Зміст курсу

Introduction to Portfolio Management with Python

1. Portfolio Analysis Basics

What You Will Learn Investing Basics What is Portfolio?Portfolio Returns Measuring Risk of Portfolio Annualized Return Annualized Risk

2. Portfolio Optimization Basics

Risk Adjusted Return Overview of Modern Portfolio Theory Markowitz Portfolios Challenge: Computing GMV Portfolio Challenge: Computing MSR Portfolio

3. Factor Investing

Introduction to Factor Analysis The Capital Asset Pricing Model The Fama-French Factor Model The 5-factor Model

The Capital Asset Pricing Model

Now, when we've covered the basics of Factor Analysis, let’s dive into the first and likely the most famous factor model - The Capital Asset Pricing Model, or simply - CAPM.

Before we move forward, however, we need to define an important component that will be essential for this model.

Excess Return

An important component to discuss is Excess Return.

Practically, excess return can be computed using the following formula:

Defining Model

Now, when we've discovered what excess return is, let's define The Capital Asset Pricing Model itself.

To do this, we will use the following formula:

Here, we also consider market's excess return in addition to portfolio's one.

The expected return of the market is practically measured using a broad market index, that reflects the overall performance of a large segment or the entirety of a particular market, typically representing a country's or region's equity market.

It usually includes a diverse mix of stocks across various sectors and industries, giving a general overview of the market's performance and economic health.

As an example of such index, we can consider S&P 500, which tracks 500 large-cap U.S. companies, broadly representing the U.S. stock market.

Alternatively, we can rewrite the following formula in the next way, with the same notation:

Here, we can see, that this expression looks like a special case of linear regression, where the bias is constant and equal to risk-free rate, while market's excessive return is an independent variable, used for predicting portfolio's expected return.

We'll use this fact later.

So, practically, The Capital Asset Pricing Model is utilized to compute the expected return of an asset or portfolio, where the market's return is taken into account as a factor.

Another key concept to introduce is Beta, which we will explore in a more detailed way in the following video, along with additional explanations and code examples:

Here is a code example of computing beta:


              123456789101112131415161718192021222324252627282930313233343536373839404142
            
# Importing pandas for data manipulations, numpy for working with vectors and statsmodels for linear regression
import pandas as pd
import numpy as np
import statsmodels.api as sm

# Creating DataFrame `stocks` with values of stock prices of Apple, Meta and Amazon for the period from `2024-09-06` to `2024-09-16`
stocks = pd.read_csv('https://codefinity-content-media-v2.s3.eu-west-1.amazonaws.com/courses/d3c6f4c2-7887-4a07-8596-d956c61f2a2a/section2/stocks_capm_example.csv')
print('Stocks:')
print(stocks)

# Creating DataFrame `sp500` with values of S&P 500 index
sp500 = pd.read_csv('https://codefinity-content-media-v2.s3.eu-west-1.amazonaws.com/courses/d3c6f4c2-7887-4a07-8596-d956c61f2a2a/section2/sp500_capm_.csv')
print('S&P 500:')
print(sp500)

# Defining list of weights  and risk-free rate
weights = [0.5, 0.3, 0.2]
risk_free_rate = 0.002

# Computing returns of stocks
returns_stocks = stocks.pct_change()

# Computing returns of S&P 500 index
returns_sp = sp500.pct_change()

# Computing returns of portfolio
returns_portfolio = returns_stocks.dot(weights)

# Computing excess returns of portfolio
portfolio_excess_returns = returns_portfolio.values[1:] - risk_free_rate

# Computing excess returns of S&P 500 index
sp500_excess_returns = returns_sp.values[1:] - risk_free_rate

# Creating and fitting linear regression model `lr`
lr = sm.OLS(sp500_excess_returns, portfolio_excess_returns)
results = lr.fit()

# Computing portfolio's beta
beta = results.params[0]
print('Portfolio\'s Beta:')
print(beta)

Here is a corresponding Google Colab.

In conclusion, it's important to emphasize that another use of beta is estimating risk.

If a portfolio has a high beta, whether positive or negative, it signifies that the portfolio is very risky, as it is highly sensitive to market price fluctuations. As a result, it is advisable to avoid using this portfolio.

Завдання

Compute excess return for an entire portfolio.
Define linear regression model for computing beta.
Retrieve value of beta from the model.

Перейдіть на комп'ютер для реальної практикиПродовжуйте з того місця, де ви зупинились, використовуючи один з наведених нижче варіантів

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Дякуємо за ваш відгук!

Секція 3. Розділ 2

The Capital Asset Pricing Model

Now, when we've covered the basics of Factor Analysis, let’s dive into the first and likely the most famous factor model - The Capital Asset Pricing Model, or simply - CAPM.

Before we move forward, however, we need to define an important component that will be essential for this model.

Excess Return

An important component to discuss is Excess Return.

Practically, excess return can be computed using the following formula:

Defining Model

Now, when we've discovered what excess return is, let's define The Capital Asset Pricing Model itself.

To do this, we will use the following formula:

Here, we also consider market's excess return in addition to portfolio's one.

It usually includes a diverse mix of stocks across various sectors and industries, giving a general overview of the market's performance and economic health.

As an example of such index, we can consider S&P 500, which tracks 500 large-cap U.S. companies, broadly representing the U.S. stock market.

Alternatively, we can rewrite the following formula in the next way, with the same notation:

We'll use this fact later.

So, practically, The Capital Asset Pricing Model is utilized to compute the expected return of an asset or portfolio, where the market's return is taken into account as a factor.

Another key concept to introduce is Beta, which we will explore in a more detailed way in the following video, along with additional explanations and code examples:

Here is a code example of computing beta:


              123456789101112131415161718192021222324252627282930313233343536373839404142
            
# Importing pandas for data manipulations, numpy for working with vectors and statsmodels for linear regression
import pandas as pd
import numpy as np
import statsmodels.api as sm

# Creating DataFrame `stocks` with values of stock prices of Apple, Meta and Amazon for the period from `2024-09-06` to `2024-09-16`
stocks = pd.read_csv('https://codefinity-content-media-v2.s3.eu-west-1.amazonaws.com/courses/d3c6f4c2-7887-4a07-8596-d956c61f2a2a/section2/stocks_capm_example.csv')
print('Stocks:')
print(stocks)

# Creating DataFrame `sp500` with values of S&P 500 index
sp500 = pd.read_csv('https://codefinity-content-media-v2.s3.eu-west-1.amazonaws.com/courses/d3c6f4c2-7887-4a07-8596-d956c61f2a2a/section2/sp500_capm_.csv')
print('S&P 500:')
print(sp500)

# Defining list of weights  and risk-free rate
weights = [0.5, 0.3, 0.2]
risk_free_rate = 0.002

# Computing returns of stocks
returns_stocks = stocks.pct_change()

# Computing returns of S&P 500 index
returns_sp = sp500.pct_change()

# Computing returns of portfolio
returns_portfolio = returns_stocks.dot(weights)

# Computing excess returns of portfolio
portfolio_excess_returns = returns_portfolio.values[1:] - risk_free_rate

# Computing excess returns of S&P 500 index
sp500_excess_returns = returns_sp.values[1:] - risk_free_rate

# Creating and fitting linear regression model `lr`
lr = sm.OLS(sp500_excess_returns, portfolio_excess_returns)
results = lr.fit()

# Computing portfolio's beta
beta = results.params[0]
print('Portfolio\'s Beta:')
print(beta)

Here is a corresponding Google Colab.

In conclusion, it's important to emphasize that another use of beta is estimating risk.

Завдання

Compute excess return for an entire portfolio.
Define linear regression model for computing beta.
Retrieve value of beta from the model.

Все було зрозуміло?

Дякуємо за ваш відгук!

Секція 3. Розділ 2

The Capital Asset Pricing Model

Now, when we've covered the basics of Factor Analysis, let’s dive into the first and likely the most famous factor model - The Capital Asset Pricing Model, or simply - CAPM.

Before we move forward, however, we need to define an important component that will be essential for this model.

Excess Return

An important component to discuss is Excess Return.

Practically, excess return can be computed using the following formula:

Defining Model

Now, when we've discovered what excess return is, let's define The Capital Asset Pricing Model itself.

To do this, we will use the following formula:

Here, we also consider market's excess return in addition to portfolio's one.

It usually includes a diverse mix of stocks across various sectors and industries, giving a general overview of the market's performance and economic health.

As an example of such index, we can consider S&P 500, which tracks 500 large-cap U.S. companies, broadly representing the U.S. stock market.

Alternatively, we can rewrite the following formula in the next way, with the same notation:

We'll use this fact later.

So, practically, The Capital Asset Pricing Model is utilized to compute the expected return of an asset or portfolio, where the market's return is taken into account as a factor.

Another key concept to introduce is Beta, which we will explore in a more detailed way in the following video, along with additional explanations and code examples:

Here is a code example of computing beta:


              123456789101112131415161718192021222324252627282930313233343536373839404142
            
# Importing pandas for data manipulations, numpy for working with vectors and statsmodels for linear regression
import pandas as pd
import numpy as np
import statsmodels.api as sm

# Creating DataFrame `stocks` with values of stock prices of Apple, Meta and Amazon for the period from `2024-09-06` to `2024-09-16`
stocks = pd.read_csv('https://codefinity-content-media-v2.s3.eu-west-1.amazonaws.com/courses/d3c6f4c2-7887-4a07-8596-d956c61f2a2a/section2/stocks_capm_example.csv')
print('Stocks:')
print(stocks)

# Creating DataFrame `sp500` with values of S&P 500 index
sp500 = pd.read_csv('https://codefinity-content-media-v2.s3.eu-west-1.amazonaws.com/courses/d3c6f4c2-7887-4a07-8596-d956c61f2a2a/section2/sp500_capm_.csv')
print('S&P 500:')
print(sp500)

# Defining list of weights  and risk-free rate
weights = [0.5, 0.3, 0.2]
risk_free_rate = 0.002

# Computing returns of stocks
returns_stocks = stocks.pct_change()

# Computing returns of S&P 500 index
returns_sp = sp500.pct_change()

# Computing returns of portfolio
returns_portfolio = returns_stocks.dot(weights)

# Computing excess returns of portfolio
portfolio_excess_returns = returns_portfolio.values[1:] - risk_free_rate

# Computing excess returns of S&P 500 index
sp500_excess_returns = returns_sp.values[1:] - risk_free_rate

# Creating and fitting linear regression model `lr`
lr = sm.OLS(sp500_excess_returns, portfolio_excess_returns)
results = lr.fit()

# Computing portfolio's beta
beta = results.params[0]
print('Portfolio\'s Beta:')
print(beta)

Here is a corresponding Google Colab.

In conclusion, it's important to emphasize that another use of beta is estimating risk.

Завдання

Compute excess return for an entire portfolio.
Define linear regression model for computing beta.
Retrieve value of beta from the model.

Все було зрозуміло?

Дякуємо за ваш відгук!

Now, when we've covered the basics of Factor Analysis, let’s dive into the first and likely the most famous factor model - The Capital Asset Pricing Model, or simply - CAPM.

Before we move forward, however, we need to define an important component that will be essential for this model.

Excess Return

An important component to discuss is Excess Return.

Practically, excess return can be computed using the following formula:

Defining Model

Now, when we've discovered what excess return is, let's define The Capital Asset Pricing Model itself.

To do this, we will use the following formula:

Here, we also consider market's excess return in addition to portfolio's one.

It usually includes a diverse mix of stocks across various sectors and industries, giving a general overview of the market's performance and economic health.

As an example of such index, we can consider S&P 500, which tracks 500 large-cap U.S. companies, broadly representing the U.S. stock market.

Alternatively, we can rewrite the following formula in the next way, with the same notation:

We'll use this fact later.

So, practically, The Capital Asset Pricing Model is utilized to compute the expected return of an asset or portfolio, where the market's return is taken into account as a factor.

Another key concept to introduce is Beta, which we will explore in a more detailed way in the following video, along with additional explanations and code examples:

Here is a code example of computing beta:


              123456789101112131415161718192021222324252627282930313233343536373839404142
            
# Importing pandas for data manipulations, numpy for working with vectors and statsmodels for linear regression
import pandas as pd
import numpy as np
import statsmodels.api as sm

# Creating DataFrame `stocks` with values of stock prices of Apple, Meta and Amazon for the period from `2024-09-06` to `2024-09-16`
stocks = pd.read_csv('https://codefinity-content-media-v2.s3.eu-west-1.amazonaws.com/courses/d3c6f4c2-7887-4a07-8596-d956c61f2a2a/section2/stocks_capm_example.csv')
print('Stocks:')
print(stocks)

# Creating DataFrame `sp500` with values of S&P 500 index
sp500 = pd.read_csv('https://codefinity-content-media-v2.s3.eu-west-1.amazonaws.com/courses/d3c6f4c2-7887-4a07-8596-d956c61f2a2a/section2/sp500_capm_.csv')
print('S&P 500:')
print(sp500)

# Defining list of weights  and risk-free rate
weights = [0.5, 0.3, 0.2]
risk_free_rate = 0.002

# Computing returns of stocks
returns_stocks = stocks.pct_change()

# Computing returns of S&P 500 index
returns_sp = sp500.pct_change()

# Computing returns of portfolio
returns_portfolio = returns_stocks.dot(weights)

# Computing excess returns of portfolio
portfolio_excess_returns = returns_portfolio.values[1:] - risk_free_rate

# Computing excess returns of S&P 500 index
sp500_excess_returns = returns_sp.values[1:] - risk_free_rate

# Creating and fitting linear regression model `lr`
lr = sm.OLS(sp500_excess_returns, portfolio_excess_returns)
results = lr.fit()

# Computing portfolio's beta
beta = results.params[0]
print('Portfolio\'s Beta:')
print(beta)

Here is a corresponding Google Colab.

In conclusion, it's important to emphasize that another use of beta is estimating risk.

Завдання

Compute excess return for an entire portfolio.
Define linear regression model for computing beta.
Retrieve value of beta from the model.

Секція 3. Розділ 2