http://quantlib.414.s1.nabble.com/random-generation-of-constrained-portfolio-allocation-weights-tp3309p3311.html
What's the old quote about most things in computer science can be solved with a level of indirection :-) Strikes again.
I too am unsure of the biases due to the nature of the conditional generation. I'm not sure if the shuffling is masking or solving the bias problem. A correct way would be to sample each variate from a correct conditional distribution... but that sounds like hard work and is not in the spirit of a lazy Monte Marlo whilst you brew the coffee ;-)
Indeed. If the number of portfolios to be generated is small, raw Monte Carlo will be less powerful than other methods anyway. You'd want to start thinking about a monte carlo grid method or some such.
Yep, it can. You can shuffle, or redirect to, functional constraints for the each variate as well. That is, if you may have a vector of functions that takes the sum so far, or whatever other conditions are required, then this can be used for the generation of each variate.
But I'm just making this up as I go along. Sounds plausible enough though.
> -Mario
>
> ----- Original Message -----
> From: "Hurd, Matthew" <
[hidden email]>
> To: "ML" <
[hidden email]>; "Hurd, Matthew" <
[hidden email]>;
> <
[hidden email]>
> Cc: "Ferdinando Ametrano" <
[hidden email]>
> Sent: Thursday, September 09, 2004 12:38 AM
> Subject: RE: [Quantlib-users] random generation of constrained portfolio
> allocation weights
>
>
> > 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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