I have fun making some MonteCarlo Simulations (which I talked about extensively in my post in Italy How to create MonteCarlo simulations in Excel) with the history series of Bitcoin.

### STATEMENT

After Bill Gates’s assertion that Bitcoin’s price will reach $ 500,000, I try to understand how this innovative asset investment can flourish by using the classic model that is common in the world of traditional finance.

Firstly, two parameters are needed to perform MonteCarlo simulations, ie volatility and average rate of return.

As you can see, volatility is very variable and the average may not be significant because it will be affected by the early years of Bitcoin presence where volatility is more than 300%.

### HOW YOU CAN READ IT

Graphs were obtained by measuring the volatility of twelve months (blue line) which then shifted from week to week, thus determining the trend of volatility called “Rolling” and the same for the red line, which is volatility at six months.

For those who understand the series of financial history, have a high rate of return, high volatility is required and Bitcoin is the highest prince in this case, perhaps also the king of the historical series with a high rate of return.

### HISTORICAL RETURN

To use the average return, I take into account the exponential graph line (which is actually a line that grows exponentially on a linear graph (as described in Post The difference between linear and logarithmic graphs).

This straight line, which is practically the SAFE Ratio of Bitcoin’s historical sequence shows that the annual average long-term return will be an incredible + 162%.

By taking the current volatility value at 12 months or 79%, and the average return + 162%, we can do a Montecarlo simulation (we have done 10,000 but we only mention 100 to allow better readable graphs) to understand how Bitcoin prices can developing in the coming months and years.

### DOLLAR MILLION QUESTION:

But are such trends sustainable in the long run?

Honestly, it is hard to imagine, even if it is the intention of the creator of Bitcoin and in theoretically scarcity logic, the price of Bitcoin could exceed the 500,000 Dollar predicted by Bill Gates.

OBSERVATION

Whether it’s the plans of the people who created Bitcoin, whether it be the elusive Satoshi Nakamoto or behind the pseudonym he used to cover the research team, you can guess from the fact that they estimate eight decimals after the decimal point, that is the price that can be achieved Bitcoin, because it is structured, remember, the stratosphere value 100,000,000,000 dollars or hundred million rupiah.

### ASSUMPTION

The most exciting of the assumptions, meaning the simulated “lucky” thousand made, the estimate of this return and this volatility can be achieved as early as 2024.

We are talking about simulations and assumptions, which are certainly supported by the almost absolute expansion of Bitcoin as a global payment system, objectively impossible to imagine, but still possible from a computational and probabilistic point of view.

### POSSIBILITY’

Looking at the numbers we can say that there is about 2% chance of Bitcoin going to reach a silly $ 100 million price by 2025.

In order for this montecarlo simulation to be reasonable, it is necessary to assume the growth in the number of users continues to exponentially, as described in the post.

Therefore, I have increased the amount of exponential growth in the number of wallets in circulation to date, with an average growth rate of 1.3% per month (last three years).

To assert that MonteCarlo’s simulations with Media = 162% and Volatility = 79% make sense in the long run, it should be said that by 2025 there should be 4.5 billion Wallets (something hard to imagine).

### OTHER ASSUMPTIONS

At this point, I think it would be more appropriate to reduce the average annual growth over time and therefore I made two further simulations, the first assuming a sad yearly return of 15% (slightly higher than the historical S stock & P500) but maintains arbitrary volatility at 79% and the resulting graph is as follows:

As you can see, with such high volatility, it can happen, to make pollution cryptic critics happy that Bitcoin (albeit with an equally low probability compared to the previous example of 100 million) can return to a sad 10 dollar value, but to be honest average yield on 10 years, with a low average rate of return but high volatility, however, is higher than 110,000 dollars.

As usual in an arbitrary way, I tried to make a MonteCarlo simulation with 10,000 assumptions with an average rate of return much lower than the current but enough against the very high volatility characterized by Bitcoin; Selected arbitrarily as usual (there is a reason but after doing this simulation three weeks ago I do not remember, please forgive me) to use an average annual return of 64% and a 79% volatility.

### SUSTAINABLE SHARPE

Why this option, you will ask yourself, because I am curious and I hope you too, to see where the Bitcoin price can go up with a Sharpe ratio lower than 1, so it all makes sense.

In this assumption there is no case where its value drops to 10 Dollars in one of 10,000 simulations.

### AS SHOWED

From this simulation, it is possible to extract the possibility of a Bitcoin price above a certain value or for example, what is the probability Bitcoin price above 5,000 in July 2018? From the graph we can conclude 98%, while reading it in the opposite way means that today we have about two percent chance that in June Bitcoin price will be under 5,000 US Dollars.

GOOD

To avoid being blamed for bringing misfortune, on the contrary, what is the probability Bitcoin price will be higher than 50,000 dollars in July 2018? From MonteCarlo simulations, a 4.2% random assumption with the characteristics outlined above would have a value of more than 50,000 dollars in July 2018.

But the interesting thing is there is a 50% chance that the price will rise above 50000 dollars in September 2023.

DO NOT CONSIDER WHAT SAY TO BE CONCLUSION ON

Obviously, the data obtained through random simulations must be considered in doubt, but useful for understanding the dynamics, potentials and risks that these innovative financial instruments offer (which I think should be considered an asset class to be owned in the portfolio, in “homeopathic” numbers of course) .

### INNOVATIVE PICTURES

Last but not least, I can only explain the Blog’s opening chart: MonteCarlo simulations in each quarter offer a return distribution derived from the simulation itself; to properly describe them as gaussians, it is necessary to use the exponential scale in the abscissa as the resulting distribution is clearly strongly influenced by the high average rate of return over the years that makes the capitalization effect of exponential results appropriately.

I hope you like this post and if so, share it on social networks so you can help me make it outstanding.

For those who want to download an excel file, you can do so by clicking here:

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