Course 2025-2026 a.y.

The course is divided into two main parts.

The first part focuses on univariate price processes and returns, covering the following topics:

1) Prices and Returns

2) The Log Random Walk Model

3) Estimation of the Log Random Walk Model

4) On the (Non-)Normality of Returns

The second part of the course addresses multivariate models to study cross-sectional variability, covering the following topics:

5) Multivariate Problems in Probability and Statistics

6) The Linear Regression Model

7) Factor Models

8) Principal Component Analysis

• Define key concepts related to asset prices, returns, and probabilistic/statistical modeling in financial markets.
• Describe the stlized facts of financial returns on an unconconditional basis.
• Estimate parameters of univariate and multivariate models using empirical data and assess the precision of such estimates.
• Identify the assumptions and the correct reading of the linear regressions in finance.
• Describe the main statistical techniques to study cross-sectional variability.

• Apply probabilistic and statistical reasoning to support data-driven financial decisions.
• Implement financial models in Python to analyze and interpret real-world market data.
• Develop reproducible and well-documented Python scripts to support empirical financial analysis.

• Lectures
• Practical Exercises

The course includes

• traditional "theory classes", where key topics are explained through a blend of rigorous theoretical concepts and practical examples
• exercise sessions, where Students first attempt exam-style questions and then review the solutions with the Instructor
• Python-based lab classes, where Students engage in hands-on learning to conduct rigorous empirical analyses in finance.

The exam can be taken either as a single final written exam or as two partial exams, with the first held during the midterm break in October and the second during the regular exam session in January. All exams will be conducted on paper.

Since the two partial exams are each equivalent to one half of the general exam, the structure of the general exam is presented first, followed by a breakdown of how it is divided into the two partials.

General Exam Structure

The general exam consists of 20 closed-ended questions and lasts 60 minutes. Questions will assess:

• Theoretical understanding of key concepts
• Simple numerical applications of these concepts
• Material covered during lab classes, including Python code seen in class

The exam includes:

• 4 true/false questions, each worth 1 raw point if answered correctly, with a penalty of 0.25 points for incorrect answers
• 16 multiple choice questions, each with four options, only one of which is correct
  • Each correct answer earns 2 raw points, with a penalty of 0.5 points for incorrect answers
  • 4 of the multiple choice questions will focus specifically on labs' materials

Unanswered questions carry no penalty.
The maximum raw score is:
4 × 1 (T/F) + 16 × 2 (MCQ) = 36 points

After the exam, raw points are rounded to the nearest integer (e.g., 22.25 rounds to 22; 24.5 and 24.75 round to 25).

The final grade, on a 31-point scale, is then determined using the following conversion table*:

Raw points/36   Final grade/30

33-36                 = 30 cum laude
31-32                 = 30
29-30                 = 29
27-28                 = 28
25-26                 = 27
23-24                 = 26
21-22                 = 25
19-20                 = 24
14-18                 = raw points +5
11-13                 = 18
 <11                   = raw points

   * changes to this conversion table, though unlikely, can only benefit students (by awarding a higher grade out of 30 for the same number of raw points out of 36)

Partial Exams Structure

Each partial exam mirrors half of the general exam:

• Duration: 30 minutes
• Number of questions: 10
  • 2 true/false questions
  • 8 multiple choice questions, including 2 on labs' materials
• Maximum raw score: 2 × 1 (T/F) + 8 × 2 (MCQ) = 18 points

The score from the first partial will be expressed in raw points (out of 18) without rounding.

Then, it will be added to the raw score from the second partial.

After the total raw score is calculated, rounding and grade conversion will follow the same procedure as for the general exam.

According to the Content Summary section of the syllabus:

• The first partial covers topics 1 to 4
• The second partial covers topics 5 to 8

Any changes to this schedule will be communicated to students in advance.

As per Bocconi rules, the second partial exam can be taken only once.

A mock version of both the general and partial exams will be uploaded to Blackboard to help students become familiar with the exam format.

Lecture notes, uploaded to BlackBoard at the beginning of the course.

These comprehensive notes cover all course topics and provide a review of fundamental concepts in linear algebra, probability, and statistics that Students are expected to have prior knowledge of.

Additional course materials, including

• exercises,
• slides,
• Excel spreadsheets and dataset,
• supplementary notes,

will be uploaded to BlackBoard as needed throughout the semester.