QuantLib - RE: random generation of constrained portfolio allocation weights

RE: random generation of constrained portfolio allocation weights

Posted by Hurd, Matthew on Sep 08, 2004; 4:40pm
URL: http://quantlib.414.s1.nabble.com/random-generation-of-constrained-portfolio-allocation-weights-tp3309p3312.html

Mario,

As I mentioned to "randomize the bias" you can shuffle an indirection.

This is what I mentioned in a later mail:
"Intuitively, you can see why as the final measure is likely to be a
biased number as it has to fit into the initial choices. A simple way
of improving the randomness is to shuffle the tuple, i.e. randomly
select the axes to constrain, before allocating the weights. That way
the bias is randomly distributed and hopefully a little nicer."

Code below produces:

0.333351/0.333322/0.333327
Press any key to continue . . .

On my machine, YMMV.

Probably good enough for what you're after. Though disguising bias and eliminating bias aren't necessarily the same thing ;-)

Hope this helps,

Matt.
[hidden email]
+61.419.602148
__________________________________________

#include <iostream>
#include <stdlib.h>
#include <vector>
#include <algorithm>

const int nn = 10000000;

int main() {

std::vector<double> ss(3,0.0);
std::vector<std::size_t> axis(3);
std::vector<double> uu(3);

axis[0] = 0;
axis[1] = 1;
axis[2] = 2;

std::vector<std::size_t>::iterator b = axis.begin();
std::vector<std::size_t>::iterator e = axis.end();

for(int j=0; j<nn; j++) {

// shuffle the indirection, as the rules are the same you could just
// shuffle the values instead which would be quicker

std::random_shuffle( b, e);

uu[axis[0]] = 0.2 + 0.2*(double)(rand()/(RAND_MAX+1.0));
uu[axis[1]] = (0.6-uu[axis[0]])
+(uu[axis[0]]-0.2)
*(double)(rand()/(RAND_MAX+1.0));
uu[axis[2]] = 1.0-(uu[axis[0]] + uu[axis[1]] );

ss[0] += uu[0];
ss[1] += uu[1];
ss[2] += uu[2];
}

std::cout << "\n"
<< ss[0]/nn
<< "/" << ss[1]/nn
<< "/" << ss[2]/nn
<< "\n";

system("pause");
}

> -----Original Message-----
> From: ML [mailto:[hidden email]]
> Sent: Wednesday, 8 September 2004 7:23 PM
> To: Hurd, Matthew
> Cc: Ferdinando Ametrano
> Subject: Re: [Quantlib-users] random generation of constrained portfolio
> allocation weights
>
> Matthew,
>
> I wrote a small piece of code (cf below) to test your suggestion. After 1
> million runs the first moments of the generated numbers are:
>
> 0.30 / 0.35 / 0.35
>
> However, the problem being symmetrical, the first moments should be equal
> (to 1/3).
>
> -Mario
>
> ===========================================================
> #include <iostream>
> #include <stdlib.h>
>
> using namespace std;
>
> const int nn = 1000000;
>
> int main() {
> double ss11 = 0.0;
> double ss21 = 0.0;
> double ss31 = 0.0;
> for(int j=0; j<nn; j++) {
> double uu1 = 0.2+0.2*(double)(random()/(RAND_MAX+1.0));
> double uu2 = (0.6-uu1)+(uu1-0.2)*(double)(random()/(RAND_MAX+1.0));
> double uu3 = 1.0-uu1-uu2;
> // cout << uu1 << "/" << uu2 << "/" << uu3 << endl;
> ss11 += uu1;
> ss21 += uu2;
> ss31 += uu3;
> }
> cout << endl << ss11/nn << "/" << ss21/nn << "/" << ss31/nn << endl;
> }
>
> ========================================================
> ----- Original Message -----
> From: "Hurd, Matthew" <[hidden email]>
> To: "Ferdinando Ametrano" <[hidden email]>;
> <[hidden email]>
> Sent: Tuesday, September 07, 2004 9:05 AM
> Subject: RE: [Quantlib-users] random generation of constrained portfolio
> allocation weights
>
>
> > The below distribution will not be uniformly random (depending on what
> > this means to you), but neither will rejecting illegal cases.
> >
> > Using your [0-40] example:
> >
> > 1. Random first number 20-40. Has to be at least 20 otherwise no viable
> > solution.
> >
> > 2. Next random number to give a sum of at least 60, so the last number
> > may be valid (it has to be <= 40). That is, if the first number is 35,
> > then the second number must be [25-40] to make a viable triple.
> >
> > 3. Obviously, the third number is 100 - sum of the first two.
> >
> > Trivial to generalise.
> >
> > Is that what you're after?
> >
> > Regards,
> >
> > Matt Hurd.
> > _________________
> >
> > Matt Hurd
> > +61.2.8226.5029
> > [hidden email]
> > Susquehanna
> > _________________
> >
> > > -----Original Message-----
> > > From: [hidden email]
> > [mailto:quantlib-users-
> > > [hidden email]] On Behalf Of Ferdinando Ametrano
> > > Sent: Tuesday, 7 September 2004 12:53 AM
> > > To: QuantLib-users
> > > Subject: [Quantlib-users] random generation of constrained portfolio
> > > allocation weights
> > >
> > > Hi all
> > >
> > > I need to generate random weights for a portfolio allocation, with max
> > > constraints on the weights, no short sale allowed (e.g. 3 assets, each
> > one
> > > in the [0%, 40%] range)
> > >
> > > I have no problem for the unconstrained generation, using
> > (quasi)random
> > > sequences of dimension 3 that I normalize so that their sum is 100%.
> > I'm
> > > not sure this approach is on solid theoretical ground, but it works.
> > >
> > > Anyway when it comes to constrained generation many problems arise,
> > and I
> > > haven't found an efficient generation algorithm. Rejection of the
> > > unconstrained portfolio is inefficient, of course.
> > >
> > > Hints, suggestions, thoughts?
> > >
> > > Even better would be a ready to be coded algorithm ;-)
> > >
> > > ciao -- Nando
> > >
> > >
> > >
> > >
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