Single Index Model : Constructing Optimal Portfolios from Nifty 50 Constituents Using Different Time Horizons and Analyzing Their Performance Against the Nifty 50 Index

Abstract

Purpose : This study aimed to construct four optimal portfolios using the single index model (SIM) with different datasets of 1, 3, 5, and 10 years of mean, variance, beta, systematic risk, unsystematic risk, and Nifty50 as an index, and to analyze all portfolios’ actual performance against the Nifty 50 Index.

Methodology : The Nifty 50 constituents, comprising 50 stocks as of October 31, 2023, were used for stock selection to construct four optimal portfolios using 1, 3, 5, and 10-year datasets. The research extracted 10 years of historical data from November 1, 2013, to October 31, 2023, and further examined all portfolio performances for one year from November 1, 2023, to October 31, 2024. The stocks were ranked based on excess return to beta, and using the cut-off rate (without short selling), stocks were selected and included in the portfolio. Z_i and X_i were used to determine the weightage of each stock in the optimal portfolio.

Findings : The findings revealed that portfolios constructed from 1-year and 3-year horizon datasets outperformed the Nifty 50 Index in the subsequent year (November 1, 2023, to October 31, 2024). The portfolio constructed using 3 years of datasets outperformed the Nifty 50 Index with a return of 44.53%, and the portfolio constructed using 1 year of datasets outperformed the Nifty 50 Index with a return of 40.36%, as compared to the Nifty 50 Index return of 26.58%.

Practical Implications : This study highlighted the practical implications for portfolio managers and retail investors seeking smart beta portfolios to beat index returns. These results underscored the dynamics of the market, which required a continuous evaluation of portfolio performance and adjustments to attain the best returns while taking calculated risks.

Originality : This study uniquely applied the SIM to construct optimal portfolios using the Nifty 50 constituents across varying time horizons (1-year, 3-years, 5-years, and 10-years), providing a comprehensive analysis of portfolio performance compared to the benchmark index, which had not been extensively explored in the context of the Indian equity market.