Predicting the Time-window for Turns, in all MarketsInexplicably, upon publishing this post, the Title Chart becomes distorted beyond recognition thus,
all references are to this Original Chart - below
Do markets trend on the medium term (months) and mean-revert on the long run (years)?
Does Black's intuition bear out that prices tend to be off approximately by a factor of 2? (Taking years to equilibrate.)
How does Technical Analysis , as a whole, act as a trend following system while Fundamental Analysis matters only once prices get way out of line?
Is mean-reversion a sufficient self-correcting mechanism to temper irrational exuberance in financial markets?
We examine these questions in the proceeding;
In his 1986 piece Fisher Black wrote:
"An efficient market is one in which price is within a factor 2 of value, i.e. the price is more than half of value and less than twice value. He went on saying: The factor of 2 is arbitrary, of course. Intuitively, though, it seems reasonable to me, in the light of sources of uncertainty about value and the strength of the forces tending to cause price to return to value. By this definition, I think almost all markets are efficient almost all of the time."
The myth that “informed traders" step in and arbitrage away any small discrepancies between value and prices never made much sense.
If for no other reason but the wisdom of crowds is too easily distracted by trends and panic.
Humans are pretty much clueless about the “fundamental value" of anything traded in markets, save perhaps a few instruments in terms of some relative value.
Prices regularly evolve pretty much unbridled in response to uninformed supply and demand flows, until the difference with value becomes so strong that some mean-reversion forces prices back to more reasonable levels.
Black imagined, Efficient Market Theory would only make sense on time scales longer than the mean-reversion time (TMR), the order of magnitude of which is set by S√TMR∼d.
For stock indices wit hS∼20%/year, makes TMR = ∼6 years.
The dynamics of prices within Black’s uncertainty band is in fact not random but exhibits trends: in the absence of strong fundamental anchoring forces, investors tend to under-react to news or take cues from past price changes themselves.
In fact, the notorious and unbridled reliance and un-anchored, speculative extrapolation is the mainstay of most investors, as well as Wall Street's itself, as it is the regular course of everyday "investing" across most asset classes.
In the following a picture emerges (and we test it), whether market returns are positively correlated on time scales TMR and negatively correlated on long time scales ∼TMR, before eventually following the (very) long term fate of fundamental value - in what looks like a biased geometric random walk with a non-stationary drift.
We have looked at a very large set of financial instruments, drawing on data sets from 1800 - 2020 (i.e. 220 years).
We applied the same method to all available data in Stocks, Bonds, FX, Commodity Futures and Spot Prices, the shortest data set going back 1955.
As it turns out that, in particular, mean-reversion forces start cancelling trend following forces after a period of around 2 years, and mean-reversion seems to peak for channel widths on the order of 50-100%, which corresponds to Black’s “factor 2”.
Mean-reversion appears as a mitigating force against trend following that allows markets to become efficient on the very long run, as anticipated previously by many authors.
Regarding the data we used for this study;
Commodity Data sets - Starting date
Natural Gas 1986
Corn 1858
Wheat 1841
Sugar 1784
Live Cattle 1858
Copper 1800
Equity Price data sets - Starting date
USA 1791
Australia 1875
Canada 1914
Germany 1870
Switzerlan 1914
Japan 1914
United Kingdom 1693
From trends to mean-reversion
The relation between past de-trended returns on scale t'< and future de-trended returns on scale t'>. Defining p(t) as the price level of any asset (stock index, bond,commodity, etc.) at time t. The long term trend over some ti scale T is defined as:
mt:=1Tlog .
For each contract and time t, we associate a point(x,y) where x is the de-trended past return on scale t'< and y the de-trended future return on
scale t>:x:= logp(t)−logp(t−t'<)−mtt'<;y:= logp(t+t'>)−logp(t)−mtm't'.
Note that the future return is de-trended in a causal way, i.e. no future information is used here (otherwise mean-reversion would be trivial). For convenience, both x and y are normalized such that their variance is unity.
Remarkably, all data,including futures and spot data lead to the same overall conclusions. See in chart; As the function of the past (time) horizon t'< (log scale) for Red & White Bars, the futures daily data and spot monthly data.
To compare the behaviour of the regression slope shown in the chart with a simple model, assume that the de-trended log-price pi(t) evolves as a mean-reverting Ornstein-Uhlenbeck process driven by a positively correlated trending noise m.
It is immediately apparent from the dashed line in the chart that the prediction of such a model with g= 0.22, k−1= 16 years and y'−1= 33 days, chosen to fit the futures data and g= 0.33, k'−1= 8 years and gh'−1= 200 days, chosen to fit the spot data.
In the short term volatility of prices is simply given by S'2k's'.
Non-linear effects
A closer look at the plot(x,y )however reveals significant departure from a simple linear behaviour. One expects trend effects to weaken as the absolute value of past returns increases, as indeed reported previously. We have therefore attempted a cubic polynomial regression, devised to capture both potential asymmetries between positive and negative returns, and saturation or even inversion effects for large returns.
The conclusion on the change of sign of the slope around yt'<= 2 years is therefore robust. The quadratic term, on the other hand, is positive for short lags but becomes negative at longer lags, for both data sets. The cubic term appears to be negative for all time scales in the case of futures, but this conclusion is less clear-cut for spot data.
The behaviour of the quadratic term is interesting, as it indicates that positive trends are stronger than negative trends on short time scales, while negative trends are stronger than positive trends on long time scales.
A negative cubic term, on the other hand, suggests that large moves (in absolute value) tend to mean-revert, as expected, even on short time scales where trend is dominant for small moves. Taking these non-linearities into account however does not affect much the time scale for which the linear coefficient vanishes, i.e. roughly 2 years
Conclusion
Here we have provided some further evidence that markets trend on the medium term (months) and mean-revert on the long term (several years).
This coincides with Black’s intuition that prices tend to be off by a factor of 2.
It takes roughly 6 years for the price of an asset with 20 % annual volatility to vary by 50 %.
We further postulate the presence of two types of agents in financial markets:
Technical Analysts , who act as trend followers, and Fundamental Analysts , whose effects set in when the price is clearly out of whack. Mean-reversion is a self-correcting mechanism, tempering (albeit only weakly) the exuberance in financial markets.
From a practical point of view, these results suggest that universal trend following strategies should be supplemented by universal price-based “value strategies" that mean-revert on long term returns. As it's been observed before, trend-following strategies offer a hedge against market draw-downs while value strategies offer a hedge against over-exploited trends.
Nonlinearregression
Bitcoin's Market CyclesI know you've probably seen this kinda chart around many times, but this is only for a reminder.
In this post, iv'e outlined the "phases" within Bitcoin's cycles and the ones it has gone through in the past and what it is most likely to do next. Not saying it will repeat itself, but it is probably best to use as a rough outline.
There isn't much to say really since iv'e outlined the phases and cycle on the price chart along with how long they each last with their % gain, but iv'e outlined the main topics.
Four Main Topics
- Bitcoin Phases & Cycles (names of phases & idea not mine)
- 20 Weekly Moving Average from Bollinger Bands (this comes from filbfilb - check him out on here, twitter and telegram)
- Puell Multiple (easily outlines tops and bottoms)
- Non Linear Regression Curve (easily outlines tops and bottoms)
The reason behind this post is because I see many folks on various social media platforms expecting price to go lower, seeing 7k, 8k mentioned often, but by looking at this price chart can't help but disagree, who knows maybe this time around the cycle might break.
When to Get in Before Next Bull Market?
Look out for 20 weekly moving average and whenever price touches during the re-accumulation phase enter into long position and forget about it. This will most likely be your last and best chance of getting in before the next cycle starts. I first saw this pattern spotted by filbfilb
When & How Sell the Top and Buy the Bottom?
Puell Multiple (make sure it is in logarithmic scale)
- Sell into the red area or close to it (don't have to be exact with it)
- Buy into the green area or close to it (don't have to be exact with it)
Non-Linear Regression Curve
- Sell into the upper band
- Buy into the lower band
In conclusion, the way I see it is this price chart is the only one, one could ever need. Why? Because it easily calls the tops, bottoms, when to buy, when to sell, phases within the cycle. Maybe I'm bias because it's my own chart or because cycles repeat just like in everything else.
Hope you enjoyed the read; simple and short, but trading/investing is best done this way.
If you liked it, like it and comment! Thank you
SPY Long Term ViewHere I've done some non-linear trend analysis on the SPY ETF. The upward sloping curves represent the long term trading range with compounding considered. Since the 2009 lows SPY has rallied vigorously from the bottom of this range (light blue) to the top end of this range (neon green). The linear trend of this rally is roughly equal to the tangent of this neon green curve at the first Elliott point and will hold as support if the bull trend remains intact. I believe there is one last secular wave toward $350 before any significant drop, based on this chart, and that prudent buying in the current price range is ideal. The inverted curves suggest some potential draw-down scenarios. The orange scenario basically represents the end of the US financial markets as we know them. A retest of the 2002 and 2009 lows would be catastrophic, to say the least, and investor confidence may never recover from such a thrashing. The pink scenario is the likely price action if October 2018 marks the top of this secular bull. In this case, heavy support should be found around the 2016 lows of $180. The current market environment could break the levee and put this price in play over the next few months. The black draw-down curve is what could happen after a wave 5 rally. Support after this run would be at one of the many upward sloping curves and will be more determined by the length of the draw-down period and any support pivots built along the way.
UPDATE: Bitcoin macro view, non-linear regressionThis is an update to my earlier post:
When I shared that chart, I emphasized that it was merely enternainment and it didn't have any predictive value to me, AT ALL. I still have this point of view. Even though it might work out in the end, it must be understood that what I'm drawing here is some next level chart fitting . Humans have a tendency to see patterns where there are none, which might very well be true here as well.
So, with that out of the way, you'll notice we are getting closer to our baseline curve. I said in my previous post I'd be starting up my weekly buy ins again if we ever got closer to that baseline. So far I haven't, partly due to fear. I still believe in Bitcoins long-term value proposition, but buying after big drawdowns reguires balls of steel that I apparently do not have. Price is still more than 4x above my last buy, and roughly 8x above my average buy in.
For those paying attention to the details: yes, I have adjusted the curves downward a bit (if you hit play in my old chart, youll see the price is closer to baseline than in this new chart). I'm not entirely sure how to draw these. I;m unsure of the regression model parameters, so I'm eyeballing it a bit as well. Baseline currently sits at around 2500 dollar. I have it even lower in another chart of mine . As I said, next level chart fitting.. Guess we'll have to wait for a few more months, so we can retrofit these curves ;).
Long term: bullish . Short term: who the hell knows..
Stay safe everyone!
Bitcoin macro-view; non-linear regressionInspired by the logarithmic regression models in the old bitcoin forum thread , I drew up the above macro chart.
Disclaimer: I don't believe this chart has any predictive value. At all. This is for entertainment purposes only. Nonetheless, I find this chart highly fascinating. Bitcoins fractal nature couldn't be more obvious. Some observations:
The baseline has been Bitcoin's absolute bottom for its entire existance. It currently sits at ~2k, and a little under 4k EOY. I consider 2k *highly* unlikely, but 4k seems within the realm of possibilities. For long term trading, this line is worth keeping an eye on; I'll restart my weekly buy-ins if we ever get close (haven't done so since ~1k). This is assuming no fundamental changes to Bitcoin, or the ecosystem.
Connecting all bubble tops will form perfectly parallel channels with the baseline.
Bubble line 1 has acted as restistance on *five* seperate occasions between 2010 and 2017. It has acted as support (short or long term) three to five times, depending on how strict your definition of support is. This single fact by itself is already pretty awesome. We're still above this line. Currently at ~7k. Could a double bubble scenario still be in play?
Bubble line 2 was the top of the March 2013 bubble and December 2017 bubble. It has acted as resistance on the May 2015 dead cat bounce, sending the price down back to Bubble line 1, and eventually baseline. Also some short-lived chop in March 2014 around this line.
Bubble line 3, aka Hopium Line, formed by the 2011 and 2013 super bubbles. Currently at ~50k, and the mythical 100k EOY. Current sentiment in the crypto scene is in the shitter, so is public interest. Hopium line seems only feasible *if* we do some sideways consolidation for a few months (getting rid of panic) *and* some fundamental development that drains alts and solidifies BTC as the one true coin (LN could achieve this).