Construction Of Optimal Portfolio Using Sharpe’s Single Index Model: An Empirical Study on Nifty 50 Stocks

Overview

This empirical study applies Sharpe's Single Index Model (SIM) to construct an optimal portfolio using daily closing prices from 50 NIFTY 50 listed stocks over a 10-year period from February 1, 2013 to February 1, 2023. The research addresses the portfolio optimization challenge of simultaneously maximizing returns while minimizing risk exposure. The study analyzes systematic and unsystematic risk characteristics of selected securities and determines optimal investment proportions for portfolio allocation. Sharpe's SIM was selected over the Markowitz model due to computational efficiency and reduced input requirements, as it relies on a single market index for portfolio construction rather than the full variance-covariance matrix.

Methods and approach

The investigation utilized daily closing share price data spanning 10 years for all 50 constituent stocks of the NIFTY 50 index. Security-level analysis examined returns in association with systematic and unsystematic risk components. Sharpe's Single Index Model was employed as the primary analytical framework, leveraging the relationship between individual security returns and market index returns. The model decomposed risk into systematic components (market-related) and unsystematic components (security-specific). Optimal portfolio weights were calculated for each security, determining the proportionate allocation across the selected stock universe.

Key Findings

The analysis yielded quantifiable optimal investment proportions for individual securities within the portfolio. The decomposition of risk characteristics revealed the relative contribution of systematic versus unsystematic risk for each stock. The computational framework demonstrated the practical feasibility of SIM application for large portfolio optimization tasks. The results provided specific allocation recommendations suitable for implementation by individual investors, financial planners, and financial advisors seeking to construct diversified portfolios aligned with the risk-return optimization principle.

Implications

The findings support the application of Sharpe's Single Index Model as a practical tool for institutional and individual portfolio construction decisions within the Indian equity market context. The model's computational efficiency, requiring fewer inputs than comprehensive variance-covariance approaches, facilitates implementation across varied investor sophistication levels. The 10-year empirical validation on NIFTY 50 stocks provides evidence regarding the model's applicability to dynamic market conditions and extended time horizons. The methodology offers a structured framework for translating security analysis and portfolio theory into operational asset allocation decisions.