Do trends exist?

[yuvaltaylor]

I’m wondering if we can use P123 to prove the existence or non-existence of trends.

The common-sense definition of a trend is a series of daily price increases or decreases. One question is whether those series exist more in the stock market than in a randomized sequence.

Here’s one possible experiment that might “prove” that trends don’t exist, but I haven’t actually tried it. First, does it hold water?

Run a rolling backtest with a screener with the following rule on a given universe (I like to use the SP1500).

Updownratio(n,0) > x and updownratio(n,n) > x

where n is any integer between 3 and 50 and x is the up-down ratio of the SP1500 at that point in time.

Note the average number of stocks bought per week.

Then run the screener with the following rule:

Updownratio(n,0) > x and updownratio(n,n) < x

Note the average number of stocks bought per week.

If the market is totally random, the numbers should be more or less the same. If the latter number is higher for most integers between 3 and 50, then upward trends do not exist. If it’s lower, then trends do exist.

The same experiment can then be done for downward trends by reversing the greater-than and less-than signs.

Is this sufficient proof or is there a flaw in my reasoning?

Conversely, is it possible to design a proof that trends do exist?

I do not know how to write the formula for the up-down ratio of the SP1500 to use in a screener, but I assume it can be done. Can anyone help with that?

Thanks,

• Yuval

[kumar]

Yuvaltor,

Based on knowledge from successful active traders for few decades.

1. Uptrend is price > sma(50)

2. Downtrend is price < sma(50)

3. RangeTrend/sideway trend price closer to sma(50) for few months.

Market is following one of the above 3 trends 1/3 of the time.

Value investor waits to buy on downtrend and hold and wait to sell on uptrend.
(ie., all legendary buy and hold systems, ValueLine, Mgerstein systems)

Growth investor waits to buy when starting of the uptrend and sell starting of the downtrend. (ie., Investor Business Daily, CANSLIM system).

Thanks
Kumar

[yuvaltaylor]

The question is whether a market with random price movements would exhibit the same characteristics. If so, paying any attention to trends would be counterproductive–it would have absolutely no value, whether you’re a growth or value investor. In order for this idea of trends to be useful, they have to have some degree of persistence or non-random probability, and it should be possible to prove that. The question is how.

[yuvaltaylor]

Also, if a stock’s price is below the SMA(50) for a few weeks and has a one-day price increase of 20% based on a positive earnings report, putting it well above its SMA(50), that is NOT a trend. Any definition of a trend has to exclude stuff like that.

[mgerstein]

I’ll leave the statistical proofs for or against to others but for a theoretical view, this is probably a good time to mention something I should have mentioned earlier; that I added a new pdf to the virtual strategy design class (now openly and fully available in Help>>Tutorials>>Courses). Rather than an addition to the end, it actually goes at the beginning, a new Introduction.

It addresses the topic of logic versus randomness in stock pricing.

The position I take is that the stock market is extremely non-random and that the challenges we face in predicting share-price movements relates not to the absence of causes but to the difficulties in identifying and assessing all the factors that make each day’s price, or change in price, what they are. I try to present it in a more anecdotal (and maybe even entertaining in places) rather than philosophical way.

In terms of this thread, I’d suggest trends persist or break depending on the persistence of or changes in the underlying factors. As a hypothesis, I’d suggest that trends are in place more often than not, but that substantial breaks tend to be idiosyncratic in nature and timing.

[yuvaltaylor]

I agree that stocks are not randomly priced at all. But any proof that trends do or do not exist would have to be measured against something, so “random” is what I chose to measure it against. My hypothesis is that mean reversion trumps trends–in other words, that at any one moment a price trend, properly defined, is more likely to reverse than to persist. But that’s just a guess, and I don’t know how to design an experiment that would prove that.

[Jrinne]

So, Guenter turned me on to R: the statistical software. And I always wanted to do a runs test, which I did. It tests whether up days and down days occur randomly. For example, if you enter heads and tails for coin flips it should generally be shown to be random (or actually you will fail to reject the null hypothesis that it is random).

The stock market is not even close to random–in the distribution of up and down days–over a long test period.

Also I was looking at exercise problems for R in one of the texts. I think it showed that after a down day there is a 60% chance that the next day will be up for that S&P 500. I am not sure what period was tested.

But I do not think it is random from the runs test alone.

Edit: below is the attachment for the runs.test of the SP500 benchmark daily returns over P123 Max period. p < 2.2 X 10^-16

---

[yuvaltaylor]

I don’t think it’s random either.

Here’s an experiment that maybe R can help with. Let’s define a trend as a series of four or more up days or down days relative to a benchmark. Can you use R to test whether the average length of a trend in a group of stocks (e.g. the individual stocks in the S&P 500) is longer or shorter than the average length of a trend with a coin toss? That might be one way to see if trends exist . . .

[quadz42]

In case you want to skip to the end (i.e., trends do exist), see below for a few select papers:

https://www.aqr.com/library/aqr-publications/a-century-of-evidence-on-trend-following-investing

https://www.researchgate.net/publication/261635941_Two_centuries_of_trend_following

[WalterW]

Doesn’t trend imply some state-dependency? Like, if today is an up-day, tomorrow is more likely to be an up-day? Maybe using a Markov chain model would be more productive. I did a quick Google search but didn’t see anything really interesting along those lines. Maybe others will have better luck.

Walter

[yuvaltaylor]

Alan -

Thanks for the links. They’re interesting, but I didn’t find them convincing.

The AQR paper says that trend-following can be profitable if you do it right, with volatility scaling and long and short options. It doesn’t address whether or not trends exist. Instead it tests a very specific strategy, and it doesn’t compare it to a benchmark. It appears that the strategy beats the stock market as a whole only a little bit more than half the time.

The Journal of Investment Strategies paper deals with currencies, bonds, commodities, and stock indexes, not with individual stocks, which is what I’m wondering about; also they define a trend as a five-month thing, which seems like cherry picking to me. I doubt they’d get the same result if n = 2 or 3.

Perhaps there’s a paper out there which proves that trends–from four days to four months–do exist in individual stock prices. If so, I’d welcome a link.

• Yuval

[primus]

Yuval,

Here is the 1997 Carhart paper which is known to have sparked the momentum frenzy: https://faculty.chicagobooth.edu/john.cochrane/teaching/35150_advanced_investments/Carhart_funds_jf.pdf

Ken French still tracks portfolios sorted by prior returns on his data library: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html. He tracks both mid and long-term trends and short-term mean reversion. The data is convincing: trends exist. While “Carhartian” momentum was once considered to be a part of the Fama-French framework, it was abandoned because no one could give a rational explanation for how it articulated within the EMH. By the way, Fama-French’s framework has predicated its entire existence on disproving that CAPM determines the optimal market portfolio. It is implied that the market is efficient but that mean-variance optimization is spurious… which it is.

By the way, AQR Capital Management stills maintains a Carhartian momentum factor in its six-factor model: https://www.aqr.com/cliffs-perspective/our-model-goes-to-six-and-saves-value-from-redundancy-along-the-way.

If more is indeed better, perhaps it won’t be that long until some expert on CNBC echoes the sagastic wisdom of Spinal Tap: “but these go up to eleven”.

So… trends exist but normative economics cannot explain why. It used to be enough to revert to fuzzy, inexact logic by simply declaring: high prices lead to speculation which lead to even higher prices. The “buy high and buy higher” – and it’s converse – paradoxes are presumably at the core of trends and momentum, but the field of behavioral economics has barely begun to objectify the crux of these behaviors… rationalizing those behaviors it still beyond our limited means.

Anyway, are markets random? To the markets themselves, I presume not. But that assertion mis-states the nature of randomness to you and me. Random doesn’t mean that random factors cause uncertain outcomes; it simply means that the nature of those sources of uncertainty are not knowable and/or cannot be observed. In this respect, markets are random to me.

To the extent that one is able to skillfully discern non-randomness, he/she may be able to eek out a long-run profit above the market’s long-run rate of return. Otherwise, it’s luck or informational asymmetry.

[Jrinne]

Anyway, are markets random? To the markets themselves, I presume not. But that assertion mis-states the nature of randomness to you and me. Random doesn’t mean that random factors cause uncertain outcomes; it simply means that the nature of those sources of uncertainty are not knowable and/or cannot be observed. In this respect, markets are random to me.

Yes. Yes. YES!!!

Just as we could, probably, tell if it was going to be heads or tails using a high-speed camera. Or, for sure, we can know which random (or pseudorandom) number will come up in Excel if we use a seed.

Whatever philosophical meaning you put on randomness, a coin flip or a pseudorandom number generator is random for our purposes.

Much of the market can be treated as random.

But also there is a point of agreement with Marc. If our null hypothesis is that the market is random and our statistics shows otherwise aren’t we showing Marc to be correct?

More commonly, I assume the market is efficient and random. This is my null hypothesis (assumption). Time and time again, I show this assumption to be wrong. Rather, factors based on the DDM generate excess revenue. If this happens to be statistically significant should it surprise anyone?

Thanks David,

-Jim

[yuvaltaylor]

David -

First, I have to say how much I like your posts. You’re such a good writer.

I think I am not such a good writer, because I gave you the impression I was talking about long-term momentum. Is momentum the same thing as a trend? I have no doubt that long-term momentum is real, and it’s easily explainable: it is slightly more likely that a company that is performing well quarter after quarter will continue to perform well than that it will reverse its performance, and it’s more likely that a company that is performing badly will continue to do so than to suddenly perform well. That doesn’t seem like an anomaly to me.

What I’m wondering about is the kinds of “trends” that technical analysts point to with their RSI(14)s and their MACD(26)s. The very existence of Ken French’s short-term mean reversion portfolio would seem to argue against those.

I think I can prove that short-term trends don’t exist. What is the chance that a stock that outperforms the benchmark every week over the past five weeks will continue to outperform the benchmark the following week? I can show using P123 that it’s less than 50%. Ditto for four weeks, three weeks, two weeks, and one week. Ditto if you substitute “underperform(s)” for “outperform(s)” in that sentence. I performed ten tests on the SP1500 and the results are 100% consistent. If stocks were random, then the chance would be an even 50%. If trends existed, the chance would be greater than 50%.

Is my logic faulty? It could be.

[primus]

@Jrinne,

Thanks you. I agree on all. And yes, I do think Marc is correct about how the burden of proof resides with disproving the null hypothesis.

@Yuval,

Thank you for the kind words, but I do you think you’re a much better writer than you admit. In all honesty, I never really drew any distinction between trends and momentum which explains the source of my confusion. Could it simply be that all momentum are trends, but not all trends are momentum? If so, what is a measure for a trend which is not a measure for momentum?

Honestly, since I’ve never distinguished between the two, I probably have missed a key idea.

[yuvaltaylor]

Momentum is a leading indicator and trend is a lagging indicator. Momentum has causality, trends don’t. The difference isn’t a big one. If you look at a chart, you don’t see momentum. You see trends. That’s what I’m trying to get at. I think that the trends you see on a chart–at least the short-term ones–are optical illusions, more or less. I also think that most people use momentum to mean long-term (five months or more) and trend to mean short-term, but there I may be very wrong, which is why I said I wasn’t as good a writer as I should have been.

Regarding randomness, I’m afraid I don’t understand your point. Marc’s argument that prices aren’t random seems convincing. I really liked the new intro he wrote. Why do you and Jim think that there’s randomness in the stock market?

Is it a semantic thing? To me, the weather is not random. Everything about it can be explained if you look at enough variables. The same goes with the stock market. Is the weather random for you?

[Jrinne]

Is the weather random for you?

3 weeks out: Chaotic to be accurate. Predictable? Not so much. You could go with a range based on the time of year. Maybe modify it based on El Nino or some other factor.

But a butterfly flapping its wings in Brazil can cause a tornado in Texas (this is the “butterfly effect”). Try to predict that!

Interesting that you pick the weather. That is where chaos theory all began: trying to periodic the weather.

Could an FBI investigation of Russian Hacking lead to the US using cruise missiles in Syria causing Xi to move troops to North Korea’s border which causes Trump to play a game of chicken with an emboldened North Korean dictator causing….? Probably not, but something unpredictable for the stock market could result.

Not without cause but not necessarily predictable either.

BTW, if you study game theory at all you will see that it pays to be unpredictable and having your opponent think you are a little crazy when playing the game of chicken. Trump and Kim Jong-un seem to have read the texts.

-Jim

[yuvaltaylor]

Maybe it is semantic. Random and unpredictable are totally different things for me. Sunspots are random, comets are predictable, and Trump and the stock market are neither.

[primus]

Momentum is a leading indicator and trend is a lagging indicator. Momentum has causality, trends don’t.

I didn’t realize that. Thank you for clearing it up. I apologize that my rant on momentum was off topic.

Is the weather random for you?

Yes. I look at my phone. 0% chance of precipitation. I look outside and it’s raining. If the weatherman cannot predict the weather, then there’s got to be an element of randomness to it.

Again, random to me doesn’t mean that there no is causation or order for a given outcome, but rather that it’s machinations are opaque to me.

Is a coin flip random? To me, yes. But if I’m god and know everything about the initial conditions: the precise atomic weights and compositions of the coin, the wind sheer and its precise effect on the coin’s surface area, the force and angular velocity of the initial toss, the precise gravitational force exerted by an nth body gravitational system, the hardness of the surface, et cetera… then perhaps the outcome of that coin toss is non-random. But then again, if I am god, then I can just make the coin land whichever way pleases me. Alas, for me, it’s random.

[Jrinne]

A one day move in the SP500 index is more likely to continue in the same direction the next day than reverse direction over P123’s Max period.

Below are the results of the turning point test in R (first attachment). The data is a download of daily returns of a sim over the Max period with the SP500 as the bench. The data column “$100 Bench Ret” is used for the turning point test.

It looks like there is a positive serial correlation over the MAX time-period used at P123 to a high level of significance. p-value < 2.2 x 10^-16

See Quandz42’s references for data on trends over longer time-periods.

The weekly data on the SP 500 does not show a statistically significant autocorrelation. And the trend is toward negative serial correlation. See second attachment.

CORRECTION: I REDID THE WEEKLY DATA A COUPLE OF TIMES AND THIS DOES NOT SEEM TO BE CORRECT. I GET A POSITIVE SERIAL CORRELATION FOR THE WEEKLY RETURNS OF THE S&P 500 USING THE TURNING POINT TEST. POSSIBLY, I USED THE WRONG EXCEL COLUMN FOR THE R DATA (WEEKLY RETURNS AND NOT TOTALS). SORRY FOR THIS ERROR. I do not know how to remove the attachment.

@Yuval, I found a quote from a paper that confirms my crude analysis of an index. But your question was about individual stocks. The answer to this question seems less clear. Link from “Autocorrelation in Daily Stock Returns”: [url=https://www.researchgate.net/file.PostFileLoader.html?id=564930816307d923b08b4590&assetKey=AS%3A296225678086169%401447637113915]https://www.researchgate.net/file.PostFileLoader.html?id=564930816307d923b08b4590&assetKey=AS%3A296225678086169%401447637113915[/url]

Quote from this link: “The results of the test show that the autocorrelation in the Index return is positive and significant. When applied to individual stock returns, the tests show a weak autocorrelation. Moreover, the sign of the autocorrelation is not always the same, and frequently the absolute values of the autocorrelations do not lead to the rejection of the null hypothesis that the autocorrelations are different from zero.”

-Jim

---

---