macrocephalopod

There's a massive gap between how optimization in finance (particularly portfolio optimizers) are viewed by non-experts, and how they are used by practitioners. That gap is responsible for some false beliefs, along the lines of "optimization never works" or ...

"portfolio optimizers always maximize errors" or "optimizers are for dweebs". Wrong! I'll try to explain why. The non-expert view of portfolio optimizers is something like - you have a vector of alphas (expected returns), a covariance matrix, a vector of costs (e.g. spread and

impact), current position x0, and some constraints, and you run a quadratic optimization to find a vector of positions "x" which maximises alpha * x - x' * covariance * x - spread * abs(x - x0) - slippage If you do this naively you will get bad results!

A better approach, the one I use, is to start with a heuristic solution that you know works (i.e. you would make money with it). Then write down an optimization problem that gives you the same result. You're now in a good place because you have a set of parameters for the

optimizer that definitely give a good result, and you can start making changes to the optimizer to try and improve it. One thing optimizers are good at is finding new solutions that are close to existing solutions, but satisfy extra constraints. That means you can change

a parameter, and be sure that the constraints will still be satisfied. That's not generally true if you start modifying a heuristic algorithm - changing one component normally requires changes elsewhere as well.

That's all very vague so let me give an example. You have a vector of signal values "s". Set target positions to be proportional to (s - mean(s)) / sum(abs(s - mean(s))) This has zero net exposure and constant gross book size.