Statistical Analysis of BTC/USD


I want to make a quantitative study on Bitcoin, perhaps to see what are the statistical properties of the market and what can we really expect from it. I am working with the [ provided data](, which only starts from August 2010. It’s bad since the inception data could be invaluable, but I guess there were no exchanges that early, however it would be invaluable to see what people thought of it before that. Well fine, so Bitcoin starts from Aug 2010, before that it was just a toy, but still influenced it’s inception into becoming money.

We have 1305 datapoints which is really small, I wish there were some hourly data at hand, and this data is bi-daily data. I don’t know why, so we have to consider that too.

# Average

The first thing we would do is to calculate the average which is `459.16$`, which doesn’t qualify as the central point of the statistical distribution since the market is [heteroskedastic]( So which would mean that the average is actually the average between the last 2 datapoints `4473.94$` or the last datapoint for even more rigorous standards. I don’t believe in that. Several quant studies have proven that the market has a `memory`, though a subtle one, nontheless it persists. So I would prefer to use and `exponential moving average`. Now I have already wrote plenty of timeseries analysis articles so go and read those if you want to dwelve deep into it, but here I just want to present it simply. Anyone can plot an EMA, it’s available in all trading softwares.

Now I have a theory whereas I would still consider the market normally distributed, but only in the long term. I think the normal distribution is natural, and eventually all distributions converge towards it, but I can’t prove it. So that would mean that eventually BTC will go back to 0, over a long time period, as it came from 0, but not shown in the early data, that would make it normally distributed.

So I will work with it as it were normally distributed, but we will have to apply a slight correction to the mean given the data we have, and it has to be probably corrected, especially if BTC were to gain new heights which we don’t know if it will.

So as a natural function we will use `n-1` as the period which in this case is 1304. Thus the corrected mean of a hypothetical normal distribution would be `462.34$`. Obviously if BTC were to rise to `100,000$` then this will have to be recalculated, as it is an evolving function in time, it would only be correct backwards, which after BTC would end, would be worthless information anyway, we have to anticipate things while in the present, and that will anyway carry margins of errors.

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Experimentally we can also use the last high point as the mean, which would be `1151$`, if we think that a mean reversion to this level would be more probable than to the earlier `462$` level which I think it is, more on this later.

# Standard Deviation

Again as shown in earlier articles, I prefer to use the [unbiased estimator](, which would yield `774.05$` instead of `772.99$`. Not a big difference but it’s good if we are accurate.

# Putting it Together

* So all that is left is just to calculate the probability of the area outside the curve. If we know the standard deviation and the mean, we can calculate the probability of the price going above the last element, especially if it’s not at the top.

The location of the current price on the curve is at the `1.986484` sigma level, which can be found using the `STANDARDIZE()` function using spreadsheet editor like `=STANDARDIZE(4602.280,462.34,774.059)`.

This translated into a probability using the cumulative distribution function `=1-NORM.DIST(4602.280,462.34,774.059,1)`, it’s `1-` since it’s the area outside it.

This shows that the probability of the price being between the maximum `4748.255$` and the current price `4602.280$` is `0.000004438044843%`. Pretty damn low, it signals an immediate retracement or crash, especially given the big rapid spike that has happened lately, which is usually always bound for a quick correction.

* Of course nothing stops this from spiking above the maximum, and this is probably not an accurate way to measure the market, so let’s experimentally swap the mean to the latest maximum point of `1151$`

Interestingly the probability has immediately jumped to `0.044718443687775%`, that is a `10076.15x` increase, just for choosing a different mean.

**So as we can see, it’s not even the standard deviation that plays a big role, but the mean itself, choosing a correct mean is imperative!**

So normally in a heteroskedastic environment the last datapoint is the mean, but that is only true if the market doesn’t hit a new high or somehow stabilize itself at a standard level like commodities usually do (which BTC would be one). Again we can only look back not forward, but there are methods to extrapolate the mean forward and then we just use this to see the areas around it.

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I am not going into extrapolation here, but simply using the latest datapoint, which is the most accurate anyway (since with extrapolation the error margin usually increases exponentially with the distance from the latest known data).

* So let’s see what the experts are saying, by using the latest datapoint as the mean of the distribution: interestingly it turns into `50%`! Why `50%`? Because that is the probability of the price remaining at this level, since we are comparing the latest datapoint to itself.

Now if we want to calculate say the probability of price at or above `10,000$`, that would make it `10.05385%`, that is the probability that the BTC market would hit `10,000$` in the foreseeable future given the current data. Pretty neat isn’t it?

But hitting `30,000$` is only `0.000000089592689%`, so not even the math thinks that irrational “moon thinking” is possible, at least not at the moment.

But the inverse is true as well. The price collapsing back to `1000$` has a probability of `19.676694%`.

**[Wow so we can immediately draw a risk reward table here if we were to buy now with a 1000$ stoploss:](**
* Risk % = `0.196766944`
* Reward % = `0.10053859`
* Risk Amount = `0.782716434`
* Reward Amount = `4.60228088333333`

So given the risk/reward formula presented in the [previous article]((

`Expectancy = 0.10053859 * 4.60228088333333 – 0.196766944 * 0.782716434`
`Expectancy = 0.30869411`

It looks like buying BTC now has an expectancy of `0.30869411`, that would be a `30 cent profit for every dollar`, if our hypothesis that it can really go to `10,000$` with a 10% probability is true.

And that is a big if, because a heteroskedastic market is a very rough one to analyze, statisticians hate it. Now there are tools to make the market more user friendly like transforming the data and doing all sorts of analysis on it but that is above my paygrade, I have only a BS degree in economics, I have no experience with advanced quantitative analysis, and I am not even sure they do exactly this, most of the time they use these tools in a different way, like predicting volatility instead for HFT trading using the microstructure of the market, or doing cross arbitrage between similar instruments like the EUR/USD and EUR/USD futures and another derivative and triangulating inefficiencies. It gets very complicated once you get into financial analysis. It wasn’t interesting to me so I didn’t get into it, and mostly just big institutions that work with this, so your average trader Joe doesn’t have to know anything other than what was presented here.

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# Conclusion

Well it remains to be seen, I personally doubt the `10%` probability figure, I think it’s much lower, perhaps below `1%`, in which case the `3000$` and around levels are more accurate means. And this is not statistical analysis, this is just my gut feeling. I have seen the market, the euphoria around it, plus we have now the Chinese cracking down on BTC and other shenanigans with the “Core” scaling, I really doubt this is a perfect time for a bullish market, especially not at all time highs.

So from my experience, event analysis and my gut feeling in general I would place the effective mean at `2962$` because it was a local maximum for some time in the past year. It is a more reasonable, conservative price level, certainly nothing good happened recently that would put the price at 4000 or even 5000. It’s pure speculation, and the adoption is slowing down with the shenanigans happening between [BTC vs BCH](

Either that or below 1 level at `1151$` , but even if the `2962$` level is solid, that still gives us a measly `0.3657%` probability for a price hitting the `10000$` mark, so that changes our table to:
* Risk % = `0.99634268`
* Reward % = `0.00365732`
* Risk Amount = `0.782716434`
* Reward Amount = `4.60228088333333`

## Thus the `Final Expectancy` in my opinion is: `−0.763021776`

So that would mean that buying now would probably make us lose `76 cents for every dollar` invested in my opinion.

Thus it is my opinion that buying BTC right now is very very foolish, and it will most likely result in a loss. And we haven’t even considered the risks from the exchanges that always get “hacked” whenever there is a price rally. Totally worthless!


***Disclaimer: The information provided on this page or blog post might be incorrect, inaccurate or incomplete. I am not responsible if you lose money or other valuables using the information on this page or blog post! This page or blog post is not an investment advice, just my opinion and analysis for educational or entertainment purposes.***




Upvote, ReSteem & bluebutton

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