I've heard ETFs mean revert more than stocks and certain ETFs mean revert more than other ETFs. Is this true? Does prior performance indicate future returns?

I have a mean reversion system I'm backtesting. I ran it with 2400+ symbols (Stocks & ETFs) for the '94-'99 period. It generated 7,732 trades and showed good results (e.g. Sharpe ratio > 1). Then I sorted the symbol list by profit and skimmed off all the profitable symbols. I know if I run just the profitable symbols on the same time period I'll get fantastic results, but that certainly seems like cheating or data fitting. So I took just those profitable symbols (648 symbols), ran the backtest for the period '00-'09 and got worse results, but not terrible (9960 trades).

So, does it make any sense to pick symbols that were profitable in the past? Thanks...

I have two questions and an observation:

1. when you ran the 94 - 99 test, did you optimize the data to get the good results?
2. when you ran both tests did you strip out the market return from your results to look at the performance of your system x the market? obviously, running a test from '00 to '09 give you two massive bear markets through which you are running your test. even if your names are outperforming the market, they could still be falling.

Observation:
you can do a statistical test for mean-reversion. one such test is to construct an Ornstein-Uhlenbeck process -- while the math is over my head, this comes down to doing a regression analysis on the stock's returns as follows:

Predicted Return(t) == K * ( M - S(t-1) ) + error(t)

to solve this somewhat involved formula, one does a very simple regression on the RetToday = Alpha + Beta ( PriceToday ), instead of using prices though, you should use the Log of Prices. So instead

Predicted LogRet(t) == Alpha + Beta * S(t) + Error ( today's log return is a function of yesterday's log price )
then,
Predicted Return(t) == K * ( M - S(t-1) ) + err(t)
== K*M - K*S(t-1) + err(t)
=> K = - Beta --> K is usually referred to as the speed of mean reversion
=> M = Alpha / K --> M is the long run average price around which the name oscillates

if the regression routine used calculates T values for the Alpha and Beta you can test the significance of the results and only consider those names when their T-Value show some amount of statistical significance.

the questions i always have though is even with good results, what are the chances that the good results are just by chance and does having good results in one period predict good results in the next.

You never know that answer, but you can estimate it by the profit distribution, and perform some t-tests. It doesn't take any regression to determine expectancy. I think a better plan is to just test on known indexes, like the NAZ100, WL100, maybe, up to the S&P500.

BTW, mean reversion is based on ratios or lognormal ratios of symbols relative the other. Mean reversion cannot be measured on single securities, but are based on symbols as in the case of a pair trade.

QUOTE:
Mean reversion cannot be measured on single securities

sure it can. here's a paper written by Andrew Lo of MIT where he describes a mean reversion strategy of buying the worst performing stocks each day and shorting the best performing stocks. http://web.mit.edu/alo/www/Papers/august07.pdf

i agree it's natural to think about mean reversion in the context of relative performance, but it doesn't need to be.

QUOTE:
I have two questions and an observation:

1. when you ran the 94 - 99 test, did you optimize the data to get the good results?
2. when you ran both tests did you strip out the market return from your results to look at the performance of your system x the market? obviously, running a test from '00 to '09 give you two massive bear markets through which you are running your test. even if your names are outperforming the market, they could still be falling.

Thanks for the reply ss161: (1) I optimized three variables using an ETF only subset of data. I'm pretty good about not over optimizing. (2) No, I didn't strip out the market return, I'm just using the WLP Performance results. It's amazing tho, the 648 profitable symbols from the first test, had nearly a 10% annual return from '00-present -- in the Buy & Hold column?!? I'm sure some of them are inverse ETFs, but I should look at those 648 symbols more closely.

I'll look at the statistical test some more. My wife would probably understand it...

I've seen that August '07 report before. My little personal quant fund suffered it's worst weekly loss ever that week. It took me a couple of months to recover from that week.

sure. i'm pretty interested in this stuff as well. that sounds like excellent results. it'd be interesting to compare the results of your system with the same system but that also goes short the s&p500 each day to net out any long exposure (assuming the system is net long of course).

here's another link that does a pretty good job of explaining O-U process -- as it relates to prices mean reverting in the electricity markets: http://www.retailenergy.com/archives/shimko2.htm

the second half of the article gives a recipe for implementing O-U process to test for mean reversion.

Steve,

Thanks for pointing out Andrew Lo’s paper. Interesting read.

When some 60% to trading is done by machines, it is required from us traders to understand how these programs function. Quantity and time slicing of trades (scaling in and out) is not new, but in this time and age, traders should be aware of their use and their repercussion on prices.

Good trading.

A few quick points.

In the test set, '94-'99 the averages were essentially up. Does your mean-reversion system go long & short or just long? If only long, the market bias was up possibly leading to better returns. In the out-of-sample we had two ferocious bears and minor bull, and not sure what this latest run will be classified but short term a good run off the bottom. So, if you trained on essentially an upward market and then experienced a few very choppy years your results on the put of sample might be expected.

Also, most ETFs were not launched until December 2008, so your backtest period really did not have enough ETF data except for SPY, MDY, and QQQQ and even the latter two were sparse. In my opinion ETFS do show more mean reversion than stocks. For your test you could go back and train on mutual funds, make sure it is dividend/cap gain adjusted. Mutual funds have many of the same characteristics of ETFs and the data goes back decades.

Mike