I introduced the notion of momersion in a recent article. In this article I present an indicator of momersion along with simple code for Amibroker.

The Momersion indicator measures momentum and mean-reversion over a specified lookback period n. It is an oscillator (0 – 100) that is calculated as follows:

Momersion(n) = 100 × MOMc/(MOMc+MRc) (1)

where MOMc is a count of momentum and MRc is a count of mean-reversion, calculated as follows (pseudocode):

For lookback period n

MOMc = 0

MRc = 0

For i = 1 to n do

{

If r(i) × r(i-1) > 0 then inc(MOMc)

If r(i) × r(i-1) < 0 then Inc(MRc)

}

}

Momersion(n) = 100 × MOMc/(MOMc+MRc)

where r(k) is the kth arithmetic return.

Below is code for Amibroker. Copy and paste the code in a new formula.

//Momersion indicator, © 2015 Michael Harris. All Rights Reserved.

//For more details visit: https://www.priceactionlab.com/Blog/2015/08/momersion-indicator/

//N is the lookback period

//Ret is the one-period return

//MOM is vector of momentum

//MR is vector of mean-reversion

//MOMC is the count of momentum MOM in lookback period

//MRC is the count of mean-reversion MR in lookback period

//Momersion is fraction of momentum in a lookback period (x 100)

N=Param(“Period”,252,0,3000,1,0);

Ret=ROC(C,1);

MOM=IIf(Ret*Ref(Ret,-1)>0,1,0);

MR=IIf(Ret*Ref(Ret,-1)<=0,1,0);

MOMC=Sum(MOM,N);

MRC=Sum(MR,N);

Momersion=100*MOMC/(MOMC+MRC);

Plot(50,””,colorBlack,styleLine,styleNoLabel);

Plot(Momersion,”Momersion(“+N+”)”,colorBlack,styleLine,styleNoLabel);

Below is a chart of Momersion(250) for S&P 500 index from 01/1989 to 08/11/2015.

When the Momersion(n) indicator is below the 50% line, price action is dominated by mean-reversion and when it is above it, it is dominated by momentum. It is clear that other than a recent surge for a short period after 2011, with the help of a lot of quantitative easing, momentum died around the peak of the tech bubble market. A few remarks:

There can be trends in mean reverting mode, as in the 2000s

Trend-following works also with trends that occur in mean-reverting mode

When mean-reversion dominates, the probability of extreme events is high

After 2011 the market is in a state of “momersion”

The most challenging markets to trade are those that are in a state of momersion, i.e., they dynamically change from momentum to mean reversion constantly.

Article updated September 19, 2020, with Amibroker code and a new chart.

Charting and backtesting program: Amibroker

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