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Created March 7, 2019 10:28
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Black Crypto-Swans.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "Black Crypto-Swans.ipynb",
"version": "0.3.2",
"provenance": [],
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
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"accelerator": "GPU"
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"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
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"source": [
"<a href=\"https://colab.research.google.com/gist/gjlr2000/bef7480a4323463d64883d82c39fe3e6/black-crypto-swans.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"metadata": {
"id": "JmM7FayxP-1E",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"# Black Crypto-Swans\n",
"\n",
"\n",
"*This article is the first in a proposed series co-authored by Gerardo Lemus from Quanto ([website](https://quanto.company)) and [Kumar Suppiah](https://www.linkedin.com/in/kumar-suppiah/) of Project Jarvis. Project Jarvis is a pre-incorporation stealth mode digital asset trading startup supported by Quanto. Gerardo does the quantitative heavy lifting while Kumar tries to break it down into layman's terms with a dash of dry humour. Our co-authored articles are published by each individual author and you may find it reproduced [here](https://)*\n",
"\n",
"\n",
"Nassim Taleb popularized the idea of '[black swans'](https://en.wikipedia.org/wiki/The_Black_Swan:_The_Impact_of_the_Highly_Improbable) in Finance ( Unfortunately, it has nothing to do with Natalie Portman's movie.). These birds were living evidence that a simple theory ('all swans are white') was wrong; Taleb happily uses the monicker to denote proof that a model is wrong.\n",
"\n",
"The financial world likes to assume normality (or normality of the logarithm) of returns for the [calculation of risk](https://financetrain.com/var-calculation-the-assumptions-of-standard-distribution/) mainly because of the nice mathematics and the possibility of deriving clean and elegant formulas, especially closed-end ones. Quantitative researchers would love to find [beautiful equations](https://www.google.com/search?q=famous+mathematical+equations&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjI96CU7-DgAhWJHxQKHfvZD9cQ_AUIDigB&biw=1676&bih=974#imgrc=5oD-dJkK2ZxZYM:) like Newton and Einstein's physics ones.\n",
"\n",
"The Financial Crisis demolished such notions: stock returns (and returns of other asset classes) do not follow 'nice' random walks. Using the black swan analogy, the theory that stock returns are normally distributed is refuted given the 50 black swans that [have appeared since 1950](https://seekingalpha.com/article/3959933-predicting-stock-market-returns-lose-normal-switch-laplace) when the normal model predicted only one every 6,900 years.\n",
"\n",
"Cryptocurrencies (hereafter referred to as cryptos affectionately which also include tokens for those of you particular about semantics) have a much higher volatility than stocks, between [2 to 4 times](https://medium.com/@petervijn/volatility-of-bitcoin-litecoin-ether-and-dash-in-comparison-with-some-us-large-cap-stocks-d6aaeb88dc3e) as volatile using common standard deviation formulas.\n",
"\n",
"\n",
"## Avoiding the black crypto-swans (or unexpectedly going broke when you least expect it)\n",
"\n",
"Trading on margin (on exchanges which list derivate products) allows you to leverage your position ( [read this](https://) for example), *but* at the risk of being forcibly liquidated if your funds fall below a [minimum level](https://www.bitmex.com/app/riskLimits). Therefore, it is very important that you have good estimates of the danger of inadvertently crossing the line.\n",
"\n",
"Usually (as in the links above), the liquidation is triggered when the margin value of your funds is halved with respect to the original value (known as 'Base Initial Margin' in BitMex). \n",
"\n",
"A back of the envelope calculation yields the percentage change that your asset can move in terms of margin:\n",
"\n",
"${{Crypto}_{now} \\over {Crypto}_{initial}} \\leq {{2 - {{margin}_{pct}} \\over 2}}$\n",
"\n",
"If you are leveraged 100 times, your margin in percentage terms is 1%; plugging it into the formula ($( 2 - 0.01) / 2 = 0.995$ ) means that a 0.5% adverse return wipes out your position.\n",
"\n",
"How often can that move happen ?\n",
"\n",
"Some people are tempted to use [z-score](http://www.z-table.com/) tables on the value of $z = {-{loss} \\over {std}}$ (how many standard deviations away is your expected loss) to compute that probability; computing standard deviation is readily available in Excel, and normalized tables are easy to find.\n",
"\n",
"That naive process is **dangerous** - crypto returns are as far from normal as a white swan is, not from a black swan, but from a turkey ! (Yes, we're exaggerating on purpose here to be all dramatic.)\n",
"\n",
"\n",
"Below we demonstrate the correct methodology to verify if crypto returns are indeed normal.\n",
"\n",
"## First, download minute by minute data:\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n"
]
},
{
"metadata": {
"id": "vwEjZGFc2KnW",
"colab_type": "code",
"outputId": "92c11b52-a4d5-4e4b-b237-2e4045e41538",
"cellView": "both",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 680
}
},
"cell_type": "code",
"source": [
"#@title\n",
"# Downloading required data and previous examples \n",
"#\n",
"\n",
"\n",
"!wget --no-check-certificate https://www.cryptodatadownload.com/cdd/gemini_BTCUSD_2018_1min.csv \n",
"!wget --no-check-certificate https://www.cryptodatadownload.com/cdd/gemini_ETHUSD_2018_1min.csv \n",
"!wget --no-check-certificate https://www.cryptodatadownload.com/cdd/gemini_ZECUSD_2018_1min.csv \n",
"\n",
"#!wget -o /dev/null --load-cookies /tmp/cookies.txt \"https://www.cryptodatadownload.com/cdd/gemini_BTCUSD_2018_1min.csv\"\n",
"\n",
"\n",
" "
],
"execution_count": 0,
"outputs": [
{
"output_type": "stream",
"text": [
"--2019-03-05 11:32:07-- https://www.cryptodatadownload.com/cdd/gemini_BTCUSD_2018_1min.csv\n",
"Resolving www.cryptodatadownload.com (www.cryptodatadownload.com)... 35.173.69.207\n",
"Connecting to www.cryptodatadownload.com (www.cryptodatadownload.com)|35.173.69.207|:443... connected.\n",
"WARNING: cannot verify www.cryptodatadownload.com's certificate, issued by ‘CN=GeoTrust RSA CA 2018,OU=www.digicert.com,O=DigiCert Inc,C=US’:\n",
" Unable to locally verify the issuer's authority.\n",
"HTTP request sent, awaiting response... 200 OK\n",
"Length: 39556884 (38M) [text/csv]\n",
"Saving to: ‘gemini_BTCUSD_2018_1min.csv’\n",
"\n",
"gemini_BTCUSD_2018_ 100%[===================>] 37.72M 58.3MB/s in 0.6s \n",
"\n",
"2019-03-05 11:32:08 (58.3 MB/s) - ‘gemini_BTCUSD_2018_1min.csv’ saved [39556884/39556884]\n",
"\n",
"--2019-03-05 11:32:09-- https://www.cryptodatadownload.com/cdd/gemini_ETHUSD_2018_1min.csv\n",
"Resolving www.cryptodatadownload.com (www.cryptodatadownload.com)... 35.173.69.207\n",
"Connecting to www.cryptodatadownload.com (www.cryptodatadownload.com)|35.173.69.207|:443... connected.\n",
"WARNING: cannot verify www.cryptodatadownload.com's certificate, issued by ‘CN=GeoTrust RSA CA 2018,OU=www.digicert.com,O=DigiCert Inc,C=US’:\n",
" Unable to locally verify the issuer's authority.\n",
"HTTP request sent, awaiting response... 200 OK\n",
"Length: 36460867 (35M) [text/csv]\n",
"Saving to: ‘gemini_ETHUSD_2018_1min.csv’\n",
"\n",
"gemini_ETHUSD_2018_ 100%[===================>] 34.77M 57.3MB/s in 0.6s \n",
"\n",
"2019-03-05 11:32:10 (57.3 MB/s) - ‘gemini_ETHUSD_2018_1min.csv’ saved [36460867/36460867]\n",
"\n",
"--2019-03-05 11:32:11-- https://www.cryptodatadownload.com/cdd/gemini_ZECUSD_2018_1min.csv\n",
"Resolving www.cryptodatadownload.com (www.cryptodatadownload.com)... 35.173.69.207\n",
"Connecting to www.cryptodatadownload.com (www.cryptodatadownload.com)|35.173.69.207|:443... connected.\n",
"WARNING: cannot verify www.cryptodatadownload.com's certificate, issued by ‘CN=GeoTrust RSA CA 2018,OU=www.digicert.com,O=DigiCert Inc,C=US’:\n",
" Unable to locally verify the issuer's authority.\n",
"HTTP request sent, awaiting response... 200 OK\n",
"Length: 20540106 (20M) [text/csv]\n",
"Saving to: ‘gemini_ZECUSD_2018_1min.csv’\n",
"\n",
"gemini_ZECUSD_2018_ 100%[===================>] 19.59M 55.0MB/s in 0.4s \n",
"\n",
"2019-03-05 11:32:11 (55.0 MB/s) - ‘gemini_ZECUSD_2018_1min.csv’ saved [20540106/20540106]\n",
"\n"
],
"name": "stdout"
}
]
},
{
"metadata": {
"id": "RmiI6RQO0WOO",
"colab_type": "code",
"cellView": "both",
"colab": {}
},
"cell_type": "code",
"source": [
"#@title\n",
"import pandas as pd\n",
"import io\n",
"import requests\n",
"import matplotlib.pyplot as plt\n",
"\n"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "sP5CwdHWTVpg",
"colab_type": "code",
"cellView": "both",
"colab": {}
},
"cell_type": "code",
"source": [
"#@title\n",
"\n",
"\n",
"btcusd_2018 = pd.read_csv('gemini_BTCUSD_2018_1min.csv', skiprows = [0], header=0)\n",
"ethusd_2018 = pd.read_csv('gemini_ETHUSD_2018_1min.csv', skiprows = [0], header=0)\n",
"zecusd_2018 = pd.read_csv('gemini_ZECUSD_2018_1min.csv', skiprows = [0], header=0)\n",
"\n",
"btcusd_2018['Date'] = pd.to_datetime(btcusd_2018['Date'])\n",
"ethusd_2018['Date'] = pd.to_datetime(ethusd_2018['Date'])\n",
"zecusd_2018['Date'] = pd.to_datetime(zecusd_2018['Date'])\n",
"\n",
"btcusd_2018.set_index('Date', inplace = True)\n",
"ethusd_2018.set_index('Date', inplace = True)\n",
"zecusd_2018.set_index('Date', inplace = True)\n",
"\n",
"btcusd_2018 = btcusd_2018.sort_index()\n",
"ethusd_2018 = ethusd_2018.sort_index()\n",
"zecusd_2018 = zecusd_2018.sort_index()\n",
"\n"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "SHGyLisdQCyU",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"The 14th of November od 2018 was quite a bad day for cryptos ..."
]
},
{
"metadata": {
"id": "1dFsrECTfUra",
"colab_type": "code",
"outputId": "c0a7d424-7b3d-496f-d926-4e59078ab54d",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 320
}
},
"cell_type": "code",
"source": [
"btcusd_2018.rename(columns = {'Open':'BTCUSD'}, inplace = True)\n",
"ethusd_2018.rename(columns = {'Open':'ETHUSD'}, inplace = True)\n",
"zecusd_2018.rename(columns = {'Open':'ZECUSD'}, inplace = True)\n",
"\n",
"dt_start = '2018-11-14'\n",
"dt_end = '2018-11-26'\n",
"btcusd_2018['BTCUSD'].loc[dt_start:dt_end].plot(figsize=(15,4))\n",
"ethusd_2018['ETHUSD'].loc[dt_start:dt_end].plot(figsize=(15,4), secondary_y = True)\n",
"zecusd_2018['ZECUSD'].loc[dt_start:dt_end].plot(figsize=(15,4), secondary_y = True)\n",
"\n",
"\n"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7f6b478e6a20>"
]
},
"metadata": {
"tags": []
},
"execution_count": 5
},
{
"output_type": "display_data",
"data": {
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AckgSAOmhqeREZAf2tweHqqIyLm4UAPtrDrChdMtpvDJxJmiahtfn7e9uCCGE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\nAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 1080x288 with 2 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "NfSNyioi7bq_",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"Lets compute the returns. Because cryptos have a zero floor (the price of cryptos will never be negative), it is usually best practice to assume returns are log-normal. At the time resolutions we are analysing (minute returns) the [simple returns and the log returns](https://fintechprofessor.com/tag/log-returns-vs-simple-returns/) are very similar. To avoid over complication, we keep the same numerical limits (0.5%). In the code below you can change a flag to see how the shapes change.\n"
]
},
{
"metadata": {
"id": "SsVStsNoQe8P",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"## Are those abnormal returns we see...\n",
"\n",
"Below I use qq-plots to visually verify the normality assumption. A qq plot graphs the theoretical quantiles versus the empirical ones. If the normality assumption holds the empirical line will coincide with a straight line.\n",
"\n",
"Before jumping on the qq-plots, lets look at the returns as histograms and cumulative distribution functions.\n",
"\n",
"Look at the first histogram: \n",
"* The red plot shows the symmetrical shape that is expected from a normal distribution - this one is derived by blindly computing the standard deviation from the original data and simulating the process as if it was normal. Look at the tails: there are very few examples when the loss is greater that 0.5% \n",
"* The blue plot shows the actual distribution of returns. There is a huge spike at 0, but more worryingly there are many more examples where the losses are not only higher that 0.5%, but there is even one case when it was close to 2.5% - remember, we are looking at *minute by minute* returns.\n",
"\n",
"If your margin system is not fully automated and you are not glued to the screen (and we do feel sorry even if you are glued becasue you might not have a life outside of the magical world of cryptos), a 100x leverage is the the stuff of nightmares - in fact, there are dozens of blogs [warning against](https://hackernoon.com/why-you-shoud-never-trade-100x-at-bitmex-the-liquidation-price-vs-bankruptcy-price-606ccd4b7528) it.\n",
"\n",
"The qq-plot is an easier, visual way of verifying non-normality. Before jumping into it, lets look at the cumulative distribution function (cdf - the ones that look like S-curves). Again, the blue represents the actual return and the red represents a theoretical normal distribution.\n",
"\n",
"In the x-axis you have the log-returns, and the y-axis represents the cumulative probability of the return being lower than the x-point. You can use the **cdf** to estimate the probability of loss: compare the probability value in the y-axis that corresponds to the loss you wish to avoid. Notice: at -0.5%, the probability of loss on the blue line is *significantly higher* that in the red line. To compute the probabilities for other leverage units all that you need to do is to look at the graph.\n",
"\n",
"You might then ask whether other models work better on fat tails. It is possible us other models but:\n",
"* the advantage of data-centric systems compared to model-based ones is that you do not need to fit diverse models and suffer from model risk;\n",
"* Although, the disadvantage of data-centric systems is that they require lots of data and strong computing power (which is not as much a barrier with inexpensive data storage and computing power on demands nowadays),\n",
"* and for both: remember that *past performance is* **not** *an indicator of future results*\n",
"\n",
"If you understood cdf plots, now you can quickly grasp qq-plots: by changing the dimensions in such a way that the S-curve that corresponds to the normal like becomes a straight line, you can visually see how much the real returns differ from the normal assumption. In this case, **a whole lot**. (And we can't emphasises this enough)\n",
"\n",
"We ran the qq plot for 1, 5, and 30 minute returns. Each one of them differs from the straight line as much as a swan differs from a pig (even if the pig had lipstick on).\n"
]
},
{
"metadata": {
"id": "kZodW7bE8glf",
"colab_type": "code",
"outputId": "21de010c-dc7f-47ee-b860-22d4f761a9b3",
"cellView": "both",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 3135
}
},
"cell_type": "code",
"source": [
"#@title\n",
"import numpy as np\n",
"from statsmodels.distributions.empirical_distribution import ECDF\n",
"import matplotlib.pyplot as plt\n",
"import statsmodels.api as sm\n",
"import pylab\n",
"\n",
"logReturnFlag = True\n",
"#logReturnFlag = False\n",
"\n",
"for diff_lag in [1, 5, 30]:\n",
" print (diff_lag)\n",
" hedge = pd.concat([btcusd_2018['BTCUSD'],ethusd_2018['ETHUSD']], axis = 1).sort_index()\n",
" if logReturnFlag: \n",
" hedge['BTCUSDret'] = hedge['BTCUSD'] / hedge['BTCUSD'].shift(diff_lag)\n",
" hedge['ETHUSDret'] = hedge['ETHUSD'] / hedge['ETHUSD'].shift(diff_lag) \n",
" data = hedge['BTCUSDret'].loc['2018-11-14'].as_matrix()\n",
" measurements = np.log(data) * 100\n",
"\n",
" \n",
" else:\n",
" hedge['BTCUSDret'] = hedge['BTCUSD'].diff(diff_lag) / hedge['BTCUSD'].shift(diff_lag) * 100\n",
" hedge['ETHUSDret'] = hedge['ETHUSD'].diff(diff_lag) / hedge['ETHUSD'].shift(diff_lag) * 100\n",
" data = hedge['BTCUSDret'].loc['2018-11-14'].as_matrix()\n",
" measurements = data\n",
"\n",
" ecdf = ECDF(measurements)\n",
" data_norm = np.random.normal(np.mean(measurements),np.std(measurements), size=len(measurements))\n",
" ecdf_norm = ECDF(data_norm)\n",
" plt.plot(ecdf.x,ecdf.y)\n",
" plt.plot(ecdf_norm.x,ecdf_norm.y, color = 'r')\n",
" plt.show()\n",
" print (np.mean(measurements),np.std(measurements))\n",
"# plt.hist(x=measurements, bins='auto', color='b', alpha=1, rwidth=0.85)\n",
" plt.hist(x=data_norm, bins='auto', color='r', alpha=0.5, rwidth=0.85)\n",
" \n",
" plt.hist(x=measurements, bins=200, color='b', alpha=1, rwidth=0.85)\n",
" #plt.hist(x=data_norm, bins=200, color='r', alpha=0.5, rwidth=0.85)\n",
"\n",
" plt.show()\n",
" ecdf_a = pd.DataFrame([ecdf.x, ecdf.y]).T\n",
"\n",
"\n",
" sm.qqplot(data, line='s')\n",
" pylab.show()\n"
],
"execution_count": 0,
"outputs": [
{
"output_type": "stream",
"text": [
"1\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
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a4/Hw1FNP8dZbb5GamsrnP/959u7dS25ubpf9MzJSMM34mhc2Kyv0qfdiXaKMJVHGAYkz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\nzsKHV3OOAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 576x396 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "stream",
"text": [
"-0.007602318921418097 0.1981901017563663\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": 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nzp0KBoMqKytTfX29gsGgsrKytHz5ci1cuFBTp06diBwAAKS1hIes77nnHv3iF7+QJH38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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 576x396 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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zTbz00kuOrJFEzL7D843pIZUCM2feQXJytYWntDbYR0A3fKT5HrvSG+BSoETk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\n",
"text/plain": [
"<Figure size 576x396 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "stream",
"text": [
"5\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": 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Q8cyTmBYLvquvbXObRk8khAtynLEqS0R6qMMQrqqqoqCgoHm5sLCQysrK5uXF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\nKQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 576x396 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "stream",
"text": [
"-0.0394286814874312 0.44543186229382936\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": 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J/q3cv5V7l8Zf/xEF8sPnk4uKirRnzx4tXLhQPp8vuLyrq0u5ubkjbqe72x/J7kfN5XLI\n6+2Nyb5MZOX+rdv7Ny9E1uz/Puv+/q3du2Ru/yMdJET0tqd169bp+vXrkqSWlhZNnz5dOTk5am9v\nV09Pj/r6+tTa2qr8/PzIKgYAwGJCjpA7Ojq0f/9+dXZ2ymazqampSW+++aY2bNigiRMnym63q7Ky\nUmlpaaqoqFB5ebmSkpK0Zs0aORzja7oAAIB4SQqEc7J3jMRqOsHUqYtYsXL/Jvdur9r32OX+rTuf\neNtu99CD4a4uM38GY83k3/9Ys3Lvkrn9R33KGgAARBeBDACAAQhkAAAMQCADAGAAAhkAAAMQyAAA\nGIBABgDAAAQyAAAGiOhe1gDMM/RGI5VxqwNAZAhkwALG8q5gAKKDKWsAAAxAIAMAYAACGQAAAxDI\nAAAYgEAGAMAABDIAAAYgkAEAMACBDACAAQhkAAAMQCADAGAAAhkAAANwL2vAQI+793Q87jvNPbCB\n2GGEDACAAQhkAAAMQCADAGAAziEDFsd5YsAMBDIwzphywReA6GLKGgAAAxDIAAAYIKxAvnr1qubP\nn6/6+npJ0o0bN7RixQqVlZVp/fr1+uqrryRJjY2NWrp0qUpKSnT69OmxqxoAgAQTMpD9fr/27t2r\ngoKC4LIPPvhAZWVl+v3vf6/vf//78ng88vv9qq6u1m9/+1t99NFHqqur0xdffDGmxQMAkChCBnJq\naqqOHTsmt9sdXNbS0qJ58+ZJkgoLC3X+/Hm1tbUpOztbDodDaWlpysvLU2tr69hVDuBbJh+s1OSD\nlfEuA0AEQl5lbbPZZLMNXa2/v1+pqamSpMzMTHm9Xvl8PjmdzuA6TqdTXq83yuUCAJCYnvhtT4FA\nYFTLH5aRYZfNlvykJYTF5XLEZD+msnL/xvY+6anHL3Y5HvvYpAd9DPfYMNuTpEmj3FdYj40Txv7+\nY8DKvUvjr/+IAtlut2tgYEBpaWm6efOm3G633G63fD5fcJ2uri7l5uaOuJ3ubn8kux81l8shr7c3\nJvsykZX7N7l3e9/dxy73e3sf+5j/6z6Ge2y47UlS3yj3Fc5j44HJv/+xZuXeJXP7H+kgIaK3Pc2e\nPVtNTU2SpObmZs2ZM0c5OTlqb29XT0+P+vr61Nraqvz8/MgqBgDAYkKOkDs6OrR//351dnbKZrOp\nqalJBw8e1Pbt29XQ0KBp06apuLhYKSkpqqioUHl5uZKSkrRmzRo5HONrugAAgHgJGcgzZszQRx99\n9K3lJ0+e/Nayl19+WS+//HJ0KgMAwEK4UxcAAAYgkAEAMACBDACAAfj4RQAR4WMggehihAwAgAEI\nZAAADEAgAwBgAAIZAAADEMgAABiAq6yBJ/S4q40lrjgGMDqMkAEAMACBDACAAZiyBsYQ09kAwsUI\nGbCAyQcrNflgZbzLADACRshAAnC7HZIIXGA8Y4QMAIABCGQAAAxAIAMAYAACGQAAAxDIAAAYgEAG\nAMAAvO0JQFRxMxQgMoyQAQAwAIEMAIABCGTAQriFJmAuAhkAAAMQyAAAGIBABgDAAAQyAAAGiOh9\nyC0tLVq/fr2mT58uSXrmmWf09ttva+vWrRocHJTL5dKBAweUmpoa1WIBAEhUEd8Y5Ec/+pE++OCD\n4Pc7duxQWVmZFi1apEOHDsnj8aisrCwqRQIAkOiidqeulpYW/epXv5IkFRYWqra2lkAGMAR38QKG\nF3Eg//Of/9S7776rO3fuaO3aterv7w9OUWdmZsrr9UatSAAAEl1EgfyDH/xAa9eu1aJFi3T9+nWt\nXLlSg4ODwccDgUBY28nIsMtmS46khFFzuRwx2Y+prNz/mPc+6anHL3Y5ovrYpAd9DPO80Zj09TbG\npMZItzdG+L9vXeOt/4gCecqUKVq8eLEk6Xvf+56++93vqr29XQMDA0pLS9PNmzfldrtDbqe72x/J\n7kfN5XLI6+2Nyb5MZOX+Y9G7ve/uY5f7vb1Rfcz/dR/DPW80+r7exljUGOn2xgL/963Zu2Ru/yMd\nJET0tqfGxkadOHFCkuT1enXr1i299tprampqkiQ1Nzdrzpw5kWwaAABLimiEXFRUpM2bN+uvf/2r\n/ve//2nPnj3KysrStm3b1NDQoGnTpqm4uDjatQIAkLAiCuTJkyerpqbmW8tPnjz5xAUBAGBFUXvb\nE5DIeLsOgLHGrTMBADAAI2TgIY8bCZs8CuazjYHEwQgZAAADEMgAABiAKWtgHErEqWounIPVMUIG\nAMAABDIAAAZgyhqwoOCU90FJqtSXm3fEsxwAYoQMAIARGCED44jb7ZCUeBd0AWCEDACAEQhkAAAM\nQCAD48Dkg5VfT1eP3fYT8b3NwHjCOWTAYIQkYB2MkAEAMAAjZADG47aasAJGyAAAGIBABgDAAAQy\nAAAG4BwyLIfzkQBMRCADBpl8sDL4gQ/xrIEPmwBijylrAI81ljciAfBtBDJgAJPvlGVqXUCiIZCB\nODI5iEN5tO7x2gdgCs4hIyEFL9ya9JTsfXeDy7lwC4CpCGQYjSuiAVgFgQzo/nRr19beUa0/0pXI\nD66W/nLzQ99Lwefcv2BqfE3xRuvq60d/Fo/+rEbrcQdt/q077y9/ZIZkyGOPwYEe4olzyEgYbrcj\n5lcGP9iflc6fhtvreD4/DsRD1EfI+/btU1tbm5KSkrRz5049//zz0d4FEHPhjg4JoG8L/kxCvL/6\n0Z8d74WG1UQ1kC9evKj//Oc/amho0L/+9S/t3LlTDQ0N0dwFEtRw046je87owvDRqdNHH/ty845R\nT2UPtw8r4eAFiExUA/n8+fOaP3++JOn//u//dOfOHX355ZeaPHlyNHcTU263Q11dkb8gR7MOSTGt\nJdzeI61t6PRy5dBzilIwCIc75xgqgCM5VxnOuWFGbkPF+mcyJMhHOE8/3PMe/X81xMFvvuzq6g3+\nDYzmb8GE1wuMT1ENZJ/Pp+eeey74vdPplNfrjVkgP0loPfqHFOr74fb9QKTh9KR/zNH8GTy6/MG/\nkY5MHzwv0pFRuM979IIpk94vy6gwfJFOdYdaHg3hvB48+vrxsEefG48D7ngZL73Go86kQCAQiNbG\nfvGLX+iFF14IjpLfeOMN7du3Tz/84Q+jtQsAABJSVK+ydrvd8vl8we+7urrkcrmiuQsAABJSVAP5\nJz/5iZqamiRJly9fltvtHtfnjwEAiJWonkPOy8vTc889p9LSUiUlJemXv/xlNDcPAEDCiuo5ZAAA\nEBnu1AUAgAEIZAAADGCJQL5165befvttrVixQqWlpWpra4t3STFz7949bdu2TW+88YaWL1+uS5cu\nxbukmLt48aIKCgp09uzZeJcSM/v27dPrr7+u0tJS/f3vf493OXFx9epVzZ8/X/X19fEuJeaqqqr0\n+uuva+nSpWpubo53OTHV39+v9evX680331RJScm4+ru3xKc9NTY26tVXX9Urr7yiixcv6v3331dt\nbW28y4qJP//5z5o4caL+8Ic/6Nq1a9qxY4c8Hk+8y4qZ//73vzp58qTy8vLiXUrMcAtbye/3a+/e\nvSooKIh3KTF34cIFXbt2TQ0NDeru7taSJUv00ksvxbusmDl79qxmzJih1atXq7OzU6tWrVJhYWG8\nywqLJQL5rbfeCn5948YNTZkyJY7VxNbPfvYz/fSnP5V0/85pX3zxRZwrii2Xy6XDhw9r165d8S4l\nZhLxFrajlZqaqmPHjunYsWPxLiXmZs2aFfxQn6efflr9/f0aHBxUcnJynCuLjcWLFwe/Hm+v95YI\nZEnyer1699131dfXp7q6uniXEzMpKSnBr+vq6oLhbBUTJ06MdwkxF+9b2JrAZrPJZrPMy9sQycnJ\nstvtkiSPx6O5c+daJowfVlpaqs8//1w1NTXxLiVsCfc/9vTp0zp9+vSQZevWrdOcOXP0xz/+UX/7\n29+0Y8eOhJyyHqn33/3ud7p8+fK4+s85WiP1b2W8s9Gazpw5I4/Hk5CvdeE4deqUrly5oi1btqix\nsVFJSUnxLimkhAvkkpISlZSUDFl28eJF3blzR9/5znf0wgsvaOvWrXGqbmw9rnfpflB98skn+s1v\nfjNkxJxohuvfariFLc6dO6eamhodP35cDocj9BMSSEdHhzIzMzV16lRlZWVpcHBQt2/fVmZmZrxL\nC8kSV1k3NzfrT3/6kyTpH//4h6ZOnRrnimLn+vXrOnXqlA4fPqynnnoq3uUgBriFrbX19vaqqqpK\nR44cUXp6erzLiblLly4FZwV8Pp/8fr8yMjLiXFV4LHGnrtu3b2v79u3q6+vTV199pV27dik3Nzfe\nZcXEoUOH9Je//EXTpk0LLjtx4oRSU1PjWFXsfPrppzpx4oT+/e9/y+l0yuVyWWIK7+DBg7p06VLw\nFrbPPvtsvEuKqY6ODu3fv1+dnZ2y2WyaMmWKPvzwQ0sEVENDgz788MMhn7K3f//+Ia8BiWxgYEC7\ndu3SjRs3NDAwoLVr16qoqCjeZYXFEoEMAIDpLDFlDQCA6QhkAAAMQCADAGAAAhkAAAMQyAAAGIBA\nBgDAAAQyAAAGIJABADDA/wPtlywNDv/qpAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 576x396 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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+5mzeYgorGMdakiiu4Rl74PluFNTlmXd+ft3vpP9GvFQXXv6qi5r+UKg11B99\n9FHmzp3L448/DsD48eN54IEHWLp0aYMLFB8fT1FREXv37uWMM84gMzOTp556isLCQp577jnS0tLY\nsWMHsbGx6nqXFuf01cdaRnif6Bx2eUI8ibW0w/3Hcylt+C+Xe1rjP9ALfy6P2hAGA7z8skaaS+tU\na6ibzeaTtlrt0aOHz2flJ9q+fTvz5s0jLy8Ps9nMypUrSUpKIj4+npSUFB555BHuuecewP2HQo8e\nPejRowf9+/cnLS0Ng8HAww8/3IhvTcT/qh9d3txD/PSwDKeYUayriuqV9OJHz7md9GMFY1nBODZw\nKWW0rTpjqLpWw8K3JtU9txaR2tUp1HNzczFUbYzwySef1OlZ93nnnccbb7zh8/yQIUOqna72pz/9\nqdZriwSL+zn4ib1HzTHAff/36QlLlwtTzvdVc8ZXuRd/KXcP9HJGRFI+8grP4i8x3c/kRuBGABxA\nEXC8a7HI39+MiNRDraF+3333cccdd/Dzzz8zePBg4uLimDdvXiDKJhJ0za8l7juwa+t2Nvx2FMv6\nT7DeU7X4S95ez7nK8wZ49hqvvHAoWK1NXnIR8b9aQ71v3778+9//5siRI1itVj3jlpB3cpAHOsB9\nh/a0afXc6MPpxLz9G+9e419swuBwuE9FRVGWeg0Vo5OpHD0GZ5dQWfxFpHXzGer33nuvp8u9OvPn\nz/dLgUQCyWYzM2NGGOXlgR7Ydnp41zu0q2E4fBjrujVVa6qvwVjgHsLtMhiwDxrs3t0sKRn7BYPA\n1JIXfxGR6vgM9YsvvjiQ5RAJKO80s0C1xL0h3hTh7eFwYP76S+9e41u+xlA15sUZE0vZ5CnuZ+OJ\no3FFd2qae4pIs+Uz1FNTUz1f5+Tk8OOPP2IwGOjTpw/nnHNOQAon0tS8Xev+DHNvgJtM8OKLTTu9\nynhgP5bMqtb4J2sx/vqr+65mM5XDR1QNcEvG0f88MNa23aiIhJJan6nPmzePNWvWeLZfffrpp5k4\ncSKzZs0KRPlEmsTkyW3JzDTR9GF+cjd6QoKTdeuaeEGkigosmz/37G5m3uld/MUR353SK692D3C7\ndCSuyPZNe28RaVFqDfVNmzbx4YcfYrG4Bw5VVFSQlpamUJdmzxvk0LRh7g5yf86lNu7ZjTVzjXu6\n2Yb1GIvdU8dcYWFUjEqiYkwKFUkpOM7t5R72LiJCHUK9c+fOJy02Y7FYiIuL82uhRBrDP8/L3UE+\ndqyBN97ww9zs0lIsWZ96W+M//uA5Ze95LmVJye4pZ8MvgfDwpr+/iISEWkM9KiqKa665hmHDhuFy\nufjiiy/o3r07CxcuBGDmzJlzSlDZAAAgAElEQVR+L6RIXTRdF/vJXeonrhPuXnClkZcH9+IvP/6A\nde0q95SzrM8wlJW5T4W3o3zceCpGuxd/cZ7dowluKCKtQa2h3r17d7p37+55PWrUKH+WR6TebDYz\n//M/YTidjRkU5g5yvzwTr2IoOoZlw3qsa1ZhzVyNKde7RZs94Tz3ALekZCqHXARhYX4pg4iEtlpD\n/c477wxEOUQaxGYzc9ttbWt/Yw3atXPy889+eDbucmHasd0z3cyyKQuD3T0K3tmhI2VXprq71EeP\nwdm1W9PfX0RanVpDfdGiRbzyyisUFVUN1HG5MBgMZGdn+71wIjVxB3qbRlzB1bRzxgFD4RGsn2R6\nVnEzHTrovpPBgP2Cge4u9aQU7IMGQx02RhIRqY9af6v861//4l//+hdnnKFlJKX5cD8/r28ourvY\nw8Lg2WebaO64w4F569feAW5bvsLgdALg7NyZsklpVYu/JOHq3Lnx9xMRqUGtvxV79erFGWecgUlL\nSkoz4R7dXp+fR1eTPis3HDyIdd0arJmrsa5bi/HIEfddTCbsQy7yPBu3/+58Lf4iIgFVa6j//ve/\n58orr6R///4nBfsTTzzh14KJnMpmMzN9ehh2e92DMiHB0fgwr6zE8uVmrGtXw/q1dN6yxXPK0S2O\n0vSb3BujjEzE1aFj4+4lItIItYb6E088wVVXXUWXLl0CUR6RatV3QJzB4KpxG9LaGPfmerrULevX\nYSw65j5htVIxcrSnNe7o01eLv4hIs1FrqJ955pkaAS9B1ZABcfUO9LIyLFmfeTdGyfnec8pxdg9K\nJ19PRVIyHa4az9ESZ73KIiISKLWG+vnnn8+zzz7LoEGDTup+Hz58uF8LJtKQzVdMJlfdNlBxuTD9\nvAtLVWvc+tkGDKXuBWZc4eGUp4z1bIziPKen93Pt2kHJsQZ8NyIi/ldrqH/xxRcn/T+AwWBQqIvf\nNOTZOcDo0XbPym/VKirC+tkGzypupj27PafsfftVTTdLpvKi4dCmMVPlRESCo9ZQf+ONN047tnLl\nSr8URlq3xmyLOm1axenzzV0uTN9le1Zws3y+EUNlJQDOyPaUT7yqqjU+BmdcfBN8ByIiwVVrqO/b\nt48lS5ZQWFgIuHdp27RpE2PHjvV74aT1qP80NTez2cULL3i72w1Hf8Wyfp1nkJtp/z7PeysHXEDF\nmGQqRqdgH3whVO08KCISKmoN9fvuu4+RI0eSmZlJeno6a9asYf78+YEom7QSDQ30uDgnW746hvmb\nrVifqVr85asvMDgcADijoym7epK7NT5qDK7Y2KYuuohIs1JrqJtMJm699VY2bNjADTfcwLXXXsv/\n/u//cvHFFweifBLCbDYzM2aEUV5ev2fnMRwiLWoF84d9iLX/GoyHDwPgMhqxDx7iXfxlwAWgRZNE\npBWpNdTLy8s5cOAABoOB3NxcunXrRl5eXiDKJiGsPvPOTdi5iE1czn8Zx0ou5CsoBN4FxxldKZ1y\no3uA28hRuDpG+bfgIiLNWK2hPm3aNLKysrj55pu56qqrMJlMTJw4MRBlkxA2Y0bNo8vj2MtYVjKO\nFaSwio4cBcBlsVBx0Uj3SPUxKTj6JWjxFxGRKrWGenJysufrzZs3U1xcTIcOHfxaKAldvka4Wynn\nEj5lHCsYxwp+x3bPud86nUXpFddSkZRC5SWX4oqIDHCpRURaBp+hXlRUxPLly/nDH/4AwNKlS/nn\nP//JWWedxezZs+msHaeknk4dEHcOuzwhnsRa2uFeo72UNvyXy+kweQz9Zo3Gcc65lKs1LiJSK5+h\nPnv2bOLi4gD4+eefeeaZZ1iwYAG//PILjz/+OH/9618DVkhpuTIywnjtNQtOJ7SllMtZxzhWcDkf\n0YsfPe/Lpm9VvI9jk/VS5j9nYEiqHUcQyy4i0tL4DPXc3FyeeeYZwL3YzLhx47j44ou5+OKL+fDD\nDwNWQGm5RiW2xZWdw8yquB7JetrgXiDmGBHY+D0rGMdKxrKHswH3rmo/NNEWqSIirY3PUA8PD/d8\nvXnzZq699lrPa4O6QsUHw29Hefu2jVjWrOIjVnImuZ5zW7jA0xrPYjiVWE/6bJNskyoi0or5DHWH\nw8Hhw4cpLi5my5Ytnu724uJiSktrWF9bWhenE/P2b9xblK5djWnTJu5wuTvNDxPNP0ljBeP4mMs4\nQFefl1Ggi4g0ns9Qv+WWWxg/fjxlZWXceeeddOjQgbKyMqZMmcJ1110XyDJKM2M4fBjrJ2urtild\ngzH/EABODGxmqKc1/gVDcFLz4i8Gg4ubb648fd12ERGpN5+hnpiYyKeffkp5eTkREREAtGnThnvv\nvZdLLrkkYAWUZsDhwPzFJu9e41u+xuByAeCMiaVs8hQ+ixzLda9M4Aid6nxZtc5FRJpWjfPULRYL\nllM2vVCgtw7Ggwc8e42zPpOoqg19XGYzlcNHePYad/Q/D4xGbhrYjiPUZblXFyYT/PGPap2LiDS1\nWhefaYy5c+eybds2DAYDGRkZDBgwwHNu9erVvPTSS1itViZMmEB6ejpOp5OHH36YH374AYvFwiOP\nPELPnj39WUQ5rqICy/HW+NrVmHd86z135pmUXpHqXor10pG4Ituf9vG8vNoHT9a637mIiDSK30J9\n8+bN7Nmzh2XLlrFr1y4yMjJYtmwZAE6nkzlz5mCz2ejYsSO33HILycnJfPvttxw7doylS5d65sMv\nWrTIX0Vs9Yy/7PGEuGXDJxiLiwBwhYVRMSqpamOUFKIvHkxRQZHP62RkhFHTHuhGo4uXXvJujyoi\nIv7ht1DPysryLDHbs2dPjh49SlFRERERERQWFtK+fXuio6MBGDZsGBs3buTw4cOe1vyZZ57Jvn37\ncDgcmLTTVtMoLcWS9am3Nf7jD55T9p7nUpaUTGVSMhXDL4ETpjTWtLa6e9lXq8/zgAJdRCRA/Bbq\nBQUF9O/f3/M6Ojqa/Px8IiIiiI6Opri4mN27dxMXF8emTZsYOnQoffr04fXXX+emm25iz5495Obm\nUlhYWOOStFFR4ZjN/gn9mJgWvsa4ywU5OfDRR7BiBXzyCZSVuc+1awdXXAGXXw5jx2I+55wafxiO\n18XSpXDffZCbW8ObT3DXXXDrrXXbja2laPE/F01IdeGluvBSXXgFui78+kz9RK6q0dLgXrzmySef\nJCMjg8jISOLj4wH3iPuvv/6aG264gT59+nDOOeec9LnqFBb6Z/R0TEwk+fnH/HJtfzIUHcOyYb1n\npLrplz2ec/Z+/T17jVcOHQZhYd4P1vC9Hq+L+myXChAX5+Shh4rJz2/Qt9IstdSfC39QXXipLrxU\nF17+qoua/lDwW6jHxsZSUFDgeX3o0CFiYmI8r4cOHcpbb70FwNNPP+1ZZ/7uu+/2vCc5OZlOneo+\nRapVcrkw7djuCXHLpiwMdndXt7NDR8quTHV3qY8eg7NrtwbdYulSuOeeduzbV7+VBGfP1uh2EZFA\n8luojxgxgueee460tDR27NhBbGysZ747uPdpnzdvHm3btiUzM5M//vGPfPfdd7z++us88cQTrF+/\nnoSEBIzGukyTal0MhUewfpLpHuCWuQbTwQMAuAwG7BcMdO81npSCfdBgMDfun9j9zByo03Q1r6go\np56ji4gEmN9CfdCgQfTv35+0tDQMBgMPP/ww7733HpGRkaSkpHDdddcxdepUDAYDt956K9HR0XTs\n2BGXy8W1115LWFgYTz31lL+K17I4HJi3bXG3xteswrzlKwxOJwDOzp0pu3ayu1t91BhcTbglbl0G\nwfny5JNqpYuIBJrBVdtD62bOX89ugv1cyHDwINZ1a7Bmrsa6bi3GI0cAcJlM2C8c6nk2bv/d+eCH\n3oz6Pj8/rl07F888E7qj3YP9c9GcqC68VBdeqguvkHqmLvVUWYnly82ejVEs327znHJ0i6M0/SYq\nRidTOTIRV4eOfiuGzWbm//4vrJ7Pz11YLHDTTVolTkQkmBTqQWTcm3vy4i/HfgPAZbVSMXK0pzXu\n6NO3xrniTaUh3e3TplUoyEVEmgmFeiCVlWH5fKN3Y5Tvv/Occpx1NqWTqp6NjxjpnkceQDabuV6B\nHh3t5IknykO2m11EpCVSqPuTy4Xp512ejVGsn23AULUXvattW8pTxno2RnGeE9w17h99NKz2N6Ew\nFxFpzhTqTa2oCOtnG7CuXYV17WpMe3Z7Ttn79quabpZM5UXDoU2b4JXzBBkZYeTl1T7YLi7OyZYt\nxQEokYiINIRCvbFcLkzfZXufjW/aiKGiAgBnZHvKJ15V1RofgzMuPsiFPV19nqNrMRkRkeZNod4A\nhqO/Ylm/zhPkpv37POcqB1zgboknJVM5eAicsh99c1K3QHdx5pkGHnywVF3uIiLNnEK9LpxOzN9s\n9e5u9tUXGBwO96noaMqunuRd/CU2NsiFrdnJU9ZqHlF/vLvdPddSgS4i0twp1H3JzyfsnX+5g/yT\ntRir1rF3GY3YB11IxZgU9+IvAy6AFrI1bH2nrKm7XUSkZVGoH2e3Y/7qS6yZ7gFubNtK+6rF9hxd\nzqD0+nT3xigjR+GKig5yYeuvvlPWpk2rUHe7iEgL06pD3bgvD2vmGvcAt08yMf52FACXxQKjRlF0\niXsBGEdC/4As/uJPCxbUL9C1oIyISMvTukK9vBzLpizv4i/ZOz2nHGeeRenV11KRlELlJZfSuUc3\nSkNo/eKcnLqtD69AFxFpuUI+1I27f64a4LYK66frMZSUAOBq08azDGvFmBQc55zb4lvjNend20l2\nds3P/hXoIiItW0iHuvXjj+iQPtnz2t6rt2cFt8rhI6Bt/Xcha6lmzarwseuai/h4Fw89pFXiRERa\nupAOdXuvPpTe+AfsAy5wL/5y5lnBLlLQuAO7lIULreTkGOnd28nMmRoMJyISSkI61J09zqHo6WeD\nXYxmIzXVrhAXEQlhdRs9JSIiIs2eQj3E2WxmLrigHbGxEcTGRjBwYDtstpDuoBERabX02z2E2Wzm\n0wbH5eUZqo5pLXcRkVCjlnoIq2nBmYUL674YjYiItAwK9RD2/fe+/3nruhiNiIi0HPrNHqJsNjNO\np+/FdHr3dgawNCIiEggK9RBks5mZMaNNje+ZObMiQKUREZFA0UC5EGGzmVmwwEp2tpGa90l3sWhR\nmQbJiYiEIIV6CKhulLsvCQlOBbqISIhS93sIqM+2qup2FxEJXQr1Fs5mM1d1udcsLMzFokWamy4i\nEsrU/d6C1afb/dln9RxdRCTUqaXegtW1233aNO3GJiLSGqil3oL5XkDGhdEIfftqe1URkdZEod6C\n9e7tJDvbdNrxhAQn69aVBKFEIiISTOp+b8Fmzap+JLtGuIuItE4K9RYsNdXOokWlJCQ4MJtdJCQ4\nNMJdRKQV82v3+9y5c9m2bRsGg4GMjAwGDBjgObd69WpeeuklrFYrEyZMID09neLiYu6//36OHj1K\nZWUl06dP59JLL/VnEVu81FS7QlxERAA/hvrmzZvZs2cPy5YtY9euXWRkZLBs2TIAnE4nc+bMwWaz\n0bFjR2655RaSk5NZvXo1PXr04J577uHgwYPcdNNNrFixwl9FFBERCSl+637PysoiOTkZgJ49e3L0\n6FGKiooAKCwspH379kRHR2M0Ghk2bBgbN24kKiqKX3/9FYDffvuNqKgofxWvxbPZzCQmhtO1awSJ\nieHYbBrzKCLS2vkt1AsKCk4K5ejoaPLz8z1fFxcXs3v3biorK9m0aRMFBQVMmDCBffv2kZKSQnp6\nOvfff7+/iteiHV90JjvbhMNhIDvbxG23tVWwi4i0cgFLAZfL5fnaYDDw5JNPkpGRQWRkJPHx8QC8\n//77dOvWjVdffZXvvvuOjIwM3nvvvRqvGxUVjtl8+rSuphATE+mX6zbW889Xf/yFF9py663+uWdz\nrYtgUF14qS68VBdeqguvQNeF30I9NjaWgoICz+tDhw4RExPjeT106FDeeustAJ5++mni4uLYvHkz\nl1xyCQB9+/bl0KFDOBwOTCbfoV1Y6J/52DExkeTnH/PLtRtr584IqttededOF/n5RU1+v+ZcF4Gm\nuvBSXXipLrxUF17+qoua/lDwW/f7iBEjWLlyJQA7duwgNjaWiIgIz/lp06Zx+PBhSkpKyMzMZPjw\n4Zx11lls27YNgLy8PNq1a1djoLdWvXs763VcRERaB7+11AcNGkT//v1JS0vDYDDw8MMP89577xEZ\nGUlKSgrXXXcdU6dOxWAwcOuttxIdHc3kyZPJyMggPT0du93OI4884q/itWizZlVUu5GLFp0REWnd\nDK4TH3a3QP7q5mmuXUg2m5kFC6x8950RqxUqK/2/xntzrYtgUF14qS68VBdeqguvYHS/a7h0M3di\niJtMYLd7n6WXl7v/X5u2iIgIaJnYZu3EqWsul+GkQD/RwoV124JVRERCm0K9Gavrfum+t2AVEZHW\nRGnQjNU1rDXqXUREQKHerNU1rDXqXUREQKHerPnaL/24+HintloVEREPjX5vho6PeM/JMdKtmxOj\nEfbtM2CxBGYKm4iItEwK9Wbm+Ij34/btc494V4tcRERqo+73ZsbXiHdNWxMRkdoo1JsZXyPeNW1N\nRERqo6RoZrRZi4iINJRCvZnxNeJd09ZERKQ2CvVmJjXVzqJFpSQkODCbXSQkODRITkRE6kSj35uh\n1FS7QlxEROpNLXUREZEQoVAPIpvNTGJiOF27RpCYGE5GRthJr202daSIiEjdKTWC5NRFZrKzTWRn\nm0567T6v5+kiIlI3aqkHSV23VdWiMyIiUlcK9SCp62IyWnRGRETqSokRJHVdTEaLzoiISF0p1IOk\ntm1Vj9OiMyIiUlcaKBdg1W2reuCAgd69nVx8sYONG03k5Bjp3Vvbq4qISP0o1JvQiYHdu7fT0xo/\nfqxLFxf79nk7R7StqoiINCWFehOpboraia/BG+KnWrjQqlAXEZFG0zP1Bjh10ZjjLfSG0gh3ERFp\nCmqp15OvFrnR6GrwNTXCXUREmoKaiKc43go3m6l2qVZfLXKLpeH31Ah3ERFpCmqpn8D3c3HvQDZf\nXeWVlXW/T3y80zPiXSPcRUSkqailfgJfrfATl2r11VXet6+z2n3Qqzv29dfF7NtXxLp1JQp0ERFp\nMmqpn8BXK/zE47NmVZw2qh3wtLirC2kFt4iIBIJa6ifw1Qo/8Xhqqr3a1reCW0REgk0t9RPU1Ao/\nka8WuYiISDCppX6Ck1vhqBUuIiItilrqpzjeCo+JiSQ/vyTYxREREakzv4b63Llz2bZtGwaDgYyM\nDAYMGOA5t3r1al566SWsVisTJkwgPT2dd955hw8++MDznu3bt7NlyxZ/FlFERCRk+C3UN2/ezJ49\ne1i2bBm7du0iIyODZcuWAeB0OpkzZw42m42OHTtyyy23kJyczKRJk5g0aZLn8x999JG/iiciIhJy\n/PZMPSsri+TkZAB69uzJ0aNHKSoqAqCwsJD27dsTHR2N0Whk2LBhbNy48aTPv/DCC9xxxx0Nvn91\n67OLiIiEMr8lXUFBAf379/e8jo6OJj8/n4iICKKjoykuLmb37t3ExcWxadMmhg4d6nnvN998Q9eu\nXYmJian1PlFR4ZjNppOOLV0Kt93mfX18Zbj27SEtre7fQ0xMZN3fHOJUF16qCy/VhZfqwkt14RXo\nughY89Xl8m54YjAYePLJJ8nIyCAyMpL4+PiT3rt8+XJSU1PrdN3CwtMHsz36aDhgOu34nDkOxoyp\n2+A390C5Y3V6b6hTXXipLrxUF16qCy/VhZe/6qKmPxT81v0eGxtLQUGB5/WhQ4dOankPHTqUt956\ni0WLFhEZGUlcXJzn3KZNmxg4cGCD712XleFERERCjd9SbsSIEaxcuRKAHTt2EBsbS0REhOf8tGnT\nOHz4MCUlJWRmZjJ8+HAADh48SLt27bBaG74/eV1WhhMREQk1fut+HzRoEP379yctLQ2DwcDDDz/M\ne++9R2RkJCkpKVx33XVMnToVg8HArbfeSnR0NAD5+fmerxuqrivDiYiIhBKD68SH3S2Qr+cVNpuZ\nhQut5OQYG7TFqZ4LeakuvFQXXqoLL9WFl+rCKxjP1EN2npfWZxcRkdZGI8dERERChEJdREQkRCjU\nRUREQoRCXUREJEQo1EVEREKEQl1ERCREKNRFRERChEJdREQkRCjURUREQkSLXyZWRERE3NRSFxER\nCREKdRERkRChUBcREQkRCnUREZEQoVAXEREJEQp1ERGREKFQr8bhw4eZNm0aN954I2lpaWzbti3Y\nRQoqu93O/fffz/XXX891113Hl19+GewiBdXmzZsZPnw4mZmZwS5K0MydO5fJkyeTlpbGN998E+zi\nBFVOTg7JycksWbIk2EUJuvnz5zN58mSuueYaPv7442AXJ2hKS0uZOXMm6enpTJo0KaC/K8wBu1ML\n8sEHH3DVVVdxxRVXsHnzZhYuXMhrr70W7GIFzfvvv0/btm355z//yQ8//MADDzzA8uXLg12soPjl\nl1/4+9//zqBBg4JdlKDZvHkze/bsYdmyZezatYuMjAyWLVsW7GIFRUlJCXPmzGH48OHBLkrQff75\n5/zwww8sW7aMwsJCUlNTueyyy4JdrKDIzMzkvPPO45ZbbiEvL4+pU6cyevTogNxboV6NP/7xj56v\n9+/fT5cuXYJYmuC78sormThxIgDR0dH8+uuvQS5R8MTExPD888/z4IMPBrsoQZOVlUVycjIAPXv2\n5OjRoxQVFRERERHkkgWe1Wpl8eLFLF68ONhFCbohQ4YwYMAAANq3b09paSkOhwOTyRTkkgXe+PHj\nPV8HOkMU6j7k5+dz++23U1xczOuvvx7s4gSVxWLxfP366697Ar41atu2bbCLEHQFBQX079/f8zo6\nOpr8/PxWGepmsxmzWb9GAUwmE+Hh4QAsX76ckSNHtspAP1FaWhoHDhzg5ZdfDtg9W/1P4zvvvMM7\n77xz0rG77rqLSy+9lHfffZdPPvmEBx54oNV0v9dUH2+++SY7duwI6A9oMNVUF+KllablRKtXr2b5\n8uWt5ndmTZYuXUp2djb33nsvH3zwAQaDwe/3bPWhPmnSJCZNmnTSsc2bN3P06FE6dOhAYmIi9913\nX5BKF3jV1Qe4A27t2rW8+OKLJ7XcQ5mvumjtYmNjKSgo8Lw+dOgQMTExQSyRNBcbNmzg5Zdf5pVX\nXiEyMjLYxQma7du306lTJ7p27Uq/fv1wOBwcOXKETp06+f3eGv1ejY8//hibzQbA999/T9euXYNc\nouDKzc1l6dKlPP/884SFhQW7OBJkI0aMYOXKlQDs2LGD2NjYVtn1Lic7duwY8+fPZ9GiRXTs2DHY\nxQmqL7/80tNTUVBQQElJCVFRUQG5t3Zpq8aRI0f485//THFxMRUVFTz44INccMEFwS5W0DzzzDN8\n+OGHdOvWzXPs1VdfxWq1BrFUwbFu3TpeffVVfvrpJ6Kjo4mJiWmV3YxPPfUUX375JQaDgYcffpi+\nffsGu0hBsX37dubNm0deXh5ms5kuXbrw3HPPtcpQW7ZsGc899xw9evTwHJs3b95Jvzdai7KyMh58\n8EH2799PWVkZd955J0lJSQG5t0JdREQkRKj7XUREJEQo1EVEREKEQl1ERCREKNRFRERChEJdREQk\nRLT6xWdEAmX+/Pl8++23lJeXs3PnTgYOHAjANddcQ25uLna7nbvvvjtg5Xn//fe56qqryM/PZ86c\nOTz77LP1vkafPn3YsWPHaUul/vzzz8ydO9ezSE10dDR/+tOf6NevX5OU/biDBw/y008/MXz4cN57\n7z0cDgeTJk3yWS6RUKcpbSIBtnfvXqZMmcL69es9x5577rmAhrrD4WD8+PGeRWQaqrrwPHLkCFdf\nfTVPPfUUF154IeBepfHee+/lX//6V5MuwvHBBx+wa9eu0+pNoS6tlX7iRZqJgwcPMmPGDH766SeG\nDh3K7NmzAffiP19//TVlZWUMGTKE++67D4PBwIsvvsi6deswm8306tWL//f//h8HDx7kf/7nf+jd\nuze9evXi9ttvr/bzGRkZni0hH330Uc8fGYcPH+aBBx7g2LFjmEwmZs+eTe/evVm4cCFZWVkAnHHG\nGfzlL3/xuVzw66+/zoQJEzyBDjB06FDGjRvHP/7xD2bOnHlS6L733nts3LiRp556ilWrVvHKK69g\ntVpxOBzMnz+f+Ph4brzxRoYPH86WLVvYvXs3d911FwMHDmTBggW4XC46duxIUVHRaX8YVVRU8Oij\nj7Jnzx6Ki4uZOHEiU6dOJScnh9mzZ2OxWCgrK2P69OmMGjXKf/+4IgGiZ+oizcSePXt45plnePfd\nd7HZbBQWFvLRRx9x8OBBlixZwvLly/nll1/IzMxky5YtfPzxx7z55pu89dZbFBYW8p///AeAXbt2\nMX36dG6//Xafn7/rrruIjo4+bTW8p59+msTERP75z38yY8YM3n//fex2O23btuWtt95i6dKlHDt2\njE8//dTn97Fz507PFpwnuuCCC9i+fXuNdfDbb7/x17/+lTfeeIPExETefPNNz7mSkhIWL17M448/\nziuvvEL37t1JTU3lyiuvPGm75BP94x//IDY2ljfeeIN33nmHDz/8kO+++463336bpKQk3njjDV5+\n+eVWvZ2whBa11EWaicGDB3u28oyKiuLYsWNs2rSJrVu3cuONNwLu9bX37t3LL7/8wpAhQzyt5aFD\nh/Ltt98yZMgQOnTowDnnnAPg8/O9e/eutgzffPONJyCHDh3K0KFDATAajUyZMgWz2cxPP/1EYWGh\nz+8jLCwMp9Pp81xNOnfuzP3334/L5SI/P98z7uB4eQC6devG0aNHa7zOcZs2beLAgQN88cUXgLvl\n/ssvvzB27Fj+/Oc/s2/fPkaPHs1VV11Vp+uJNHcKdZFm4tS9p10uF1arleuuu46bb775pHOvv/76\nae89vq3jid3ivj6/d3gJHnYAAAKSSURBVO/eastgMBhOC+SvvvqKd999l3fffZfw8HBmzJhR4/fR\nq1cvtm7dyuWXX37S8W+//ZY+ffqc9v7KykrP/8+aNQubzcbZZ5/NkiVLTmrZn/h8vK5DgaxWK9On\nT2fcuHGnnfvPf/5DVlYW7733Hh988AFPP/10na4p0pyp+12kGRs8eDCrVq3CbrcD8Pzzz7N7924u\nuOACNm3a5AnErKwszj///Dp/3mg0eo6daODAgWzYsAFw7zR1//33c/jwYeLi4ggPDycvL4+tW7dS\nUVHhs8xTpkzh3//+N59//rnn2Ndff81HH33E9ddfD0BERAT79+8H3K1pgOLiYoxGI3FxcZSXl7Nm\nzZoa7wPuP0Kq+z5O/P4/+ugjAJxOJ0888QS//vorb7zxBgcOHCApKYnHH3+cbdu21XgfkZZCLXWR\nZuyyyy5j69atpKWlYTKZSEhIoHv37px99tlMmDCBG264AaPRSP/+/Zk4cSL79u2r0+ddLhedO3fm\n6quvZt68eZ73z5w5kwceeIDMzEwAHnroIbp3785rr73G9ddfT69evbjrrrt44YUXuOiii6ot8/Gd\n62bPnk1paSng7jL/29/+RufOnQG49dZbufnmmznrrLPo27cv+/fvp2PHjkycOJFrr72Wbt26cfPN\nN3Pfffd5Qrk6F154IXfffTcWi+W0ng6AG264gR9++IHJkyfjcDgYNWoUHTt25JxzzuGee+6hXbt2\nOJ1O7rnnnvr9w4g0U5rSJiJ+s3v3btLT0/nwww/p0KFDsIsjEvLU/S4ifnP22Wdz6623kpaW5pmi\nJyL+o5a6iIhIiFBLXUREJEQo1EVEREKEQl1ERCREKNRFRERChEJdREQkRCjURUREQsT/By8afu3/\naR2+AAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 576x396 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "stream",
"text": [
"30\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": 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Xdf7v//6PSy+9NKXFiYhkg9HUiGvx2yQOqcTyFex33V0TdVSUejNRmvQwbYbw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\nRQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 576x396 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "stream",
"text": [
"-0.2445661238416933 1.2162007946460807\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": 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AYXUBAIDYc5ZvCrk+ULImQZUgUpwhAwBgAAIZAGIge0up1SUgyRHIAAAYgEAGAMAABDIA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\n",
"text/plain": [
"<Figure size 576x396 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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ioym9czquCZNw974kKGWtWgV33dW+QTuv6ZS7iEjw1BnqV1xxRSDr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\nVPutawp0ERFpKM3UA6yue9C/+ab66+7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vXsx4HCH+X0hPXYg5bNOmTTgcDlJSUvD392fN\nmjVoNBq0Wi1JSUmkp6ejUqlYu3YtRqORnp6eWZX3+XyEhoaSnJzM8ePHle1zc3MpLCykqakJgKNH\nj6LRaLh69SqpqanodDpycnK4cOEC69evn7LOvzLXWSwWvn//DowNmV++fJnQ0FAAsrKyyMzMZOXK\nlaxevZre3l7UajVGo5GdO3cSFhZGZmYm+fn5SlCeSkxMDAcOHCAwMHDSSAdAeno67969Y/fu3Xi9\nXuLj41Gr1URERJCXl8eiRYsYHR0lLy/vn10YIeYo+aRNCPHbOJ1O9uzZQ0NDAyEhIf/r6ggx78nw\nuxDit9FqtWRlZZGSkqJ8oieE+H2kpy6EEELME9JTF0IIIeYJCepCCCHEPCFBXQghhJgnJKgLIYQQ\n84QEdSGEEGKekKAuhBBCzBN/AVCkYYjK3aSDAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 576x396 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "dQYPeLPuTOix",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"## Cryptos are risk loving junkies\n",
"\n",
"The above analysis hopefully educates those among you who consider yourselves as crypto traders on how risky and volatile an asset class cryptos are. (If you're in it to HODL, you've obviously dialled the wrong number to have reached us.)\n",
"Risk minimization requires:\n",
"* A good understanding of risk profiles; the normal assumption of returns can be lethal\n",
"* Dynamic active management as losses can pile up very quickly; in minutes or even less\n",
"* Active management of Exchange margin; you might need a 'rainy day' buffer to avoid being margin called.\n",
"* Understanding the tail optionality against you when trading on margin (many crypto traders [complain](https://www.reddit.com/r/BitMEX/comments/8sdljm/bitmex_scam/) they are being closed down at a profit for the exchange.)\n",
"\n",
"Now you should be able to extend your methodology to better manage your liquidation risk if you're trading leveraged derivatives or your loss risk if you're trading spot cryptos. You can decide on the acceptable probability of loss/liquidation, change the horizon (shorter, longer), etc.\n",
"Or you could liquidate your cryptos into fiat, withdraw your fiat balances, log out of your exchange accounts and call your stock broker to discuss your healthier investment portfolio construction. One where the volatility is healthier for your heart. (We're not medical professionals but we consider this to be some solid medical advice)"
]
}
]
}
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