In the previous post I showed how one can implement “regime” switching to create a strategy that switches between a mean-reverting and a momentum sub-strategy.
Can we do something similar (or better) using Fuzzy Logic?
Here’s the setup: (here for some Fuzzy Logic backround)
We create a basic membership function for the RSI(2) indicator: “Low”, Medium” and “High” We create a basic membership functions for the Correlation* indicator: “Low”,”High”.
We implement these rules: 1.//mean revert – LOW Autoccorelation IF “rsi” is “Low” AND “autocorrel” is “Low”, “Action”, 1 ; //Buy IF “rsi” is “High” AND “autocorrel” is “Low”, “Action”, -1 ; //Sell
//MOM – HIGH Autocorrelation IF “rsi” is “Low” AND “autocorrel” is “High”, “Action”, -1 ; //Sell IF “rsi” is “High” AND “autocorrel” is “High”, “Action”, 1 ; //Buy
Here’s the Equity:
Conclusion: As with Regime switching we can use Fuzzy Logic to solve the problem of using one strategy for trading pre- and post-2000 SP500. Furthermore, we have more robust and less specific rules to deal with (buy on “Low” RSI rather than Buy=RSI2<30).
————— *By “Correlation Indicator” I am referring to the 22-day Correlation (see previous post) between the current return and the previous day’s return. In Amibroker Code: Dayreturn=ROC(C,1); AutoCor=Correlation(Dayreturn,Ref(Dayreturn,-1),22);
Let us consider two possible ways to trade the SP500.
1. If the index falls today, we buy tomorrow at the open. This is a “mean-reversion” strategy.
2. If the index rises today, we buy tomorrow at the open. A “follow-through” strategy.
From the graphs below, we can see that neither of these strategies worked well from 1960 to today.
Mean Reversion Trading On SP500
Follow-Thru (momentum) trading on SP500
Let’s introduce a qualifier that will tell us which strategy to trade at what time.
We will try the most basic one: The correlation between today’s return (close to yesterday’s close) to the previous day’s return. If it is negative we ‘ll use a contrarian logic. If the correlation is positive we ‘ll use a momentum logic.
The indicator of choice is the 2-period Relative Strength Index (RSI).
So if correlation between yesterday’s and today’s return is less than zero we buy on a correction. Otherwise we buy on strength. We trade at the next Open.