Propositional Logic

Developing a trading strategy first requires one to categorize events, or one particular event, within a "set". From there, a decision tree can be made assuming an event fits into the proposition, and various actions (trades) develop from evaluation of the tree.

A simple example is of the form:

If P, then Q.

P.

Therefore, Q.

A trading situation that takes this form is:

If the 'Stock is going up', then 'It is bullish'.

'Stock is going up.

Therefore, It is bullish.

From there, another conditional claim, resulting in a trade entry can be produced:

If the 'Stock is bullish', then 'Buying it "low" will result in profit'

This form of argument is called Modus Ponens, and in the formal notation of propositional logic is described by:

I've been using this structure in designing my trading algorithms (as well as the inverse), but have run into an interesting challenge, that I assume you may have as well. The crux of the challenge is that trading strategies are relying on assumptions of consequent "momentum" or "mean reversion" or in the case of statistical arbitrage "convergence" or "divergence" for profit.

But to properly anticipate these consequences requires one to properly assess the market forces (the "regime") in power at that period of time. For example, if you buy a stock every time volume goes up by a significant amount, this will work in a regime of momentum. However, in a regime of mean-reversion, this will most likely lead to losses.

So what's the solution? My last two optimization posts were different breeds. Volatility optimization was "entry selectivity", so it confirmed or denied establishing a position. Stop-loss optimization was "exit selectivity", so it managed an open trade based on price performance. It appears to me now that I have to pursue further depth in the logic of strategy development. My strategies need to establish a better assessment of market regime.

The strategies I have now are marginally net profitable across my testing set, but not yet desirable in terms of robustness across cross-sections of time. For example, in a 30 trading day set, it performs well in certain time frames (like 5 or 10 day), but draws down in other time frames. I want to see if I can produce a strategy that is profitable "within any 10-day time frame" or have a similar strong performance metric. How do I prevent the draw-downs?

I believe I have to produce a "higher order function" over the strategy. Volatility optimization was already higher order over the null, but future development has to proceed farther.