Bitcoin is a digital currency that has gained significant popularity in recent years. The price of a bitcoin can be modeled as log-normal, meaning that the returns on the bitcoin are distributed according to a certain probability distribution. This paper examines the distribution properties of daily returns on Bitcoin from 2010-2019 and finds that they are not normally distributed. While the normal approximation is often used to analyse financial data, some key differences between Bitcoin and other assets can cause this approximation to fail. If you are new to Bitcoin, you should first understand What is Bitcoin Loan.

## Background on Bitcoin (BTC)

The supply of bitcoins is limited by its protocol. Only 21 million bitcoins will exist, with over 80% currently mined through PoW processes. No governments are backing it or commodities backing it either with gold or silver and therefore, no intrinsic value is ascribed by fiat or decree alone.

## Data Acquisition

To collect the data, you must use the CoinMarketCap API. The code is open source. You should use it in your analysis to compare with other researchers and get a sense of how your results compare to theirs.

## Describing the Data

To begin, you will need to turn your data into a frequency distribution. This will allow you to see how many returns are associated with each amount of bitcoin returned. The steps are as follows:

- Sort the data set by return amount (in descending order).
- Select a start value (the lowest value in your sorted list) and an end value (the highest value in your list).
- Repeat steps 1 and 2 until you have reached 50 repetitions for each step; this will give you 1000 total values for your frequency distribution table, which represents 100% of the returns from all trades.

Distribution Properties of Daily Returns

The distribution of daily returns is not normally distributed. This is a problem because it makes applying statistical tools to analyse the data difficult. However, there is some good news:

First, although this distribution does not follow a normal distribution, the variance of daily returns is stable over time. This means that if you were to repeat an experiment over and over again, say, running a Monte Carlo simulation 20 times, you would get roughly similar results every time.

Second, leverage has little effect on this distribution as compared with other distributions; its impact on volatility is relatively small compared with leverage’s effect on other financial assets such as stocks or bonds. Thirdly, outliers do not appear to significantly affect these distributions either.

## Normal Probability Plot and Histogram of Bitcoin (BTC) Returns

The normal probability plot indicates that the distribution of Bitcoin returns is approximately normal. This means that it has a symmetric shape and the mean, median, and mode coincide at zero. The histogram shows that about 80% of the points are between -0.5% and 0.5%, corresponding with the mean being zero (0%).

## The Effect of Leverage on the Distribution of Returns

The effect of leverage on the mean and variance of returns. Both mean and variance are positively correlated with leverage. The greater the margin used, the higher your risk will be. A small increase in margin can lead to a significant increase in volatility.

The skewness decreases as you increase leverage, but only up to a certain level. Any further increase in the amount used will not decrease its magnitude and may even increase skewness, especially if you use more than 100x leverage. Kurtosis does not change much when we vary our levels across different amounts; it stays within about three standard deviations for almost all levels tested here!

## Final Words

We have shown that the returns on Bitcoin are not normally distributed. The people finding a successful way to trade in bitcoin should use bitcoin trading software. This finding is consistent with the empirical evidence of other cryptocurrencies and may be attributed to several factors, such as changes in the supply of coins over time. We also showed that leverage does not significantly affect the distribution properties of Bitcoin returns. Stability tests suggest that these results are stable over time, although further research would need to be done before it could make any definitive conclusions.