topic Re: portfolio optimization under nonlinear constraint in SAS/IML Software and Matrix Computations

portfolio optimization under nonlinear constraint

JANET1987 — Thu, 06 Oct 2016 18:26:18 GMT

Hello,

In this program I’m trying to maximize portfolio skewness under constraints.

Nevertheless , I have one more problem. In my case, I have one linear constraint and one Nonlinear constraint (quartic constraint about portfolio kurtosis which is less than a scalar). As I understand while reading chapter 14 about Nonlinear optimization examples, I must use NLPQN instead of NLPNRA! IS that sufficient?

In the other hand, I still think about the mining of “optn”! and if x0 must take always only two initial values?

Finally, I want to state decision variables wi as positive, I question whether it been subject to a further constraint.

Sorry for those lots of questions. Thank you in advance!

proc iml;

M3 = {32 -7 -7 -8,

-7 -8 -8 17};

start skpf(p) global(M3);

w = p`; /* w is column vector */

return w` * M3 * (w@w);

finish;

/* specify linear constraints */

con = { 0 0 . ., /* min w[i] */

1 1 . ., /* max w[i] */

1 1 0 1}; /* sum(w) = 1 */

x0 = {0.5 0.5};

optn = {1 /* maximize objective function */

1 }; /* summarize iteration history */

call nlpnra(rc, xOpt, "skpf", x0, optn, con);

maxVal = skpf(xOpt);

print rc, xOpt maxVal;

Re: portfolio optimization under nonlinear constraint

Ksharp — Fri, 07 Oct 2016 04:33:36 GMT

Yes. If you have nonlinear constraint , you have to switch into NLPQN.

if you have three assets , then you have to have three initial value for x0.

con={} already constraint 0<= w1 ,w2 <=1,

if you have nonlinear constrain condition,you need add one more option in it.

Re: portfolio optimization under nonlinear constraint

JANET1987 — Mon, 10 Oct 2016 09:48:11 GMT

Hello,

Thank you very much! Your recommandations are highly appreciated. I'm still trying to solve the problem.

Re: portfolio optimization under nonlinear constraint

JANET1987 — Mon, 10 Oct 2016 15:04:25 GMT

Hello,

Sorry, but what about if I have 500 assets, should I have 500 initial values for X0?

thank you in advance

Re: portfolio optimization under nonlinear constraint

Ksharp — Tue, 11 Oct 2016 11:24:39 GMT

Yes. I think so .

You can easily define it as

x0=j{1,500,1}/500;

Re: portfolio optimization under nonlinear constraint

JANET1987 — Tue, 11 Oct 2016 14:46:49 GMT

Great!!! Thank you so much!