portfolio optimization: risk parity

[Theodosis Athanasiadis]

hello,

I am trying to code the risk parity algo from the following Python notebook to MATLAB 

https://nbviewer.jupyter.org/github/MOSEK/Tutorials/blob/master/portfolio-riskparity/riskparity.ipynb

I am using MATLAB (2019) and the latest MOSEK. 

I am getting Error(1311): Tyring to append a too big cone.

I am not sure if I define the cones properly. Can you take a look at my code below and tell me what I am doing wrong?

function wgts = erc(n,GT,c,b) 

name = 'symbcon';

[~,~, res] = evalc('mosekopt(name)');

prob = [];

% Objective vector: r-c*b'*t (x,t,r)

prob.c = [zeros(n,1);-c*b;1];

% budget constraint 

prob.a = [ones(1,n),zeros(1,n+1)];

prob.blc = 0;

prob.buc = inf;

% Bounds exclude shortselling (x,t,r)

prob.blx =  zeros(2*n+1,1);

prob.bux = inf.*ones(2*n+1,1)];

% An affine conic constraint: [1, r, GT*x] in rotated quadratic cone

% [ 0  0  0]  [ x ]     [ 1 ]

% [ 0  0  1]  [   ]  +  [ 0 ]  \in Q_r

% [ GT 0  0]  [ r ]     [ 0 ]  

prob.f = sparse( [ zeros(1,2*n+1); [zeros(1,2*n),1]; [GT, zeros(n,n+1)] ]);

prob.g = [ 1; 0; zeros(n,1) ];

prob.cones = [ res.symbcon.MSK_CT_RQUAD n ];

% Logarithmic bounds  (xi,1,ti)∈Kexp

% (1,r,Fx)

%  [ 0  0  0]  [ x ]     [ 1 ]

%  [ 0  0  1]  [   ]  +  [ 0 ]  \in Q_r

%  [ GT 0  0]  [ r ]     [ 0 ]  

prob.f = [prob.f; sparse( [ [ones(1,n),zeros(1,n+1)]; zeros(1,2*n+1); [zeros(1,n),ones(1,n),0] ]) ];

prob.g = [prob.g;  [ 0; 1; 0] ];

prob.cones   = [ prob.cones repmat([res.symbcon.MSK_CT_PEXP 3], 1, n)];

% Maximize problem and return the objective value

[rcode,res] = mosekopt('minimize echo(0)', prob, []);

wgts = res.sol.itr.xx;

end

[Michal Adamaszek]

Hi,

Towards the end of your code you extend the conic description with 3 rows in f, 3 rows in g, but increase the total dimension of cones by 3n. That's a mismatch.

The quadratic cone to begin with also has a mismatch: f, g have n+2 rows, so you probably want to use n+2 as cone dimension.

So ultimately the error comes from the fact that the total dimension of cones specified in prob.cones is bigger than the number of row s in f.

Michal

[Theo]

Hi Michal,

Thank you for your prompt response. I did fix it and it runs fine but the results I am getting do not look right. 

I believe the error is in the exponential cone. Can you take a quick look at the code and see if you can spot the error?

Theo

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[Theo]

actually I think it is correct now 

On Tue, Feb 16, 2021 at 12:27 PM Theo <theodosis.a...@gmail.com> wrote:

I think my exponential cone was wrong. I think I fixed it. It runs fine but the results dont look correct. Please disregard the previous code and use this one 

On Tue, Feb 16, 2021 at 3:05 AM Michal Adamaszek <michal.a...@mosek.com> wrote:

[Theo]

I think my exponential cone was wrong. I think I fixed it. It runs fine but the results dont look correct. Please disregard the previous code and use this one 

On Tue, Feb 16, 2021 at 3:05 AM Michal Adamaszek <michal.a...@mosek.com> wrote: