Why is the function PORTOPT from the Financial Toolbox 3.5 (R2008b) unable to find portfolios to satisfy given constraints?

I run PORTOPT after specifying some constraints with PORTCONS function. I also specify a minimum asset allocation in the 'Custom' option of PORTCONS. I get the following error message when I run PORTOPT:

??? Error using ==> portopt at 260

No portfolios satisfy all the input constraints

This seems fine.

Now if I omit the last constraint, PORTOPT runs fine and I notice that some results seem to satisfy the last constraintl. This seems to contradict error message above.

Answer 1

[MathWorks Support Team]

The first step in PORTOPT finds a point at the top of the efficient frontier. This is a linear programming problem that uses LINPROG which sometimes fails for problems with really tight or "unusual" constraints.

To work around this issue, bound all the weights from above, and relax the constraints very slightly, PORTOPT calls LCPROG (instead of QUADPROG), which may work better for the problem. You can relax the constraints, for example, by changing the constraints weight_i=0 to 0 <= weight_i <= smallTol