Locklin on science

BTC bubbles

Posted in econophysics by Scott Locklin on April 17, 2013

Not surprisingly, Bitcoin prices are well described by the  log periodic power laws describing the dynamics of bubbles. A reminder of what a LPPL model looks like; here is a simple one:

\log(p(t)) = A + B(t_c - t)^\beta + C(t_c - t)^\beta \cos( \omega \log(t_c-t)+\phi)

I didn’t profit from this. I thought of applying LPPL to the BTC bubble well before the crash during a bullshit session with a friend, but I didn’t run the analysis until after. I have better things to do with my time than play with weird monopoly money, and the “exchanges” presently offering shorts are not even close to useful. I also think anyone who trades on LPPL is basically gambling. The most interesting parameter, t_c is hardest to fit, and, well, with all those parameters I could fit a whole lot of elephants. Just the same it is a useful enough concept to justify further research. No, I won’t be telling the world about that research on my blog. A man’s got to eat, after all. Doing bubble physics costs money.

If you don’t know about LPPL models, click on these two helpful links. The “hand wavey” idea is, if the price is formed by market participants looking at what other market participants are doing, as with Dutch tulips, pets.com, and market prices in various eras, the price is an irrational bubble which will eventually burst. This isn’t an original idea: Charles Mackay was talking about it 180 years ago. The original idea is mapping this behavior onto an Ising model,  running some renormalization group theory on it, and fitting to the result to get a forecast of bubble burstings.  Sornette, Ledoit,  Johanson, Bouchaud and Freund did it and told the world about it; may the eternal void bless them with healthy returns for being kind enough to share this interesting idea with us.

Here’s a plot of BTC close prices from MtGox (via quandl), with the LPPL model fit 10 days before the bubble pop. I wasn’t real careful with the fit; no unit root tests were done, no probabilistic estimates were made and no Ornstein Uhlenbeck processes were taken into account. This is just curve fitting. The result is compelling enough to talk about. As you can see, with these parameters, the out of sample top is fit fairly well. Amusingly, so is the decline.


What can we learn from this? You can see a “fair value” of around $20/BTC due to be hit in a few weeks, with perhaps a full mean reversion to $10/BTC.  BTC doesn’t seem to have a helpful “anti-bubble” decay; if anything, it is decaying faster than expected so far (it is possible I mis-fit the \omega). The fit parameters for this version of the model tell us a few interesting things about the herding behavior which you can read about in Sornette’s book.

I don’t have any strong opinions about using BTC as a currency. I think most of its enthusiasts  are naive and do not understand the nature of money and what it is good for. I do think BTC would work a lot better as a store of value with a properly functioning foreign exchange futures market. There are no properly functioning BTC futures exchanges at present; just an assortment of dreamers and borderline crooks cashing in on hype. This is more of an engineering and legal problem than it is an inherent problem with using BTC as a currency. The way things are presently set up, without shorts, any extra media attention will result only in people buying the damn things. Without the ability to easily short them, price discovery is impossible, and herding behavior is the rule. It ain’t a market without shorts. It’s a bubble maker. Shorts don’t guarantee there will be no bubbles; we see plenty in shortable markets, but a lack of shorts will virtually guarantee future BTC bubbles.

40 Responses

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  1. chloe said, on April 17, 2013 at 3:00 pm

    If you think of 2011:

    Bitcoin was at a high of almost $32. Then a low of about 2 (maybe less). A 16 times reduction.
    Then, from 2 we got a high of $266. 133 times more.

    Extrapolating, a 16 times reduction from 266 would mean 16-17 dollars.
    And then, 133 times in value would mean above $2000

    • Scott Locklin said, on April 17, 2013 at 3:05 pm

      I don’t think LPPL is a great model, though it seems to be pretty good in this case, but at least it’s a model based on something observed in people’s behavior. Just extrapolating is … just extrapolating.

  2. Steven Jones said, on April 17, 2013 at 3:22 pm

    what a pathetic useless report, absolute nonsense, the writer clearly doesn’t have a clue about bitcoins.

    • Scott Locklin said, on April 17, 2013 at 3:49 pm

      I love religious nuts. You will note that the LPPL model doesn’t depend on the properties of bitcoins, which is one of the reasons I didn’t mention any of them; it only depends on how people buy and sell.

      • Spheeler said, on April 17, 2013 at 5:34 pm

        Bitcoin is a network protocol, the network is where the value lies. Visa, mastercard all charge 3% for a “network” and now bitcoin has a free network. Bitcoin miners are providing this network, so they get payed in bitcoin.
        The big issue right now with bitcoin is MT.GOX or “magic the gathering online exchange” and the idiots who keep dumping their money into it.
        Maybe bitcoin’s wont last but the concept of “bitcoin” will change the economic system as we know it.

        Yes we are in a bitcoin bubble, but I would bet it wont be the last and its certainly not the first. Smart individuals have already cashed out and made a killing on this most recent rise and fall.
        And I personally think the crash is linked to bots dragging the price down, and just how terrible the largest exchange is managed.
        I also have a sneaking suspicion the winklevoss twins were involved so they could get in cheap.
        Bitcoin is a sellers market, but the price is only based on the last trade. Regular stocks don’t function this way..
        So a bot that’s throwing out low bids for .001 bitcoin exchanges with another bot selling some coins for cheap and the price goes down. These two bots could even be part of the same botnet, so the owner would never loose money.
        Either way, someone with some big money started playing around with bitcoins recently, you can see the transactions.

        • Scott Locklin said, on April 17, 2013 at 5:48 pm

          An order book system would probably help matters. Though it isn’t the only solution. Since BTC are a decentralized system, I figure people who are interested should play to its strengths and invent a decentralized exchange.

          I figure the “big money” is simply due to the hype machine pumping money into it. If you have some evidence of naughty people manipulating the price, I’d be happy to have a look.

          I agree with you that such decentralized systems have the potential to create radical changes in the world. It doesn’t work all that differently from Visa.

            • Scott Locklin said, on April 18, 2013 at 1:34 am

              Yeah, naughty folks were doing that sort of thing with NASDAQ as I recall. Auctions are a good way of doing business. Making your transport layers and your crossing algorithm solid is, of course, mandatory. Nobody has done this so far. Most of it seems to be written in phucking javascript, which seems like a bad joke to me.

              I would be interested to know about any verifiable BTC market manipulations. There seems to be a lot of speculation about it anyway.

              • asciilifeform said, on April 18, 2013 at 2:46 am

                One should also regard BTC exchanges like MtGox “guilty until proven innocent” of front-running. The temptation is overwhelming.

                • Scott Locklin said, on April 18, 2013 at 9:24 pm

                  Unless there is legal prohibition against it, I assume “first look” is happening. For example, all consumer spot FOREX, and a lot of the pro stuff has “first look.”

                  • asciilifeform said, on April 18, 2013 at 11:30 pm

                    And with the wild swings you see in BTC, “second look” is arguably just “crumbs from the master’s table.”

  3. Roger Bigod said, on April 17, 2013 at 6:42 pm

    The gold chart sure don’t look like a LPPL model. I don’t think it’s an honest bubble.

    • Scott Locklin said, on April 17, 2013 at 9:09 pm

      Ya know, someone in the comments section of the previous LPPL post pointed out that the model actually did predict the gold bubble pop. I never looked myself, since I only believe in LPPL on a part time basis, but it doesn’t seem to have liked being at 1900$ much.

      • noko said, on April 18, 2013 at 2:00 am

        Gold correlates with oil, so gold falls because oil falls. Not a bubble.

        • Scott Locklin said, on April 18, 2013 at 2:07 am

          The gold bubble, if there was one, popped in October of 2011. What you’re seeing now ain’t real bubble-like; it’s just a commodity going down.

          • noko said, on April 18, 2013 at 2:30 am

            Because crude oil entered bear market in October 2011

            • Scott Locklin said, on April 18, 2013 at 2:43 am

              Actually, it didn’t, and what correlations exist between crude and gold are on something like a 2 year time scale.
              The soy crush is a correlated market. Gold and crude: no.

      • Roger Bigod said, on April 19, 2013 at 1:49 am

        I got the mistaken idea from the news that there had been a recent bubble in gold. But the only one has been Oct 2011, called by Sornette. His formulation is that after a peak, markets enter a different regime. A retrace to the beginning of the bubble may not occur. So this is consistent with his prediction.

        Gold is the only commodity that evokes religious intolerance. One side views ownership of gold as a rejection of a corrupt temple, full of money-changers and harlots. After the coming day of judgment, the pure and righteous will inherit the earth. To the other side, an asset with zero yield violates the injunction to be fruitful and multiply. It’s fiscal onanism, at best. The earth will belong to those like St. Warren who patiently reap a market rate (plus a little edge), not the spillers of seed.

        I try to avoid religious controversy, but before I make up my mind, I want to hear more details about the harlots.

  4. Rod Carvalho said, on April 17, 2013 at 11:38 pm

    In case you haven’t yet read Stanislav’s latest blog post, here’s something surreal:

    How to fail – the Scott Locklin method

    • Scott Locklin said, on April 17, 2013 at 11:59 pm

      I’ll give credit to him for actually quoting our exchange accurately. Why he thinks this makes him look like anything but an insecure dipshit is kind of beyond my psychological knowledge.

      • maggette said, on April 18, 2013 at 9:08 pm

        I am not sure…but I think I met (from left to right) his Chief Information& Technology Manager, Head of Sales& Marketing and the Public Relations guy a while ago.:)

        • Scott Locklin said, on April 18, 2013 at 9:11 pm

          If this were NP, I’d make the clappy thing.

          clappy thing

  5. Deniz said, on April 18, 2013 at 6:42 pm

    With 7 free vars you can fit anything, and without error bars they are meaningless. A better way to to do the backtest would be to pick many random windows and then make prediction and test against Pt = a+b*Pt-1. A distribution of the difference between the two predictors would be interesting.

    Or you can revisit this post in 100 days to see if bitcoin is at 20 😉

    • Scott Locklin said, on April 18, 2013 at 6:53 pm

      Feel free to do so if you’re interested. You’re not going to get much from a random walk: that much is obvious.

      • Deniz said, on April 18, 2013 at 8:23 pm

        Really? I think there is 50% chance that it would beat LPPL forecasts or anything else with 7 vars. And no I am not interested in fitting elephants and making their tails or trunks wiggle or whatever. You should not either, you know better.

        • Scott Locklin said, on April 18, 2013 at 9:22 pm

          I’ve put plenty of caveats in my description of LPPL. I think anyone who bets on something like what I did above is crazy-pants. However, I also think LPPL is a useful idea, and find it compelling that chucking it at a well-motivated, but random point before the popped bubble gave such a ridiculously perfect fit. It isn’t surprising, since the underlying process which generated the BTC bubble is exactly described by LPPL. Since you have never fit LPPL, you aren’t aware of the fact that most of the variables are constrained such that it doesn’t fit much of anything BUT bubbles, but, well, look at the damn equation.
          Were I to use this idea in a more serious way, of course I’d do something more clever than curve fitting. For a pop science blog post: good enough. If you think you can fit a random walk to that data and get better forecasts: great. Show me. Otherwise, there are at least 100 published articles in refereed journals that disagree with you.

  6. Marcus said, on April 23, 2013 at 9:37 am

    Bitcoin is completely unworkable as a currency as it deflationary by design,as there is only 20million or so bitcoins and mining them gets progressively harder so it resembles a classic pyramid scheme rather than an honest medium of exchange.How the fuck would you ever pay back a bitcoin loan and what advantage would you get for ever ‘spending’ bitcoins?
    Technically the long term “fair” value should be a timeseries with a decaying inflationary component and linked to the energetic cost to produce the things (which is also a waste of human effort) but now we are in classic bubble territory.
    The LPPL is a fascinating model but models generally need about 6 months of hard work to turn them into a trading strategy.

  7. miles said, on May 10, 2013 at 3:25 pm

    Hi Scott. Totally off topic here but I don’t know a better place to ask. You posted a link a while back to an article that your friend had written about SSRIs/Antidepressants, but I can’t remember where. I’d really like to read it again if you remember the one I’m talking about.

  8. Craig said, on May 16, 2013 at 3:27 am

    Well, looks like this was off by a long shot.

    • Scott Locklin said, on May 16, 2013 at 3:36 am

      Maybe: as others pointed out, the model is mostly about picking the top, which it did in this case. I’ll certainly continue to monitor BTC for log periodic oscillations though.

  9. […] actually really do like the timing analysis Locklin tried in trying to fit a log-periodic power law. Usually pure technical signals are not to be trusted- but in this case the analysis explicitly […]

  10. Jamal Rabani said, on July 24, 2015 at 10:02 am

    of all making a profit. My conclusion is the majority of these cloudhashing businesses is they have little if any purchasing power, the hardware mining industry is extremely cut-throat and it is difficult enough to make money from mining as an end user least of all attempting to make money after these cloudhashing companies try to get in-between. At a glance at most of the contracts available the they are quite depressing especially when some easy mining profitability calculations are carried out. This is caused by one or all factors misleading statements, lack of knowledge of Bitcoin mining (e.g. difficulty increases), and perhaps just wanting to be part of the community.

  11. Nick Backer said, on August 9, 2017 at 10:11 pm

    Hi Scott, I am writing a paper about bitcoin and the Lppl model. Can I ask you a couple more questions? I believe you will receive my email with this comment so please answer me there if you can help me. Thank you very much in advance.

  12. Christos Kouyountas said, on February 26, 2020 at 12:47 pm

    Hello 2020 here and Bitcoin is at over 9,000 USD, narf. How would you commend on the current state of affairs?

    Also, decentralized exchanges are being developed now and as I understand it, futures and shorts are possible for Bitcoin at present.

    Moreover, Proof of Work is not the only method implementation possible for distributed system Cryptography. I am thinking Proof of Stake but there are others as well.

    It’s a fascinating subject, perhaps it’s worth revisiting it with a new post. There’s definitely enough bullsh1t flying around as well to make evisceration suitably entertaining 🙂

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