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Distributional Assumption for Equity Returns – Normality vs. Standardization

You have been assigned a project, "Distributional Assumption for Equity Returns – Normality vs. Standardization" that will enhance your skills and enable you to think like an analyst.

This project aims to provide a comprehensive understanding of the process of analyzing and predicting the risk of an equity investment. It involves extracting historical time-series data of equity stock, calculating equity returns, and constructing a return distribution. The project also involves generating additional returns from the identified probability distribution using either the actual statistics computed or the standard statistics of the identified distribution.


Prerequisites

Module: Equities | Modeling Systematic Risk

Lectures: Historical Time-Series Data & Equity Shocks | Equity Risk – Systematic & Unsystematic | Equity Risk – Extreme Value Theory


Please carefully read the relevant materials, as they will serve as the foundation for you.

  1. Obtain the historical time-series data for a specific equity stock with a minimum lookback period of 3 years.

  2. Calculate the equity returns for the time series and construct a return (probability) distribution.

  3. Fit the constructed return distribution to a probability distribution, compute the relevant statistical parameters, and determine the type of probability distribution that the returns followed in the past.

  4. Generate additional returns from the identified probability distribution using either:

    1. the computed statistical parameters, or

    2. the standard statistics of the identified distribution.

Make a list of observations and assumptions, and explain the difference between the actual return distribution (4(a)) and identified standard distribution (4(b)).



Understanding How Analysts Use a Probability Distribution for Data Analysis and Forecasting

Analysts use a probability distribution to understand the range of possible returns for a given investment, and by analyzing historical data on the returns of the investment, the analyst can construct a probability distribution that shows the likelihood of different return outcomes. This can help the analyst understand the potential risk and return of the investment.

 

Team Collaboration and Selection Requirement:

for this project, candidates have the flexibility to choose their mode of operation:


Standalone Mode: If you feel confident and would like to take on the challenge individually, you're welcome to work on the project as a standalone participant. This will give you an opportunity to showcase your individual strengths and decision-making skills.


Team Collaboration: Alternatively, if you believe that collaboration will enhance the quality and depth of your analysis, you are encouraged to form a team. Collaborative efforts often bring diverse perspectives, leading to richer insights and more comprehensive results.

  • Self-Selection: Candidates are free to select their own teammates. If you already have someone in mind, align with them, and inform the project coordinator of your team composition.

  • Team Size: While there's no strict limit, we recommend teams of 2-3 members for effective collaboration and equitable distribution of work.

  • Commitment Agreement: Ensure that all members of the team are equally committed to the project.

Please note: Whether you choose to work individually or in a team, the assessment criteria will remain consistent. The emphasis will be on the depth of analysis, quality of insights, and presentation of findings.

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