# [R-SIG-Finance] maxratioPortfolio

Diethelm Wuertz wuertz at itp.phys.ethz.ch
Mon May 11 03:08:18 CEST 2009

```Michael Schulman wrote:
> Hi,
>   First wanted to thank everyone for a lot of very good hard work done on R and the subsequent packages.
>
>   So I've been looking at the maxratioPortfolio code in fPortfolio.  One thing I notice is how the range is decided for the search.  It looks like the range is decided by passing "interval = range(getMu(Data))"  While this works well in a completely unrestrained situation it does not work when there are constraints.  To give an example.  I am trying to optimize a portfolio with 3 assets with the following constraints :
>
> c("minW[1:nAssets] = -0.5", "maxW[1:nAssets] = 0.5", "eqsumW[1:nAssets] = 1e-7", "Partial")
>
> In other words I want a dollar neutral portfolio with no weight greater or less than .5, -.5 respectively.  As a side note having to pass in 1e-7 is somewhat counterintuitive but I could not find another way as passing in 0, removed that constraint.
>
> My mu and sigma are :
>
> \$mu
>            S           VZ            T
>  0.007075173 -0.001899547 -0.001357274
>
> \$Sigma
>              S           VZ            T
> S  0.008534089 0.0015257184 0.0015642080
> VZ 0.001525718 0.0009147493 0.0008163796
> T  0.001564208 0.0008163796 0.0009165100
>
>
> Now just taking the min and max of my mu as the range is wrong.  They are not feasible portfolios as I can not allocate 100% to that.  In general in other optimizers I've seen the range is decided by solving for the max return given the constraints and no constraint on the variance.  Its usually a simple linear programming problem.
>
Also in the most generic case for a non linear objective? I think no.

> In my case the weights would be 0.5, -0.5, 0 to get me the maximum returns within my portfolio and within my constraints.
>
> Sorry if anything above is incorrect, out of context, or just stupid.   I'm fairly new to R so I have no doubt I'm mistaken on many things.
>

For the moment, a quick and dirty fix in this special case  (when we
have a unique solution for the max ratio) is to replace the line

portfolio = optimize(f = ratioFun, interval = range(getMu(Data)),
maximum = TRUE, data = Data, spec = spec, constraints = constraints)

by

portfolio = optimize(f = ratioFun, interval = c(-BIG, BIG),
maximum = TRUE, data = Data, spec = spec, constraints = constraints)

with BIG big enough.

We will check this and take care for a better solution.

Thanks a lot, such examples are really helpful for us.

Diethelm Wuertz

> Thanks... mike
>
>
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>
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```