[R-SIG-Finance] Parma Package QP optimization Failing and Ignoring Leverage Constraint

[alexios ghalanos]

1. This works just fine: (LB and UB should be a vector)
myspec<-parmaspec(S=cov(R),forecast=100*abs(colMeans(R)),LB=rep(-0.05,15),UB=rep(0.05,15),budget=0,risk='EV',riskType='minrisk',target=0.0030346)
mysol <- parmasolve(myspec,type='QP')
+---------------------------------+
|        PARMA Portfolio          |
+---------------------------------+
No.Assets               : 15
Problem                 : QP
Risk Measure            : EV
Objective               : minrisk
Risk                    : 3e-07
Reward                  : 0.0030346

    Optimal_Weights
EWG          0.0293
EEM          0.0206
EWL          0.0174
TLT          0.0120
EZA          0.0107
EWA          0.0107
EPP          0.0106
EWC          0.0094
IWO          0.0061
IWN          0.0051
IWF         -0.0078
EWJ         -0.0214
EWU         -0.0221
IWD         -0.0309
EWQ         -0.0500


2. You've set leverage with a quadratic solver. How do you suppose the
absolute value function can be accommodated in this problem?
This works:
myspec <-
parmaspec(scenario=as.matrix(R),forecast=100*abs(colMeans(R)),LB=rep(-0.05,15),UB=rep(0.05,15),leverage=0.1,risk='EV',riskType='minrisk',target=0.0030346)
mysol <- parmasolve(myspec, type='NLP', w0=rep(0.01,15))
sum(abs(weights(mysol)))

i.e. use a scenario matrix instead and solver as NLP (and make sure to
provide a set of starting weights 'w0').


I suppose I should add more checks/warnings.


Regards,

Alexios



On 30/09/2013 22:52, Preston Li wrote:
> *Can someone please tell me why the following is not giving me a solution?*
> 
> 
> if (!is.loaded('etfdata')) data(etfdata)
> 
> R = timeSeries::returns(etfdata)
> 
>> myspec <-
> parmaspec(S=cov(R),forecast=100*abs(colMeans(R)),LB=-0.05,UB=0.05,budget=0,risk='EV',riskType='minrisk',target=0.0030346)
>> mysol <- parmasolve(myspec,type='QP')
>> mysol
> 
> +---------------------------------+
> |        PARMA Portfolio          |
> +---------------------------------+
> No.Assets               : 15
> Problem                 : QP
> Risk Measure            : EV
> Objective               : minrisk
> Risk                    : NA
> Reward                  : NA
> 
> Error in Math.data.frame(list(Optimal_Weights = logical(0)), 4) :
>   non-numeric variable in data frame: Optimal_Weights
> 
> *Whereas if I do the following I get a solution (and why is the "leverage"
> constraint ignored?):*
> 
>> myspec <-
> parmaspec(S=cov(R),forecast=100*abs(colMeans(R)),LB=-0.05,UB=0.05,budget=0,risk='EV',riskType='optimal',leverage=0.1)
>> mysol <- parmasolve(myspec,type='QP')
>> mysol
> 
> +---------------------------------+
> |        PARMA Portfolio          |
> +---------------------------------+
> No.Assets               : 15
> Problem                 : QP
> Risk Measure            : EV
> Objective               : optimal
> Risk                    : 3e-07
> Reward                  : 0.0030346
> 
>     Optimal_Weights
> EWG          0.0293
> EEM          0.0206
> EWL          0.0174
> TLT          0.0120
> EZA          0.0107
> EWA          0.0107
> EPP          0.0106
> EWC          0.0094
> IWO          0.0061
> IWN          0.0051
> IWF         -0.0078
> EWJ         -0.0214
> EWU         -0.0221
> IWD         -0.0309
> EWQ         -0.0500
>> sum(abs(mysol at solution$weight)/2)
> [1] 0.1321498
> 
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> 
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