# From Regime Switching to Fuzzy Logic -SP500

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).

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*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);

# Simple Regime Switching for SP500

 image from  http://brucekrasting.com/

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.

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.

Here’s the Amibroker Code:
<!–more–>
Dayreturn=ROC(C,1);
AutoCor=Correlation(Dayreturn,Ref(Dayreturn,-1),22);