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Introduction to Financial Portfolio Management with Python
course content

Course Content

Introduction to Financial Portfolio Management with Python

Introduction to Financial Portfolio Management with Python

1. Portfolio Analysis Basics
Investing BasicsWhat is Portfolio?Portfolio ReturnsMeasuring Risk of PortfolioChallenge: Annualized Return and Risk
2. Portfolio Optimization Basics
Risk Adjusted ReturnOverview of Modern Portfolio TheoryMarkowitz PortfoliosChallenge: Computing GMV PortfolioChallenge: Computing MSR Portfolio
3. Factor Investing
Introduction to Factor AnalysisChallenge: The Capital Asset Pricing ModelThe Fama-French Factor ModelChallenge: The 5-factor Model

Challenge: Annualized Return and Risk

What is Annualization?

First, let’s define what is annualization in terms of return and risk.

Note that there is other term with similar name, but another meaning:

So, in terms of previous example, the main difference between them is that annual return/risk is exact return of an asset for a specific year/risk associated with this return, while annualized return/risk is return/risk over different time periods converted into equivalent annual return.

Another aspect, why annualization is important - is standartization.

Let's define it:

Annualized Returns

Let's assume next notation:

  • N - length of time period we are working with in years;
  • R - return over entire period of time;
  • R_a - annualized return.

Then we can compute annualized return using the following expression:

Alternatively, we can assume that N represents the number of months in our period, which will give us the following expression:

Coming back to the previous example with stocks of Nvidia and AMD, here is a code, which will help us compute annualized returns for them, using corresponding formulas:


              
12345678

            
# Computing annualized return for Nvidia
Nvidia_annualized = (1 + 0.27) ** (12/6) - 1
print('Nvidia: \n')
print(Nvidia_annualized)
# Computing annualized return for AMD
AMD_annualized = (1 + 3.93) ** (1/5) - 1
print('AMD: \n')
print(AMD_annualized)
copy

Annualized Risk

In terms of risk, which is measured by standard deviation, the annualized value can be calculated using the following expression:

Here:

  • σ- basic risk;
  • σ_a - annualized risk;
  • T - time period, used for computing risk.

So, for example, if σ denotes monthly risk - then T = 12 and annualized risk could be computed using the next expression:

Or, in case of daily risk σ, to annualize we use T = 252, since it is an approximate number of trading days in a year (excluding weekends and holidays), and the following expression is used for computing:

Task

In this task you need to:

  1. Compute annualized return R_annualized with a given return R for a 7 month, by specifying necessary power into formulap.
  2. Compute annualized risk σ_annualized with a given risk σ for a 5 month, by specifying necessary time period T.

Task

In this task you need to:

  1. Compute annualized return R_annualized with a given return R for a 7 month, by specifying necessary power into formulap.
  2. Compute annualized risk σ_annualized with a given risk σ for a 5 month, by specifying necessary time period T.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Section 1. Chapter 5
toggle bottom row

Challenge: Annualized Return and Risk

What is Annualization?

First, let’s define what is annualization in terms of return and risk.

Note that there is other term with similar name, but another meaning:

So, in terms of previous example, the main difference between them is that annual return/risk is exact return of an asset for a specific year/risk associated with this return, while annualized return/risk is return/risk over different time periods converted into equivalent annual return.

Another aspect, why annualization is important - is standartization.

Let's define it:

Annualized Returns

Let's assume next notation:

  • N - length of time period we are working with in years;
  • R - return over entire period of time;
  • R_a - annualized return.

Then we can compute annualized return using the following expression:

Alternatively, we can assume that N represents the number of months in our period, which will give us the following expression:

Coming back to the previous example with stocks of Nvidia and AMD, here is a code, which will help us compute annualized returns for them, using corresponding formulas:


              
12345678

            
# Computing annualized return for Nvidia
Nvidia_annualized = (1 + 0.27) ** (12/6) - 1
print('Nvidia: \n')
print(Nvidia_annualized)
# Computing annualized return for AMD
AMD_annualized = (1 + 3.93) ** (1/5) - 1
print('AMD: \n')
print(AMD_annualized)
copy

Annualized Risk

In terms of risk, which is measured by standard deviation, the annualized value can be calculated using the following expression:

Here:

  • σ- basic risk;
  • σ_a - annualized risk;
  • T - time period, used for computing risk.

So, for example, if σ denotes monthly risk - then T = 12 and annualized risk could be computed using the next expression:

Or, in case of daily risk σ, to annualize we use T = 252, since it is an approximate number of trading days in a year (excluding weekends and holidays), and the following expression is used for computing:

Task

In this task you need to:

  1. Compute annualized return R_annualized with a given return R for a 7 month, by specifying necessary power into formulap.
  2. Compute annualized risk σ_annualized with a given risk σ for a 5 month, by specifying necessary time period T.

Task

In this task you need to:

  1. Compute annualized return R_annualized with a given return R for a 7 month, by specifying necessary power into formulap.
  2. Compute annualized risk σ_annualized with a given risk σ for a 5 month, by specifying necessary time period T.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Section 1. Chapter 5
toggle bottom row

Challenge: Annualized Return and Risk

What is Annualization?

First, let’s define what is annualization in terms of return and risk.

Note that there is other term with similar name, but another meaning:

So, in terms of previous example, the main difference between them is that annual return/risk is exact return of an asset for a specific year/risk associated with this return, while annualized return/risk is return/risk over different time periods converted into equivalent annual return.

Another aspect, why annualization is important - is standartization.

Let's define it:

Annualized Returns

Let's assume next notation:

  • N - length of time period we are working with in years;
  • R - return over entire period of time;
  • R_a - annualized return.

Then we can compute annualized return using the following expression:

Alternatively, we can assume that N represents the number of months in our period, which will give us the following expression:

Coming back to the previous example with stocks of Nvidia and AMD, here is a code, which will help us compute annualized returns for them, using corresponding formulas:


              
12345678

            
# Computing annualized return for Nvidia
Nvidia_annualized = (1 + 0.27) ** (12/6) - 1
print('Nvidia: \n')
print(Nvidia_annualized)
# Computing annualized return for AMD
AMD_annualized = (1 + 3.93) ** (1/5) - 1
print('AMD: \n')
print(AMD_annualized)
copy

Annualized Risk

In terms of risk, which is measured by standard deviation, the annualized value can be calculated using the following expression:

Here:

  • σ- basic risk;
  • σ_a - annualized risk;
  • T - time period, used for computing risk.

So, for example, if σ denotes monthly risk - then T = 12 and annualized risk could be computed using the next expression:

Or, in case of daily risk σ, to annualize we use T = 252, since it is an approximate number of trading days in a year (excluding weekends and holidays), and the following expression is used for computing:

Task

In this task you need to:

  1. Compute annualized return R_annualized with a given return R for a 7 month, by specifying necessary power into formulap.
  2. Compute annualized risk σ_annualized with a given risk σ for a 5 month, by specifying necessary time period T.

Task

In this task you need to:

  1. Compute annualized return R_annualized with a given return R for a 7 month, by specifying necessary power into formulap.
  2. Compute annualized risk σ_annualized with a given risk σ for a 5 month, by specifying necessary time period T.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

What is Annualization?

First, let’s define what is annualization in terms of return and risk.

Note that there is other term with similar name, but another meaning:

So, in terms of previous example, the main difference between them is that annual return/risk is exact return of an asset for a specific year/risk associated with this return, while annualized return/risk is return/risk over different time periods converted into equivalent annual return.

Another aspect, why annualization is important - is standartization.

Let's define it:

Annualized Returns

Let's assume next notation:

  • N - length of time period we are working with in years;
  • R - return over entire period of time;
  • R_a - annualized return.

Then we can compute annualized return using the following expression:

Alternatively, we can assume that N represents the number of months in our period, which will give us the following expression:

Coming back to the previous example with stocks of Nvidia and AMD, here is a code, which will help us compute annualized returns for them, using corresponding formulas:


              
12345678

            
# Computing annualized return for Nvidia
Nvidia_annualized = (1 + 0.27) ** (12/6) - 1
print('Nvidia: \n')
print(Nvidia_annualized)
# Computing annualized return for AMD
AMD_annualized = (1 + 3.93) ** (1/5) - 1
print('AMD: \n')
print(AMD_annualized)
copy

Annualized Risk

In terms of risk, which is measured by standard deviation, the annualized value can be calculated using the following expression:

Here:

  • σ- basic risk;
  • σ_a - annualized risk;
  • T - time period, used for computing risk.

So, for example, if σ denotes monthly risk - then T = 12 and annualized risk could be computed using the next expression:

Or, in case of daily risk σ, to annualize we use T = 252, since it is an approximate number of trading days in a year (excluding weekends and holidays), and the following expression is used for computing:

Task

In this task you need to:

  1. Compute annualized return R_annualized with a given return R for a 7 month, by specifying necessary power into formulap.
  2. Compute annualized risk σ_annualized with a given risk σ for a 5 month, by specifying necessary time period T.

Switch to desktop for real-world practiceContinue from where you are using one of the options below
Section 1. Chapter 5
Switch to desktop for real-world practiceContinue from where you are using one of the options below
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