[R-SIG-Finance] fPortfolio and leverage

Thu Aug 21 19:12:22 CEST 2008

Brian,

I don't think you can remove the target alpha. When you create a portfolio
spec, it's there by default.

I tried the constraints you mentioned:

frontier = portfolioFrontier(Data, Spec,
c("minsumW[1:22]=0.5","maxsumW[1:22]=2"))

and

frontier = portfolioFrontier(Data, Spec,
c("minW[1:22]=0.2","maxW[1:22]=0.6"))

which puts the constraints on the single weights.

In the second case there is no solution. In the first again all the weights
add to 1

I debugged the whole thing and it seems that .setBoxGroupConstraints fixes
a budget constraints forcing the weights to add up to 1. It seems that the
constratin sum(w_i)=1 is added automatically and cannot be removed.

I guess I should really set up the QP problem myself if I want to
experiment with the sort of thing... :(

Cheers,

// Giuseppe

             "Brian G.                                                     
             Peterson"                                                     
             <brian at braverock.                                          To 
             com>                      Giuseppe1 MILICIA/IBEU/HSBC at HSBC    
                                                                        cc 
             21/08/2008 16:16          r-sig-finance at stat.math.ethz.ch     
             Mail Size: 7779                                       Subject 
                                       Re: [R-SIG-Finance] fPortfolio and  
                                       leverage                            
                                                                    Entity 
                                       Investment Banking Europe - IBEU    

The Chekhlov, Uryasev, and Zabarankin paper you reference can be found
here:

http://www.ise.ufl.edu/uryasev/drawdown.pdf

for anyone else who is playing along.

Note how on page 8 of the paper, which you quote, they set limits on the
total weight range to develop a particular leverage model, but not on
the alpha or performance of the model.

So, to your original example:

# Load Data and Convert to timeSeries Object:
Data = as.timeSeries(data(smallcap.ts))
Data = Data[, c("BKE", "GG", "GYMB", "KRON")]

# Set Default Specifications:
Spec = portfolioSpec()

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 not possible to be leveraged/under invested?

This suggests that you should remove your setTargetAlpha constraint, and
see what the optimizer does only with constraints of maxsumW[1:22]=2
*and* minsumW[1:22]=0.1, which I believe can be specified in your
portfolioSpec() call.

Regards,

   - Brian

giuseppe1.milicia at hsbcib.com wrote:
> 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 wrote:
>> 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.
<...>

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