This report analyses a range of bitcoin (BTC) statistical metrics from April 28, 2013. The data below measures BTC price movements over time, its moving averages, daily expected returns and its daily high, low and closing prices.
The below chart depicts bitcoin’s price from May 1, 2017 to May 21, 2018 as well as its 20-, 60- and 250-day moving average.
Its 250- and 60- day moving average crossed on April 21, 2018. As of May 10, 2018, bitcoin’s price dropped below its 250-day moving average. These are both indications of an upcoming continued downward trend for bitcoin’s 250-day moving average.
Bitcoin’s 60-day moving average has tracked consistently above its price since its cross back on January 16, 2018 (apart from outliers on March 3 - 5, 2018). It has been trending downwards since reaching its all-time high on January 29, 2018, of $14,324.12. This downward trend has shown signs of slowing down, having flattened out in the last month or so.
From the below high-low-close chart, we can see bitcoin’s daily price range went through a period of highs during the months when it was trading at its highest. This indicates an increase in volatility of daily price as bitcoin’s price increases.
Legend: Yellow line – daily close price
<table class="custom-table custom-table--non-responsive js-tablesorter"><thead></thead><tbody><tr><td>Mean</td><td>0.31%</td></tr><tr><td>Median</td><td>0.20%</td></tr><tr><td>Mode</td><td>0.00%</td></tr><tr><td>Range</td><td>64.61%</td></tr><tr><td>Standard Deviation</td><td>4.49%</td></tr><tr><td>Count</td><td>1,850</td></tr><tr><td>Min; Max</td><td>-22.93%; 41.68%</td></tr><tr><td>Sample variance</td><td>0.20%</td></tr><tr><td>Skewness</td><td>49.01%</td></tr><tr><td>Kurtosis</td><td>958%</td></tr></tbody></table>
The mean is the average daily return for bitcoin since data first became available on CoinMarketCap (April 28th, 2013) to May 21, 2018. It is the difference between each day’s closing and opening price expressed as a percentage of the opening price. This is the expected return of buying on the open and selling on the close. Between the periods specified above, Bitcoin’s expected average daily return is 0.31%.
The median is the middle number of the range in values of bitcoin daily returns. As the median of daily returns from bitcoin is positive (0.20%), we can see that there are more days of positive return than negative. The median is also smaller than the mean. This means that bitcoin’s daily expected returns are positively skewed with its positive outliers more extreme than its negative outliers.
Kurtosis and Skewness:
Looking at the kurtosis and skewness, we can surmise that bitcoin’s distribution is not normal. The positive skewness tells us that the distribution is positively skewed and therefore the positive values are more extreme than the negative ones.
The range is the difference between the highest and lowest expected daily return over the 1,850 days that were analysed. Bitcoin’s range is 64.61% – its lowest value was -22.93% while its highest value was 41.68%.
The count is the total number of bitcoin trading days we have analysed which is currently 1,850.
Proportion of negative and positive returns:
Out of the 1,850 trading days analysed, there have been 1,002 (54.16%) positive return days and 845 (45.68%) negative return days. There were also three days (0.16%) of zero return.
One actual standard deviation for the data that has been analysed is 81.14%. This means that 81.14% of the values lies within one standard deviation (4.49%) either side of the mean.
In conclusion, bitcoin’s historical returns have a standard deviation of 4.49%. This means that 81.14% of daily returns are between -4.19% and 4.80% while 98% lie between -13.17% and 13.79%.
<table class="custom-table custom-table--non-responsive js-tablesorter"><thead><tr><th>Standard Deviation</th><th>1</th><th>2</th><th>3</th></tr></thead><tbody><tr><td>Lower and Upper bounds</td><td>-4.19% to 4.80%</td><td>-8.68% to 9.30%</td><td>-13.17% to 13.79%</td></tr><tr><td>Count of returns within the bounds</td><td>1,501</td><td>1,741</td><td>1,813</td></tr><tr><td>% of returns within the bounds</td><td>81.14%</td><td>94.11%</td><td>98.00%</td></tr></tbody></table>