In this introduction notebook, we simply displayed the distribution of the returns and see that tails are heavy, meaning that standard quant models cannot be applied to cryptocurrencies either…

import numpy as np
import scipy
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
import seaborn as sns

We load historical data for ETH/USD and BTC/USD prices into pandas dataframe:

histo_BTC = pd.read_csv('BTCUSDT.csv')
histo_ETH = pd.read_csv('ETHUSDT.csv')

We convert the time in seconds of the ‘date’ column into dates:

histo_ETH['date'] = pd.to_datetime(histo_ETH['date'],unit='s')
histo_BTC['date'] = pd.to_datetime(histo_BTC['date'],unit='s')

We take a look at the dataframes, we display the tail and head of the dataframe for ETH/USD prices:

histo_ETH.tail()
date high low open close volume quoteVolume weightedAverage
32805 2017-06-21 16:30:00 330.00000 326.000000 327.953902 330.00000 176417.191868 537.719509 328.084046
32806 2017-06-21 17:00:00 330.00000 323.415775 330.000000 325.99900 235115.812230 721.174679 326.017841
32807 2017-06-21 17:30:00 325.99900 309.700000 325.999000 314.00000 1600835.815479 5082.966612 314.941242
32808 2017-06-21 18:00:00 321.49800 310.986006 314.000000 317.00007 636047.132561 2016.865421 315.364191
32809 2017-06-21 18:30:00 330.01475 317.001070 319.100000 323.05000 379339.250364 1165.505294 325.471924 
histo_ETH.head()
date high low open close volume quoteVolume weightedAverage
0 2015-08-08 06:00:00 1.85 1.61 1.65 1.85 90.024655 53.0404 1.697286
1 2015-08-08 06:30:00 1.85 1.71 1.85 1.71 20.686119 12.0898 1.711040
2 2015-08-08 07:00:00 1.85 0.50 1.75 1.85 33.717419 18.8862 1.785290
3 2015-08-08 07:30:00 1.85 1.85 1.85 1.85 0.000000 0.0000 1.850000
4 2015-08-08 08:00:00 1.85 1.85 1.85 1.85 0.000000 0.0000 1.850000

Below, we display their price time series:

plt.figure(figsize=(15,10))
plt.plot(histo_ETH['date'],histo_ETH['close'])
plt.plot(histo_BTC['date'],histo_BTC['close'])
plt.legend(['ETH','BTC'],loc=0)
plt.show()

png

And the volumes traded for the two crypto/USD rates:

plt.figure(figsize=(15,10))
plt.plot(histo_ETH['date'],histo_ETH['volume'],'.')
plt.plot(histo_BTC['date'],histo_BTC['volume'],'.')
plt.legend(['ETH','BTC'],loc=0)
plt.show()

png

We can also compute the returns for ETH/USD and BTC/USD:

returns_BTC = pd.DataFrame(np.diff(np.log(histo_BTC['close'].get_values()),axis=0))
returns_BTC.index = histo_BTC['date'].get_values()[1:]
returns_BTC.columns = ['returns']

returns_ETH = pd.DataFrame(np.diff(np.log(histo_ETH['close'].get_values()),axis=0))
returns_ETH.index = histo_ETH['date'].get_values()[1:]
returns_ETH.columns = ['returns']

And we display them:

plt.figure(figsize=(15,10))
plt.plot(returns_BTC,alpha=0.5)
plt.plot(returns_ETH,alpha=0.5)
plt.show()

png

We can also display the distribution of their returns. We display them alongside the Gaussian distribution. We can see that both ETH/USD and BTC/USD returns are heavy-tailed! Be careful of when using standard quant models and value-at-risks.

plt.figure(figsize=(15,10))
x = np.random.normal(0,np.std(returns_ETH['returns']),len(returns_ETH['returns']))
plt.hist(returns_ETH['returns'],bins=100,log=True,alpha=0.95)
plt.hist(returns_BTC['returns'],bins=100,log=True,alpha=0.95)
plt.hist(x,bins=100,log=True,alpha=0.95)
plt.legend(['ETH','BTC','Normal'])
plt.show()

png