Flirting With Models

There is quite a bit written about the 6-1 momentum model, which ranks investments by their previous 6 month return, minus the previous 1 month return, and holds for 1 month.

The idea behind the method is that average returns over the long run should be stable in the short run, made superior by taking into account short-term reversionary factors.

To explore this concept and see exactly how stable the 6-1 model is, I explored 30 diverse ETFs (equities, commodities, currencies, bonds, et cetera) over a period of 400 days, changing my momentum, reversion, and prediction periods.

To begin, I transformed adjusted closing prices into cumulative log returns.
I calculate the prediction returns as follows (in matlab syntax):

pastReturns = (cumulativeReturns(today, :) - cumulativeReturns(today-n, :)) - (cumulativeReturns(today, :) - cumulativeReturns(today-m, :));

and the future returns as

futureReturns = (cumulativeReturns(today+p, :) - cumulativeReturns(today, :));

I then sort both sets of returns and calculate the difference between their sorted order to get the total estimation error

[v, idx] = sort(returns);
[v, futureIdx] = sort(futureReturns);
error = sum(abs(idx - futureIdx));

I do this, looping through n, m, and p. To generate the total error for a given (n,m,p) tuple, I loop through all available days, compute the prediction error for that day, and average the errors.

The results are visualized as follows (please note, axes must be scaled by a factor of 5 and that the data base been interpolated to fill in missing spots):

To me, there are two very intriguing things about this visualization.

First, there seems to be a region of stability (or am I just seeing what I want to see?) in the 90-110 day momentum, 25-50 day reversion, and 20-30 day prediction area, indicating that there may be some validity to the 6-1 momentum method. However, it is not the ONLY region of stability, bringing into question its validity.

Secondly, the line where the momentum look-back period equals the reversion look-back period (i.e. when there is NO prediction data and all stocks are expected to perform equally well), we get the minimum error. However, to keep a consisten equal balance in the portfolio would incur incredibly high turn-over, and I suspect that the benefit of this error decrease would actually be more costly due to trading costs & slippage.

So while 6-1 may out-perform buy and hold, it seems that a constantly equally rebalancing portfolio may be worth exploring further.