Market Risk Analysis of S&P BSE Energy Index Using Minimum Variance Portfolio and Markovitz Theory

ABSTRACT:
This project explores the construction and analysis of the efficient frontier and indifference curves for a portfolio of stocks within the S&P BSE Energy index, using Markowitz's Modern Portfolio Theory. Utilising historical return data and a variance-covariance matrix of the constituent companies, the efficient frontier is derived, representing the set of optimal portfolios that offer the maximum expected return for a given level of risk. Indifference curves, reflecting the investors' risk-return preferences, are superimposed on the efficient frontier to identify the optimal portfolio. Through a combination of mathematical optimisation and visualisation techniques, this study provides insights into the optimal asset allocation and the interplay between risk aversion and expected returns. The findings highlight the practical application of portfolio theory in achieving efficient investment strategies, aligning with investors' utility functions and risk tolerances.

A list of major companies constituting the S&P BSE ENERGY Index and their contribution can be seen towards the left.

Key Concepts:

S&P BSE Energy Index: Tracks the performance of major energy sector companies, such as Reliance Industries Ltd., ONGC, and Indian Oil Corporation.
Efficient Frontier: Represents portfolios that offer the highest expected return for a given level of risk.
Markowitz Theory: Aims to maximize returns by diversifying investments, and reducing risk through mathematical optimization.

Data and Analysis

Data from FY 2021-2024 was used to calculate the expected returns and risks for individual companies in the S&P BSE Energy Index. Key companies like Reliance Industries Ltd. and Indian Oil Corporation dominated the index, with Reliance alone contributing 54.07% to the index's weight.

Portfolio Optimization

Minimum Variance Portfolio: Through Python-based optimization, the minimum variance portfolio was constructed, aiming to reduce risk while maintaining returns. The optimal weights assigned to companies such as Petronet LNG (30.53%) and Gujarat Gas Ltd. (44.39%) resulted in a minimum variance of 1.31E-07.
Markowitz Market Index: Using the efficient frontier, the optimal portfolio was identified at the point where the investor's highest indifference curve intersects the efficient frontier. The expected return for this portfolio was 105.8%, with a focus on diversified asset allocation.

To find the minimum variance portfolio using the given data, the following steps were followed: 1. Extract the variance-covariance matrix from the data.
2. Set up the optimization problem.
3. Implement the optimization in Python

The above is a variance-covariance matrix. Covariance is a measure of how returns of two securities move together. It is the statistical measure that indicates the interactive risk of a security relative to others in a portfolio of securities. To get the covariance matrix we will use the return percentage data from Figure 1 table. The covariance matrix is made via Python coding using Python's inbuilt function cov matrix.

Conclusion

The analysis showcases how diversification and efficient frontier optimization help in constructing portfolios that minimize risk and maximize returns. By applying Modern Portfolio Theory to the S&P BSE Energy Index, investors can achieve a balanced and efficient investment strategy.

This study underscores the practical relevance of Markowitz's portfolio theory in creating optimal investment portfolios, aligning with investors' risk preferences.

MS6621 Report-ED21B001.pdf

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