Flirting With Models

Now if we check our prediction error, where returns are sorted relative to their variance over the period the returns were generated, we see more stability.

However, at the end of the day, we are only working with ~30 assets. So let’s look at the 6-1-1 region (which seems relatively stable). We are effectively looking at an error of ~(265/30)=8.3 per asset. i.e. The mean prediction error in index for each asset, at each step, is about 8.3 spots. That … isn’t very good. In fact, that is about 25% of the assets…

Perhaps if instead of predicting the exact index, we looked at deciles?

Do I spy, with my little eye, stability at 12-1 and 6-1?

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.