I'm looking to optimize a portfolio maximizing expected return for a particular risk budget, but with absolute constraints on the individual instrument positions.

I've been experimenting with QP, but I was wondering if anyone could guide me to a suitable solution?

  • 1
    $\begingroup$ When you say absolute constraints, what exactly do you mean? For instance, you could mean the positions are between -10% and +10% or you could mean that you take the absolute value of all the positions, sum them up and see it is equal to or less than some number. $\endgroup$
    – John
    Aug 23, 2013 at 16:22
  • $\begingroup$ I'm aware that the problem might be a bit unorthodox, but I mean absolute in terms of dollar market value. $\endgroup$
    – user5980
    Aug 27, 2013 at 8:33
  • $\begingroup$ Your response does not clarify anything. The first thing I mentioned is completely basic (and equivalent to the absolute value of individual positions being less than 10%). It is the same as just putting lower and upper bounds on the variables and every QP optimizer I've seen allows it. The second is called a booksize constraint and requires more work to set up. You basically have to create auxiliary variables (with appropriate constraints) that represent the positive values and the negative values of the securities separately. Then just add together. $\endgroup$
    – John
    Aug 27, 2013 at 14:45


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