**Greatly reduced volatility, smooth exponential decrease of the Bitcoin price, regulators' and short sellers' profits, boredom, even higher Bitcoin fees, exodus**

One week ago, I discussed the plan of the CME group to allow trading of Bitcoin futures. See a CME web page, a press release, and its review in Business Insider, underlying reference rates (BRR real-time and BRTI daily rate).

Last night, Business Insider brought us

[We just got] a glimpse of how bitcoin futures will workThere are many details over there. Let me look at them first.

At this moment, when I write this sentence, the Bitcoin price is $7,400 so I will refer to it as the current price. We learn a lot of details about the trading.

In particular,

- there is probably no leverage, the Bitcoin is sufficiently volatile even without it (I suppose that the short positions must still be insured by some margin call when, assuming no reserve funds, the Bitcoin price doubles or something like that)
- the expiration moments when the futures are settled in cash will be on some days (probably all days from Monday to Friday, 5 a week), 4 p.m. London time – the settlement prices are probably exactly the BRTI daily reference rate that already exists
- one contract is 5 Bitcoins ($37,000 at current price); the article implicitly suggested you can't buy any fractions but I am not quite sure
- the maximum that one entity may hold is plus minus 1,000 contracts i.e. 5,000 future Bitcoins ($37 million at current price) so that no one gets the monopoly to individually corner the market (manipulate price in a way that only the biggest fish can use) – well, I suppose that traders from 10 big banks who talk to each other might corner it, anyway
- the price where you buy/sell futures must be a multiple of $5 per Bitcoin (i.e. $25 per contract), so the price may change from $7,400 to $7,395 and $7,390 etc., with a downtick every 5 minutes, for example LOL
- trading is from 5 p.m. of the previous day to 4 p.m. Central Time – 23 hours a day, 5 days a week

*Current BTC price*

As I have repeatedly mentioned, the Bitcoin price dynamics is the ultimate random walk. Various people may follow some strategies – they may try to extrapolate the recent momentum, or – on the contrary – bet that recent swings will get reverted. They have various time scales etc. And the result is a random walk or Brownian motion, a Markov process where the price is de facto described as\[

{\rm Price}_{\rm Bitcoin} = P_0\cdot \exp [ W(t) ]

\] where \(W(t)\) is a random walk i.e. \(\langle W(t)^2 \rangle = t/t_0\). The typical deviation of the logarithm of the price behaves like \(\sqrt{t}\) divided by the square root of a time scale \(t_0\) – that's some proportionality constant.

For years, there's been some additional "clear momentum upwards" but that will probably be over, as I will discuss momentarily.

To have some idea how to calculate \(t_0\), it may be fun to divide the random walk to individual transactions. These days, there are roughly 300,000 transactions a day and the daily volume is $2.5 billion i.e. 340,000 Bitcoins. Also close to 300,000. So it's an excellent approximation to say that the average Bitcoin transaction is about BTC 1. Note that the median transaction is just some BTC 0.1, one order of magnitude smaller – due to the big "wealth inequality". It's the rich folks who primarily decide about the average.

It may be helpful to eliminate transactions that are much smaller than the average one. I guess that we could say that there are just 100,000 "not tiny" transactions and their average is BTC 3 per transaction. A great model to visualize a random walk. If each transaction moves the Bitcoin price by \(\Delta P\) in a random direction, 100,000 such transactions move it by \(\sqrt{100,000}\sim 300\) times \(\Delta P\). Because the daily price changes are of order 5% in average, one transaction changes the price by some 5/300=0.017%. That's $1.2 at current price.

OK, so my model for the natural trading is that a bunch of random traders buy and sell 100,000 times BTC 3 every day. Every time they do it, the price moves by $1.2 in a random direction (away from some number comparable to $7,400 now). Most of them cancel, only roughly "300" transactions don't cancel well – the square root of the number of transactions.

That's a funny picture because it suggests that the uncancelled momentum builder only comes from some 300 transactions per BTC 3 i.e. from the traders involving some BTC 1,000 ($7.4 million) a day. That's 1/5 of the maximum limit per entity that can trade the Bitcoin futures. So there is a lot of potential to insert non-randomness through the futures traders.

What will be the implications of the trading on the Bitcoin price?

First, try to assume that the futures traders assume that in the next month, the Bitcoin price will continue skyrocketing – the table at the very bottom shows that trading will be up to the last Friday of a month, 4 p.m. London time, and some 4 next such Fridays will be available at each moment. If the market thought so, the (end-of-)December futures could be traded at $15,000 per Bitcoin. But the big traders of actual Bitcoin could almost lock a profit – to be realized on the expiration date, by closing both real Bitcoin and futures positions – by shorting the future and buying the real Bitcoin more cheaply at the same moment! In effect, they would buy a cheap real Bitcoin and sell a negative Bitcoin at a higher price, which means profit.

This arbitrage opportunity will immediately push the difference to zero or some small technical values. The futures shouldn't be traded well above the current Bitcoin price, I think. The futures' price should always indicate that the Bitcoin's future is not bright, to put it mildly.

Note that the opposite mechanism doesn't really work because you can't short the real Bitcoin effectively. For this reason, it's generally assumed that the Bitcoin futures will indicate the future price

*below*the current price, or below the current price plus some technical, profit-dictated constant which includes some fees and other expenses. The rational real Bitcoin traders will be able to look at the futures, see that the future Bitcoin price doesn't look really higher than today, so it's better to sell.

OK, at what levels should the big fish buy or sell the futures?

First, before we discuss the trend, it seems obvious that the futures trading should restrict any volatility. Because almost all the volatility is rationally unjustifiable, the trading of the futures may kill the volatility

*completely*. The Bitcoin is an example of the perfect ultimate bubble but it should also be an example of an "asset" where the noise may be suppressed completely. There's a difference from gold or other commodities. The traders of gold futures must really make an estimate

*at what gold price the supply and demand are sustainable*. If the gold price is too low, the system runs out of gold. But the Bitcoin is equally sustainable at

*any price*. The Bitcoin price lives

*exclusively*in the people's heads.

So I think it makes sense for the traders to assume that the "actual" Bitcoin price is an extremely smooth function of time. They should buy the future Bitcoin whenever its price gets beneath this smooth curve, and they should sell it whenever it gets above it. They should only spend some of their limit on positions for these purchases – to have a reasonable probability that they won't hit the limit of 1,000 contracts before the expiration day.

At the beginning, one could wait for the rest of the market to push the prices somewhere. But maybe it's not a good idea to wait because the real profits start right away. I don't know what to do. Everyone who trades the futures probably realizes that the other traders are rather intelligent – each of them may afford $37,000 for this fishy position. ;-)

I don't know what to do with the initial "one time" kicks into the real Bitcoin price and the futures price. However, I find it totally sensible that just hours or days later, the Bitcoin traders could try to target some decreasing exponential function for the price:\[

{\rm Price}_{\rm Bitcoin} (t) = {\rm Price}_{\rm Bitcoin} (0) \cdot \exp(-t/t_1)

\] After the moment \(t=0\) where this behavior begins, it may be assumed that the price of the Bitcoin is decreasing exponentially with the time scale \(t_1\). One tries to adjust \(t_1\) at every moment. And one tries to buy short or long positions according to the deviations from this function, but estimate the rate at which you're buying so that you don't run out of your wiggle room – the limit of 1,000 contracts – before the expiration moment. Because of the limit of 1,000 contracts per entity, no single entity will be strong enough to eliminate the fluctuations away from a smooth curve completely. But lots of entities trading the futures actually

*might be*– they might collectively behave as the perfect removers of all the noise.

**I expect further decrease of transactions in the real Bitcoin, and even higher fees**

It's pretty funny but the future Bitcoin price may really be very close to a seemingly predictable smooth function of time, such as the decreasing exponential above. This will have consequences for the real Bitcoin traders, too. Lots of them will start to believe it – for good reasons. The market might be trained to sustain one smooth function of time or another. This tendency to co-operate on the "apparent hypothesis about the future price" may also be described as a self-fulfilling prophesy. I believe that since the Czech National Bank interventions against the Czech currency that began exactly 4 years ago, this "trained market" has shown itself in numerous stages. Also, it is pretty clear that these days, the EURCZK volatility is some 1/2 of what it was 5-10 years ago (e.g. in 2009 when the EURCZK changed by more than 0.5 almost every month), because of the lots of crowns that were printed during the interventions and are held by foreigners.

At any rate, I find it obvious that after a sufficient number of the Bitcoin futures exist – and I assume that some of these traders trade both and use the arbitrage opportunities – the Bitcoin price loses much of its daily volatility. That's what the futures generally do. But once the real Bitcoin price becomes much more stable, there will be many fewer reasons to buy or sell right now. The room for daily traders of the real Bitcoin will shrink.

Lots of people and bots may just follow a funny strategy – try to wait when the Bitcoin price drops by $30, buy, then it goes up $30, sell, and you make a profit that beats the fees. (Obviously, in the long run, you don't earn anything on it because sometimes the price refuses to return where you want it to return, so you may either be caught with Bitcoins during a collapse, or without Bitcoins during a growth you missed.) But when it will be harder for the Bitcoin to move by $30 up or down, the frequency of these transactions will diminish.

In the previous blog post, I discussed the high Bitcoin fees – one transaction costs $10 in average now. I mentioned that the fees went up because the Bitcoin price went up hugely

*but the daily number of transactions only increased some 20%*from a year ago. So if the number of transactions decreases, because the lower volatility makes it less interesting and exciting to buy or sell – and it's harder to beat the fees (which is a description of the change that is independent of emotions) – it will mean that the

*average transaction fee will increase further*.

If and when the futures are sufficiently numerous to reduce the volatility of the Bitcoin price to 1/5 of the present value, the average transaction fee may very well go from $10 to $50 as the number of real Bitcoin transactions drops from 300,000 to 60,000. This increase of the transaction fees would

*discourage transactions further*. This trend of the transaction fees and the boring evolution of the Bitcoin price will probably lead some of the smaller Bitcoin holders to sell everything – millions of small Bitcoin users couldn't afford a single fee, millions of others could only afford to pay a fee few times, and so on.

*BTCUSD in recent 7 days*

As the number of people who are meaningful members of the Bitcoin network drops, so will the idea that it's the money of the future, and even the larger investors realize that the game is over and it is meaningless to hold it. The wise short sellers should still try to buy the dips and sell the upticks from a smooth function, even if that function began to drop rather dramatically.

Let me say that the allowed daily drop (or rise) of the futures is 20%. It means to multiply the price by 0.8 a day. 0.8 to the fifth power is 0.32768 i.e. the fall by 2/3 a week, or by some 99% a month. It's plausible that the Bitcoin market understands the fate of this "asset" earlier and the Bitcoin price will systematically fall by more than 20% a day. In that case, however, I believe that the futures won't actually matter much.

While the futures open the trading to lots of big new investors and there are opportunities to make the price swings really volatile and unpredictable, I am convinced that – while there will be some events I can't predict – the overall appearance of the effect of the futures will clearly be "a huge reduction of the volatility". This fact by itself will repel the real Bitcoin trading and bets, reduce the number of transactions, increase the fees, and gradually encourage everyone to sell the Bitcoin.

Even though I can't really exclude the rise of the Bitcoin price above $10,000 or something like that – when millions of teenagers bet their parents' houses not only on the real Bitcoin but also the long futures positions – I find it unavoidable that if the trading of the futures begins at all, the path towards the incredibly shrinking Bitcoin will become obvious within a month or at most months, if not days. The potential for big gains in a month or two should evaporate because the futures will indicate a similar price as the current price or lower (otherwise there is the arbitrage opportunity I mentioned); the daily variations and the related gambling will also shrink (so the traders who basically do daily gambling will also fade away); and the fees will go up as the number of real Bitcoin transactions decreases, so lots of the normal Bitcoin users will disappear because they won't be able to afford the fees.

It seems somewhat plausible to me that those who decided to create the CME Bitcoin futures market – or who are actually behind the project – realize these things and they are doing it deliberately in order to deflate the Bitcoin bubble which some of them may be annoyed by (like me) or which others may even feel threatened by. It's also possible that the banks were intensely buying BTC in recent weeks – therefore the growth – and they will be selling real Bitcoins along with short positions to make the profit once the futures are available.

There are lots of unknowns that may invalidate the reasoning above. In particular, it seems totally plausible to me that most of the people – and even when weighted by their wealth – who trade the real Bitcoin are so financially illiterate (or obedient to the cult) that they won't understand or they won't use the arbitrage opportunity I mentioned, and they will buy the long futures to drive their price well above the current Bitcoin price, although it's clearly better to buy the real Bitcoin and wait for the expiration date instead. When BTC split to BTC and BCH, their total price – wealth of the old BTC holder – jumped discontinuously. Such irrational discrepancies do occur in the world of the Bitcoin because a big fraction of the traders really don't understand basic identities that hold in efficient markets, they don't understand key tricks to make profit. But I tend to think that when others, rational participants are allowed to enter – both short and long future positions, plus the Bitcoin itself – they will exploit the opportunities that the Bitcoin fans fail to exploit.

**Bonus: a table about the CME contracts**

One must realize that on top of the random walk above, there exist "legitimate" reasons for price changes, e.g. expected bans and other regulatory stories – negative and positive – as well as the worries about the potentially devastating SegWit2x fork next week, the subsequent exodus from BTC of those traders who think that the fork is a "dividend for free" they went to pick, and so on.

**Daily movements**

This is an update. The Bitcoin went from $7,100 to some $7,800, a new record, and then back to $7,100 or so, at Bittrex.com. The brutal 1-hour 10% drop in the evening was apparently because the 2x fork was called off by an e-mail by utterly sensible proponents who realize that the BTC straitjacket is already too tight. This should be good news for BTC – a huge existential threat has disappeared – but as I could already have predicted, for the clueless millennial "traders", it's bad news because they think that they won't get their "free dividend". ;-)

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