fPortfolio and leverage

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

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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