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├── Efficient _Frontier_implementation.ipynb
└── README.md
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FILE: Efficient _Frontier_implementation.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Efficient Frontiner from Modern Portfolio Theory implemented in Python"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"My personal interest in finance has led me to take an online course on Coursera. It is a 5-course specialization by the University of Geneva partnered with UBS. It is not specifically for financial modelling, but more for general introduction in investment strategies and the theories surrounding them. As someone who doesn't have any experience in the industry, the course is really helpful to understand the big picture. I am currently on the 3rd course within the specialization, and I learned something very interesting called \"Modern Portfolio Theory\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"While I was going through the course, I thought it would be a very good material to practice my Python skills. Even though the course did not provide any technical details of how to implement it in Python, with some digging I found a couple of very useful blog posts I can refer to."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Series of Medium blog post by Bernard Brenyah (https://medium.com/@bbrenyah)\n",
"- Markowitz’s Efficient Frontier in Python [Part 1/2] (https://medium.com/python-data/effient-frontier-in-python-34b0c3043314)\n",
"- Markowitz’s Efficient Frontier in Python [Part 2/2] (https://medium.com/python-data/efficient-frontier-portfolio-optimization-with-python-part-2-2-2fe23413ad94)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Blog post by Bradford Lynch (http://www.bradfordlynch.com/)\n",
"- Investment Portfolio Optimization (http://www.bradfordlynch.com/blog/2015/12/04/InvestmentPortfolioOptimization.html)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Based on what I have learned through the course, and also from the above blog posts, I have tried to replicate it in my own way, tweaking bit and pieces along the way."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Modern Portfolio Theory"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Modern Portfolio Theory (MPT) is an investment theory developed by Harry Markowitz and published under the title \"Portfolio Selection\" in the Journal of Finance in 1952.\n",
"\n",
"There are a few underlying concepts that can help anyone to understand MPT. If you are familiar with finance, you might know what the acronym \"TANSTAAFL\" stands for. It is a famous acronym for \"There Ain't No Such Thing As A Free Lunch\". This concept is also closely related to 'risk-return trade-off'.\n",
"\n",
"Higher risk is associated with greater probability of higher return and lower risk with a greater probability of smaller return. MPT assumes that investors are risk-averse, meaning that given two portfolios that offer the same expected return, investors will prefer the less risky one. Thus, an investor will take on increased risk only if compensated by higher expected returns. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Another factor comes in to play in MPT is \"diversification\". Modern portfolio theory says that it is not enough to look at the expected risk and return of one particular stock. By investing in more than one stock, an investor can reap the benefits of diversification – chief among them, a reduction in the riskiness of the portfolio.\n",
"\n",
"What you need to understand is \"risk of a portfolio is not equal to average/weighted-average of individual stocks in the portfolio\". In terms of return, yes it is the average/weighted average of individual stock's returns, but that's not the case for risk. The risk is about how volatile the asset is, if you have more than one stock in your portfolio, then you have to take count of how these stocks movement correlates with each other. The beauty of diversification is that you can even get lower risk than a stock with the lowest risk in your portfolio, by optimising the allocation. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I will try to explain as I go along with the actual code. First, let's start by importing some libraries we need. \"Quandl\" is a financial platform which also offers Python library. If you haven't installed it before, of course, you first need to install the package in your command line \"pip install quandl\", and before you can use it, you also need to get an API key on Quandl's website. Sign-up and getting an API key is free but has some limits. As a logged-in free user, you will be able to call 2,000 calls per 10 minutes maximum (speed limit), and 50,000 calls per day (volume limit). https://www.quandl.com/"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import pandas as pd \n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"import quandl\n",
"import scipy.optimize as sco\n",
"\n",
"plt.style.use('fivethirtyeight')\n",
"np.random.seed(777)\n",
"\n",
"%matplotlib inline\n",
"%config InlineBackend.figure_format = 'retina'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to run the below code block, you will need your own API key. The stocks selected for this post is Apple, Amazon, Google, Facebook. Below code block will get daily adjusted closing price of each stock from 01/01/2016 to 31/12/2017."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
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" | 0 | \n",
" 2016-01-04 | \n",
" AAPL | \n",
" 101.783763 | \n",
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" 2016-01-05 | \n",
" AAPL | \n",
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" 2016-01-06 | \n",
" AAPL | \n",
" 97.291172 | \n",
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" 2016-01-07 | \n",
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" 93.185040 | \n",
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" 2016-01-08 | \n",
" AAPL | \n",
" 93.677776 | \n",
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" AAPL | \n",
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" AAPL | \n",
" 97.291172 | \n",
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" AAPL | \n",
" 93.185040 | \n",
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" AAPL | \n",
" 93.677776 | \n",
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" 101.783763 | \n",
" 636.99 | \n",
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" 759.44 | \n",
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" | 2016-01-05 | \n",
" 99.233131 | \n",
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" 97.291172 | \n",
" 632.65 | \n",
" 102.97 | \n",
" 759.33 | \n",
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" | 2016-01-07 | \n",
" 93.185040 | \n",
" 607.94 | \n",
" 97.92 | \n",
" 741.00 | \n",
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\n",
" \n",
" | 2016-01-08 | \n",
" 93.677776 | \n",
" 607.05 | \n",
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## Efficient Frontier using Scipy's optimize function
prerequisite: [Quandl](https://github.com/quandl)
```
pip install quandl
```
In order to import quandl in your environment, you first need to register and get an API key from [Quandl's website](https://www.quandl.com/)