September 27th, 2004, 3:45 pm
I put together something for you to play with. According to this theory of recurring phenomena and trader learning as I laid it out, you could jump to a couple of hypotheses:1) Simple, high-frequency patterns - the things that happen every minute like higher highs - shouldn't work, because they will be so obvious that everyone quickly figures them out.2) Complicated, high-frequency patterns - such as an intraday consolidation coincident with a runup and selloff in other instruments - shouldn't work, because these oddities won't keep happening or last very long.3) Simple, low-frequency patterns - things that only happen once a year - should work because they are simple enough to keep happening, but because it will also take a while for people to notice them.So I put together a crude test to see if simple patterns, such as breakouts, 1) recurred, and 2) recurred for longer the lower their frequency, meaning the longer it took for people to get used to them and learn to trade them. I applied a strategy of buying a new high close, and selling a new low close, to a sloppy gold chart going back to the 1970's. I tried buying or selling the close when it was higher or lower than 1) yesterday's close, 2) the highest or lowest close of the last 2 days, 3) the highest or lowest close of the last 4 days, 4) the highest or lowest close of the last 8 days, and 5) the highest or lowest close of the last 16 days. Here is a rough plot of the profits to the same strategy at different frequencies, over the last 30 years:What we are hoping to see is a starting point, or some time period where the strategy works at all five frequencies. Of course this period could be to the left of our chart, so that the experiment begins after they all stop working. But in general, the highest-frequency strategy could only make money for the shortest periods, whereas the lowest-frequency strategy could make money for longer periods, since people have the fewest examples, and the fewest recent examples, of it actually making money.What we do see, is that I got lucky. The lowest-frequency 16-day strategy kept making money, or at least not losing money, the longest. And the highest frequency 1-day strategy, lost the most money. The only strategy really out of order was the 2-day strategy, which made more money than the 4-day strategy or the 8-day strategy.You could say, well, this order of profitability is similar to the one predicted, but it also could have been produced at random, and your methods were crude. But something to consider, is that the highest-frequency 1-day strategy should actually be expected to make more on paper, since it will have to make more money on paper before someone can make money in real life after commissions and slippage. In other words, a strategy which requires me to buy or sell a 100 million dollars worth of some commodity every day, will have to make more money on paper than one that lets me spread out my orders, to make money in practice.So if a low-frequency strategy works on paper, people will trade it until it stops working. If a high-frequency strategy works on paper, people might not be able to trade it since the commissions are too high. So the high-frequency strategy which nobody can actually trade - since no one can guarantee himself the closing price every day - should continue to work on paper. For example, consider that S&P futures trade back and forth at a .25-point increment, very predictable. On paper, you could effectively buy at the bid and sell at the offer, by buying at close of every minute that was a downtick, and selling at the close of every minute that was an uptick. You would make a zillion dollars a day, on paper. But if you were limited to buying or selling only once every day and holding all day, these imaginary profits would disappear.So my chart above, in theory, should show more imaginary profits for the high-frequency strategy which we couldn't actually trade, than for the more realistic buy-and-hold strategy. Paper profits should equal commissions, and should therefore be larger at higher frequencies. But instead, it shows profits consistent with my "theory of trader learning" completely canceling out and reversing this effect. To test whether this result is just sloppy random nonsense, you could run the same experiment on copper, deutschmarks, yen, and other instruments than just gold.