00_diy_quant_investing.md

DIY Quant Investing

DIY Quantitative Stock Market Investing

Dr. Yves J. Hilpisch | The Python Quants & The AI Machine

Saarbruecken, 6. SaarPython Meetup, 30. August 2022

(short link to this Gist: http://bit.ly/spm_diy)

Slides

You find the slides under http://certificate.tpq.io/spm_diy.pdf

Resources

This Gist contains selected resources used during the talk.

Dislaimer

All the content, Python code, Jupyter Notebooks, and other materials (the “Material”) come without warranties or representations, to the extent permitted by applicable law.

None of the Material represents any kind of recommendation or investment advice.

The Material is only meant as a technical illustration.

Leveraged and unleveraged trading of financial instruments, and of contracts for difference (CFDs) in particular, involves a number of risks (for example, losses in excess of deposits). Make sure to understand and manage these risks.

01_financial_data.ipynb

02_asset_allocation.ipynb

03_risk_budgeting.ipynb

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    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>"
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   "source": [
    "# DIY Quantitative Investing"
   ]
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   "source": [
    "### Risk Allocation & Risk Parity"
   ]
  },
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   "metadata": {},
   "source": [
    "&copy; Dr. Yves J. Hilpisch | The Python Quants GmbH\n",
    "\n",
    "http://tpq.io | [@dyjh](http://twitter.com/dyjh) | [team@tpq.io](mailto:team@tpq.io) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports and Data"
   ]
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  {
   "cell_type": "code",
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   "metadata": {
    "uuid": "b5c2a3e0-81d2-4aab-bee0-a9239fc9ffa6"
   },
   "outputs": [],
   "source": [
    "from mvp_portfolio import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "url = 'https://certificate.tpq.io/eod.csv'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "raw = pd.read_csv(url, index_col=0, parse_dates=True).dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "universe = ['AAPL.O', 'SPY', 'GLD', 'BTC=']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = raw[universe]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rets = np.log(data / data.shift(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "noa = len(universe)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Equally Weighted Portfolio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.array(noa * [1 / noa])\n",
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cov = rets.cov() * 252"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "vol = portfolio_volatility(w, rets)\n",
    "vol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "vol / noa  # \"average\" risk contribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.dot(cov, w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mvols = np.dot(cov, w) / vol  # marginal volatilities\n",
    "mvols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rc = mvols * w  # risk contributions (%-points)\n",
    "rc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rc.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rc / rc.sum()  # relative risk contributions (%)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sum(rc / rc.sum())  # checking for sum of relative risk contributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Risk Parity Portfolios"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rel_risk_contributions(weights, rets=rets):\n",
    "    vol = portfolio_volatility(weights, rets)\n",
    "    cov = rets.cov()\n",
    "    mvols = np.dot(cov, weights) / vol\n",
    "    rc = mvols * weights\n",
    "    rc = rc / rc.sum()\n",
    "    return rc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rel_risk_contributions(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mse_risk_contributions(weights, target, rets=rets):\n",
    "    rc = rel_risk_contributions(weights, rets)\n",
    "    mse = ((rc - target) ** 2).mean()\n",
    "    return mse * 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mse_risk_contributions(w, w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "bnds = noa * [(0, 1),]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cons = {'type': 'eq', 'fun': lambda weights: weights.sum() - 1}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "target = noa * [1 / noa,]  # risk parity as target\n",
    "target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt = minimize(lambda w: mse_risk_contributions(w, target=target),\n",
    "               w, bounds=bnds, constraints=cons)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rel_risk_contributions(opt['x'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "portfolio_volatility(opt['x'], rets)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random Risk Contributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "target = np.random.random(noa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "target /= target.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "target.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt = minimize(lambda w: mse_risk_contributions(w, target=target),\n",
    "               w, bounds=bnds, constraints=cons)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rel_risk_contributions(opt['x'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rel_risk_contributions(opt['x']) - target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "portfolio_volatility(opt['x'], rets)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Target Volatility"
   ]
  },
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   "outputs": [],
   "source": [
    "cons = {'type': 'eq', 'fun': lambda weights:\n",
    "        portfolio_volatility(weights, rets) - 0.15}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "target = noa * [1 / noa,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt = minimize(lambda w: mse_risk_contributions(w, target=target),\n",
    "               w, bounds=bnds, constraints=cons)"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt"
   ]
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt['x'].sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rel_risk_contributions(opt['x'])"
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "portfolio_volatility(opt['x'], rets)"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"30%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://tpq.io\" target=\"_blank\">http://tpq.io</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a> | <a href=\"mailto:team@tpq.io\">team@tpq.io</a>"
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mvp_portfolio.py

#
# Mean-Variance Portfolio Class
# Markowitz (1952)
#
# Python for Asset Management
# (c) Dr. Yves J. Hilpisch
# The Python Quants GmbH
#
import math
import numpy as np
import pandas as pd

def portfolio_return(weights, rets):
    return np.dot(weights.T, rets.mean()) * 252

def portfolio_variance(weights, rets):
    return np.dot(weights.T, np.dot(rets.cov(), weights)) * 252

def portfolio_volatility(weights, rets):
    return math.sqrt(portfolio_variance(weights, rets))