In principle "mean-reversion" is the opposite to "trend-following", but there are many other strange terms in that pedagogical PDF file as well.

The "strange" terms in the PDF - including "mean-reversion" - are standard trader lingo. Traders know what they mean.

Standard lingo is very often misleading exactly because everyone thinks he understands it, but eventually it turns out that every individual had an interpretation of its own. My favourite example is trend itself: so far I have never seen any definition of this phenomenon, and yet traders operate it as if it were well defined.

It doesn't matter that some definitions are not 100% mathematically precise so long as they make money. That's the difference between practice and academia. I write my papers with practitioners in mind, because I am one of them. This paper has over 1900 downloads on SSRN, so evidently people know what "mean-reversion" means. The academic lingo is "contrarian investment strategies", and most traders would have no idea what that means. "Trend" is another one of those academic words. On a trading desk it's called a momentum strategy.

interesting paper. I contribute an additional download counting. ;)

As for the lingo statement, disagree if by academia we mean academic studies on finance (especially for research stream of asset pricing).

"Mean-reversion" is a term from econometrics/statistics, of course widely accepted and used in finance academically. "contrarian investment strategies" is a term defining the industrial strategies, you can see it in the textbook but less frequently in "pure" academic journals.

Similar for the "trend" vs. "momentum". Asset pricing studies on "trend" are more likely to self-identify as topics on "momentum phenomenon".

Actually this is funny... A journal reviewer for this very paper insisted that I use "contrarian investment strategies" instead of mean-reversion because for academics "mean-reversion" is confusing. I come from quant trading, I used to trade this stuff with large book sizes, and if I said "contrarian investment strategies" on the trading desk, no one would know what that means. There is even a footnote in the paper I put in to address the reviewer's point. This is a real story, so what I said above is largely the case. Of course, there are traders who are familiar with both terms, and academics are mostly familiar with both, but apparently there's a disparity in usage. E.g., here are 3 well-known and oft-cited papers using "contrarian":

* Lo, W.A.; MacKinlay, A.C. When are contrarian profits due to stock market overreaction? Rev. Financ. Stud. 1990, 3, 175–205.

* Jegadeesh, N.; Titman, S. Returns to buying winners and selling losers: Implications for stock market efficiency. J. Financ. 1993, 48, 65–91.

3) Jegadeesh, N.; Titman, S. Overreaction, delayed reaction, and contrarian profits. Rev. Financ. Stud. 1995, 8, 973–993.

Hi,

I am not a quant, nor do I hold a phd or master's degree in math or whatever. So, you would forgive me if after a few pages, i closed the paper with a headache looming on the horizon.

As Alex stated, we all have our own definition/view/use of mean reversion. This is what is means to me (okay, start laughing already) :

I run models on say 20 currency pairs and I know from the longer term system performance history what to expect from each curpair in tems of returns. I now have the option to trade all 20 curpairs, each with a certain %allocation, or I can concentrate on those that have performed poorly over the recent history to give them more weight in the portfolio for the next period, expecting them to catch up with the rest and undo their underperformance. And so I did and guess what ? It is beating the "all 20 curpair" portfolio and producing a less volatile equity curve. Call me stupid, uneducated or crazy, but that is what I see n the real world.

no disrespect to any of the contributors above (and below).

I thought mean reversion was simply stated "things", price, volume and all tend to come back to average or the mean.

@David That's not quite the case when it comes to mean-reversion statarb. As explained in the paper, what mean-reverts is not the prices (that would make little sense), but the returns.

@Marc The paper deals with equities, not currencies. There's a prosaic practical diff twixt equities and currencies: you don't have 2000 currencies to do statarb on. If you did, your "real world" would not be 20 currency pairs but more like an equities statarb trading desk with 2000 x 2000 matrices and all the good stuff described in the paper. That's the real world in equities statarb. Vanilla pair trading hasn't worked since eons ago...

Hi Zura, I got that, that you were referring to stocks.I was only following up on Alex's comment and wanted to share how I (as an 'uneducated' market participant) applied something that we could call mean-reversion (overweighing underperformers). kind regards

Dear Zura, very good paper!

calibrating the ornstein uhlenbeck model:

http://www.sitmo.com/article/calibrating-the-ornstein-uhlenbeck-model/

@Guy Thanks!

sophisticated mean reversion algo's are pretty much closely held proprietary info unless they are mediocre in performance. mean reversion alone much like trend following will not work at all without trade management rules. those management rules are probably more closely held than the actual mean reversion method itself.

@mark Indeed, prop details are important. However, mean-rev methodologies have been closely held as well (the field is overly secretive), until now that is. This paper takes the lid off that unnecessary secrecy to a degree. Hence 2100+ downloads on SSRN. People must find it useful, I gather. :)

congradulations.

Would not, or at least may not, the "trade management rules" depend on mean reversion?

@David Yes

Then it might be only a single indicator in set of rules. Where no one single rule is a deciding factor, but simply an "indicator"?

There is nothing complicated about reversion to the mean algos. They assume that markets are fair (often a wrong assumption at that) so that when any quantity like price or vwap start deviating from their historic means (averages) by 1,2,3 standard deviations it is treated as a signal that market is no longer fair, and that there is expectation that those values will revert back to their historic means. Depending on whether the deviation is above or below the mean, one can take a short or long position. Of course, even if the values revert, they may take a long time.

These algos are often tripped up by corporate actions which permanently alter the market.

The change of X number of deviations might also be based on some event, such as the publication of say quarterly results, yes? Then one expects a change, although I must admit i never look at that change in terms in Std Dev, but tend to look at % changes. I will often look at current price in relation to 2 or 3 moving averages and almost always in the form of a graph. Some times in relation to 52 week high and low, also. On the other hand none of these "views" is looked at alone either.

@Alexander That's a very simplistic view. That doesn't work in real life for equities. I suspect all this misconception stems from retail trading of a limited # of stocks with low Sharpe and high PNL vol. That's not how real statarb operates, it's more like 1000-2500 names, the portfolios are often optimized,it's not all that simple, as one can see from the paper.

Well, moving averages are just an attempt to incorporate trend information into the averages, but basically the approach is similar. Sounds like you are just "winging" it, no offense is intended. My unsolicited advice is to program whatever it is you are doing and trade by computer. At least when things don't go well you have data for forensic analysis.

This forum is not designed for complicated discussions, but be my guest and dig into it.

BTW. You have missed mentioning that real life statistical arbitrage often establishes market neutral positions. Morgan and DEShaw used to trade pairs 20 years ago, but it has evolved since into trading industrial groups, etc...

@Alexander Clearly you haven't read the paper nor do you know my background, so I'll leave it at that. Not serious.

Is Quantigic® Solutions LLC a one man show? Clearly you are coming across as very full of yourself, and leave it at that. If you actually knew something worthwhile you'd be making millions right now and keeping the fly hole closed.

@Alexander Unacceptable language. Won't respond.

Alexander,

Winging it is not inaccurate. Almost everything I do is in Excel and I start with graphs. The first uses 3 moving averages (close, 5 day avg, 13 day avg and and 21 day avg). Then a graph with the close and +2 std dev and -2 std dev. Then a 14 day RSI graph. Then I do a graph of dividends paid with % change div to div.

Then the next is Pivot Point tables doing a std PivPts, then Fibonacci PivPts, then Woodies PivPts and a Floor PivPt.

Below this in Excel I bring in data from Morning Star which is 10 yr Growth Profit and Financial Ratios. And 10 year key ratios, profitability ratios and growth ratios. From these 10 year data I graph Revenue, EPS and Dividends, and cost of sales as % of sales.

If the above data appears good, then I comb recent news.

I have never traded pairs. All of this I have created myself and I do not claim to be a great or even good "trader". In fact I do not even really "trade", I look to buy stocks that are down, but have paid dividends and will continue to pay dividends. It is buy and hold short of catastrophic events.

Thanks, David

@David As I surmised above, what you're describing is not strictly mean-rev statarb. You're looking at fundamentals, etc. It's sounds more like technical analysis with elements of fundamental analysis, and it's likely got some elements of mean-rev in it. Not mean-rev statarb though.

Thanks Zura.

Thank you for a detailed description, David. :)

Zura, as far as I am aware none of serious market participants today use "plain math" with any method, be it mean rev, trend following, breakout, whatever. A good deal of non-price information is incorporated into the analysis, and not necessarily just fundamental factors in their classical sense. The key point here is that you need to somehow identify the correct time to get into the market and out of it.

@Alex Krishtop That's the "secret sauce". Everyone's got their own variation on the theme. The theme being mean-reversion in this case. I describe the theme. That can be done mathematically in a relatively compact way, in a particular style of mean-rev I describe. In fact, everything that can be coded by definition can be described mathematically. It's a separate issue that the description in some cases might not be particularly aesthetically pleasing. At any rate, what's the claim? That math is not used by serious players?

Zura, where can you see any claim?

What I was trying to say is something different. Imagine that you sit in front of a Bloomberg terminal and chat with your fellow traders from various banks. Evidently you will have an advantage over many other market participants, especially your bank's clients (the very reason which brought Dodd-Frank and then Volker rule to life). Now even if you don't have direct access to this information but know (from statistics) that the most probable times when these traders would start to manipulate the market is then, then and then, you can create a probabilistic model which indeed gives you an edge. So, no "secret sauce", it's rather the very engine which drives the cart, while any selected method (mean rev or any other) is only its body.

I am not sure about all serious players, but if by serious players we mean regular funds with 100M+ AUM, then indeed, surprisingly or not, but mathematical models are not much favoured by them.

@Alex Krishtop That is a very distorted view of statarb. We were running a 10-digit book (so by your definition we were serious players) and I can tell you unequivocally that everything was automated and purely statistical and we weren't talking to anyone on the other side, there was a Chinese Wall in place. Let me not go into any confidential details, but I can tell you that in another shop it was the same story, there was no "other side" there at all in the first place, it was 100% automated statarb prop trading, no one was talking to anyone. Maybe there are some crooks out there, but that doesn't mean everyone is like that. That's just not the case. And everything I describe above was 100% mathematical/coded. I'm really have no idea where all these conspiracy theories come from...

I'm sorry that I was not able to convey the idea that you don't need to be one of the market manipulators to have an edge, but simply understanding of how market operates really helps, also in math models. This is basically all I wanted to say. Also I am sorry that I didn't attach a label "Example" to the example I suggested. I totally appreciate you sharing this sensitive information about 10-digit books, and I am sure that you had a very strong track record before late 2012-2013. However let me just humbly point out that I suggested to classify regular funds as serious players in this discussion. As far as I could understand you worked at a prop shop, so this is something different (although no intention is made here to claim that you were not serious!)

Where I worked is not a secret, it's in my profile. I'm sure no one would doubt these are serious players. The bottom lines is that the serious players I know use math. In fact, some of the serious players I know won't hire anyone who doesn't have a PhD in quantitative discipline (math, physics, CS, etc.). Clearly, they don't use all these PhDs to chat over the phone. Check out this paper (posted yesterday and please do note who co-authored it), it gives a glimpse into how serious players do statarb: http://ssrn.com/abstract=2657603

Imho there is a lot of convergence in opinion here. Is there a track record of statistical arbitrage during major market paradigm changes or should we come to the conclusion that there is no research on this or that this research, should it exist, indicates that "human" trades have an advantage during these periods?

My previous post implies that we are talking about comparable holding periods and that the advantage lasts only as long as the quants have not integrated the new paradygm in their models...

Alex, I would be extremely interested in seeing such a study, it would be very useful to determine a) is traditional trading still worthwhile (overall) or should we see it as an approach better suited for certain periods with a clearly defined trend within a larger paradigm of (sudden) higher volatility. Or the opposite. But whilst reading the paper posted here by Zura I am getting rather pessimistic as to the future of the "trader" as models I have contributed to, along the same lines as what is published here, had more than decent returns, really significantly higher than the S&P (perhaps you remember I posted the back-tests of such a model one a thread of yours roughly a year ago), without human intervention..... Sorry Zura, I did not mean to hack the thread, nor is there any implied skepticism between the lines of these posts as to the results of the advocated model(s).

Guy, now I do feel that we both hijacked Zura's thread, because the discussion has deviated from a particular approach to mean rev to discussing manual trading vs algo. This is something different, and I am sorry that it went this way as in no post of mine did I suggest to do it: when I refer to "pure" algo of any kind I simply mean that its input is time series only, and I was curious to see performance of these algos without adjustments in given periods vs. models that incorporate non-price information or — even better — account for the market structure and changes in it — and it doesn't mean that they are not automated or even require zero human intervention. Somehow my example explaining the reasons why prices move at all was considered as a statement of discretionary trading being superior to algo. Since I am not able to convey this relatively simple idea I think I will try my luck elsewhere. Sorry again for interrupting.

@Guy No worries :) At the end it boils down to what people want to do, and what their risk appetites are. The future of quant trading is machines mining enormous amounts of data for billions of alphas and combining them (see http://ssrn.com/abstract=2657603).

@Alex No worries at all, pls feel free do discuss whatever you'd like, this is an open forum. I only reply to what concerns my paper, e.g., math being or not being used, etc.

@Zura you posted while I was replying to Alex. At least the compilation of the "simple" approach would indicate if it is a worthwhile path to investigate further. Nice topic for a research paper imho, pity there is hardly any transparency.

@Guy Indeed. This is an empirical topic and to convince anyone would require the proprietary data I mentioned, and in all likelihood no one's going to share it.

@Alex - major misunderstanding in all directions but in the end I guess I tricked you in co-hijacking the thread, sorry it was not on purpose .... no more comments from my side ... you are right this is a different debate, I guess I got sidetracked by some posts in the thread Zura had the elegance of ignoring.

@Guy Marcelis, I remember your test results of last year quite well. Those were impressive results. What happened next, if I may ask?

@Zura, great paper, like the math. Half way through and intend to read it all. Studies like that take a lot of time and effort to put on paper. Thanks for so generously sharing.

@Guy Fleury Thank you very much! You're correct, it took several weeks. It was worth it. :)

There are 2 different definitions of reversion to the mean. see:

https://en.wikipedia.org/wiki/Regression_toward_the_mean

This board is discussing the finance version, which has become popular since Jeremy Siegel coined it to represent the tendency of variance (volatility) to return to long-term averages when it is way too large (or small). Since Siegal coined it, others have expanded the definition of the finance version even further, to represent behavior of financial variables on average rather than their variance. At this point I would say the finance mean reversion is whatever the author talking about it says it is.

@Guy Fleury - I'll reply to your question offline - backbone of it are very much along the lines of what is published here by @Zura with a meta layer on top, making this post very interesting for me...

Late to the discussion, but curious: What’s the problem with simply defining momentum/trend-following and mean-reversion/contrarian strategies as those relying on positive and negative autocorrelation, respectively, in the relevant series? Autocorrelation is a well-defined term. No doubt this is too general for some thorny corner-cases, but I yet have to see one where this paradigm fails? The examples in this paper seem to fit it.

Security returns, pair ratios, and factor returns typically exhibit both positive and negative autocorrelation over varying time scales. So the autocorrelation paradigm also covers the practically successful hybrid strategies which rely on both trend-following and mean reversion.

Thank you for your comment, Greg. Your definition is fine, albeit perhaps it doesn't cover every case under the Sun. As mentioned in the paper there are myriad ways of doing mean-reversion. I discuss one approach known on the Street as the DE Shaw/RBC style statarb. On another note, not everyone is familiar with autocorrelations. I'd guess more people are familiar with linear regression than autocorrelation.