# Optimal trading given frequently delivered directional forecast

I am interest in trading by optimally exploiting a directional forecast given by an oracle.

The oracle predicts directionally the price of an asset (higher or lower than at the moment of forecast delivery) in a forecast horizon H, say 180 minutes. The forecast is delivered several times within a single forecast horizon: it is delivered every D minutes, say, 20.

It is known that:

• The oracle is correct a certain fraction of the time, say 60%.

Furthermore, let's make the simplifying hypothesis that:

• The distribution of the absolute value of the realized price change is the same for all 4 pairs: [predicted up - right, predicted up - wrong, predicted down - right, predicted down - wrong]

A trivial strategy to exploit this oracle would be to treat every single forecast independently, and execute a trade in the direction of the forecast at every delivery, closing each order after its forecast horizon has expired.

Nevertheless, the forecasts predict quantities that are all but independent of one another (consecutive price points of the same asset at a frequency of 1/D). The forecast formulated at time T-D, for example, is relevant information when deciding what to do at time T, because it informs about the price at T+H-D, which in turn is very much predictive of the price at T+H.

How can I exploit completely all the relevant information available? I tried looking into reinforcement learning techniques such as Temporal Difference Learning, but I can't find the perfect fit. Where should I look?

• The area that handles these sorts of problems is market microstructure. Have you looked through the market microstructure literature? This seems like simple execution optimization a la Bertsimas and Lo (1998) or Almgren and Chriss (2001). Also: You should consider that your trading will help others learn the oracle information as in Kyle (1985). Aug 16, 2020 at 2:19
• Thank you for the pointer, I tried looking into that. I mainly found modifications to the classical contributions you listed, in which a central point is market impact and then they try to integrate signals in the MJB equations. This is interesting for institutional investors but is overkill for me. In the meantime, I discovered I can model my problem as a Markov Decision Process (MDP) tailored to the information I have on the stochastic processes involved, and find an optimal policy to this idealized setting. Aug 20, 2020 at 7:29
• I do not think those models are overkill: they model almost exactly your situation. You assume you will not have price impact, but alpha worth acting upon or illiquidity both make that a poor approximation. (I've seen this even for "small" trades.) Some models have a noisy signal (like yours); for some it's an easy modification. The key is to use a strategic trader model to allow for price impact. MDPs are useful (hence my recommending Puterman elsewhere) but they are already used in the microstructure literature -- so your problem may already have been solved. Aug 20, 2020 at 15:15