A Stochastic Method for Optimizing Portfolios Using a Combined Monte Carlo and Markowitz Model: Approach on Python

Abstract

The main of the study is to comprehend how the mean variance efficient frontier method may be used in conjunction with Markowitz portfolio theory to produce an optimal portfolio. The study uses daily observations 8 pharma companies closing price namely Auropharma, Granules, Glaxo, Lauruslabs, Pfizer, Sanofi and Torntpharma. Further, Nifty pharma index is considered as benchmark index to check the performance of the chosen companies. The study chosen the reference period from 2020 to 2023 and required data has been extracted from the National Stock Exchange (NSE). This research is based on implementing a stochastic method for efficient portfolio optimisation employing a blended Monte Carlo and Markowitz model. In order to forecast the price of these indices in the future and to determine the likelihood of profit or loss while investing in a portfolio of stocks representing the aforementioned indices, the study also uses Monte Carlo simulation. The study involves two algorithms, namely the deterministic optimisation algorithm, which uses Markowitz Portfolio Theory, and the probabilistic optimisation algorithm, which uses Monte Carlo simulation. The study employed correlation matrix to find the exist relationship between the chosen companies and benchmark index. Also, expected return and volatility has been identified with the help of standard deviation using Python. The study found that the NIFTY Pharma index offers a higher return of 14.35. In addition to this, NIFTY Pharma portfolio’s volatility is considerably higher. The study concludes that the NIFTY pharma portfolio is more suitable for those investors who have an appetite for risk.