[R-SIG-Finance] fPortfolio and leverage

Thu Aug 21 15:41:09 CEST 2008

Brian,

You are right. But I was thinking of a slighly different setup for the
problem. Say you want to leverage at different levels for each of the
assets, with only a global risk target as goal. I thought that the easiest
way out was to leave that to the portfolio optimizer. My assets are not
equities and I assume they are traded on margin.

I believe that approach was taken, for instance, in "Portfolio optimization
with drawdown constraints" Checkhlov, Uryasec and Zabrankin.

From the paper:

"As for the technological constraints (8), we chose x_min = 0.2 and x_max
=0.8  . This choice was
dictated by the need to have the resultant margin-to-equity ratio in the
account within admissible
bounds, which are specific for a particular portfolio. In this futures
trading setup, these
constraints are analogous to the “fully-invested” condition from classical
Sharpe-Markowitz
theory. They define bounds on the leverage of the strategy and make an
efficient frontier to be
concave. If all positions are equal to the lower bound 0.2, then the sum of
the positions equals
0.2 ×32 = 6.4 and the minimal leverage equals 6.4. However, if all
positions are equal to the
upper bound 0.8, then the sum of the positions equals 0.8× 32 = 25.6 and
the maximal leverage
equals 25.6. The optimal allocation of weights picks both the optimal
leverage and proportions
between instruments."

Cheers,

// Giuseppe

             "Brian G.                                                     
             Peterson"                                                     
             <brian at braverock.                                          To 
             com>                      Giuseppe1 MILICIA/IBEU/HSBC at HSBC    
                                                                        cc 
             21/08/2008 14:31          r-sig-finance at stat.math.ethz.ch     
             Mail Size: 5454                                       Subject 
                                       Re: [R-SIG-Finance] fPortfolio and  
                                       leverage                            
                                                                    Entity 
                                       Investment Banking Europe - IBEU    

your example can still account for leverage.

the w vector can be interpreted as percentage allocations from your
total dollars to invest.

Your leverage is unconstrained from the optimization.  Whether you have
100 euros to invest or 200 million euros to invest, you will still apply
the weights from the output of the optimization.

Regards,

   - Brian

giuseppe1.milicia at hsbcib.com wrote:
> Guys,
>
> I'm playing a bit with fPortfolio and looking at the examples and unit
> tests, it seems that the weights returned always sum up to 1.
>
> I was wondering whether there is a way to have a leveraged portfolio with
> weights summing up to W > 1. Say I target a certain risk level R and I
want
> the weights to be totally unconstrained. From the docs I see that
> Constraints = "Short" should given me unconstrained weights:
>
> "Short": This selection defines the case of unlimited short selling. i.e.
> each weight may range
> between -Inf and Inf. Consequently, there are no group constraints. Risk
> budget constraints are
> not included in the portfolio optimization.
>
> But, say if I try this:
>
> # Load Data and Convert to timeSeries Object:
> Data = as.timeSeries(data(smallcap.ts))
> Data = Data[, c("BKE", "GG", "GYMB", "KRON")]
> Data
>
> # Set Default Specifications:
> Spec = portfolioSpec()
> Spec
>
> setTargetAlpha(Spec) = 0.6
>
> # Allow for unlimiConstraints = "Short"ted Short Selling:
> Constraints = "Short"
>
> # Compute Short Selling Minimum Variance Portfolio
> frontier = portfolioFrontier(Data, Spec, Constraint)
>
> I seem to get always weights adding up to 1, no matter what I do...
>
> I tried:
>
> frontier = portfolioFrontier(Data, Spec, "maxsumW[1:22]=2")
>
> Weights add up to 1 again.
>
> frontier = portfolioFrontier(Data, Spec, "minsumW[1:22]=2")
> frontier = portfolioFrontier(Data, Spec, "minsumW[1:22]=0.1")
>
> The last two calls give back no portfolio. I wonder why? Is it no
possible
> to be leveraged/under invested?
>
> I can't find anything of that sort on the unit tests either.
>
> Cheers,
>
> // Giuseppe

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