    portfolio at title = "Maximum Risk Portfolio"
    portfolio
}
minriskPortfolio(Data,Spec,constraints)
maxriskPortfolio(Data,Spec,constraints)
portfolioFrontier(Data,Spec,constraints)





-------- Original Message --------
Subject: Re: [R-SIG-Finance] fPortfolio - Maximum Return Portfolio
From: Diethelm Wuertz <wuertz at itp.phys.ethz.ch>
To: Yaakov Moser <ymoser at gmail.com>
CC: r-sig-finance at stat.math.ethz.ch
Date: 27 May 2009 10:05:42
Diethelm Wuertz
#
Yaakov Moser wrote:
This works


maxriskPortfolio <-
function (data, spec = portfolioSpec(), constraints = "LongOnly")
{
   Data = portfolioData(data, spec)
   data <- getSeries(Data)
   targetRiskFun <- function(x, data, spec, constraints) {
       setTargetReturn(spec) = x[1]
       Solver = match.fun(getSolver(spec))
       ans = Solver(data, spec, constraints)
       # DW:
       # Take care that the status ans$status is always 0
       #  If the solver fails set the value of the risk to the global
       #    min risk portfolio!
       # Use the function try() that the calculation does not break!
       targetRisk = -ans$objective
       attr(targetRisk, "weights") <- ans$weights
       attr(targetRisk, "status") <- ans$status
       return(targetRisk)
   }
  
   # DW:
   # Take care that the interval range may be large enough if short selling
   # is allowed, that requires an adaption of the range!
   # DW:
   # Increase the tolerance to be sure that optimize has converged!
   portfolio <- optimize(targetRiskFun, interval = range(getMu(Data)),
       data = Data, spec = spec, constraints = constraints,
       tol = .Machine$double.eps^0.5)
     
   setWeights(spec) <- attr(portfolio$objective, "weights")
   setStatus(spec) <- attr(portfolio$objective, "status")
   portfolio = feasiblePortfolio(data, spec, constraints)
   portfolio at call = match.call()
   portfolio at title = "Maximum Risk Portfolio"
   portfolio
}

maxriskPortfolio(SMALLCAP.RET[, 1:3])


-d