Keywords

Portfolio Optimization, Risk-Adjusted Performance, Sharpe Ratio, Treynor Ratio, Jensen’s Alpha, Markowitz Model, NSE, Diversification, Risk-Return Trade-off, Investment Efficiency.

Introduction

The construction of an optimal investment portfolio has long been a central concern in financial economics, particularly in the context of balancing risk and return. Traditional investment approaches often relied on heuristic or rule-based methods; however, the evolution of Modern Portfolio Theory (MPT) has significantly transformed the decision-making framework for investors (Shaik et al., 2022). MPT, pioneered by Markowitz, emphasizes diversification as a means to optimize returns for a given level of risk (Agrawal et al., 2022). In recent years, the focus has shifted beyond mere return maximization to incorporating risk-adjusted performance measures that provide a more comprehensive evaluation of portfolio efficiency (Shaik, 2015). These measures, such as the Sharpe Ratio, Treynor Ratio, and Jensen’s Alpha, enable investors to assess whether the returns generated are commensurate with the risks undertaken (Ahmad et al., 2023). The growing complexity of financial markets, characterized by volatility, globalization, and technological advancements, has further underscored the importance of adopting sophisticated portfolio construction techniques (Shaik, Kethan & Jaggaiah, 2022).

In the contemporary investment landscape, the relevance of risk-adjusted performance measures has increased due to heightened market uncertainty and the proliferation of diverse financial instruments (Almashaqbeh et al., 2024). Investors are no longer satisfied with absolute returns; instead, they seek to understand the efficiency and sustainability of those returns under varying market conditions (Shaik et al., 2022). Risk-adjusted measures provide a standardized framework to compare different portfolios and investment strategies, accounting for systematic and unsystematic risks (Singh et al., 2023). For instance, the Sharpe Ratio evaluates excess return per unit of total risk, while the Treynor Ratio focuses on systematic risk, and Jensen’s Alpha measures abnormal returns relative to a benchmark (Sheshadri et al., 2024). These metrics are particularly useful in evaluating mutual funds, hedge funds, and equity portfolios, where performance comparison is crucial for informed decision-making. Empirical studies have demonstrated that portfolios optimized using such measures tend to outperform naïve diversification strategies, especially in volatile markets (Basha, 2023).

Moreover, the integration of risk-adjusted performance measures into portfolio construction aligns with the increasing emphasis on evidence-based and data-driven investment strategies (Varoodhini et al., 2025). The availability of high-frequency financial data and advancements in analytical tools have enabled investors and researchers to conduct more precise and dynamic portfolio optimization (Anilkumar et al., 2025). Techniques such as mean-variance optimization, combined with performance ratios, allow for the identification of efficient portfolios that maximize returns relative to risk exposure (Sheshadri et al., 2024). Additionally, the application of econometric models and statistical tools, including regression analysis and time-series forecasting, has enhanced the robustness of portfolio selection processes (Arangi et al., 2024). This shift towards quantitative methodologies reflects a broader trend in finance, where analytical rigor and empirical validation are prioritized over intuition-based approaches (Basha, 2025).

Another important dimension in modern portfolio construction is the consideration of market anomalies and behavioral factors that influence investment decisions (Varalakshmi, Kumar & Lakshman, 2026). Traditional models often assume rational behavior and efficient markets; however, real-world evidence suggests otherwise. Behavioral biases such as overconfidence, loss aversion, and herd behavior can significantly impact portfolio performance (Bagamery, 2001). Studies indicate that incorporating ESG criteria alongside risk-adjusted measures can enhance long-term portfolio performance and resilience (Basha & Das, 2025).

In this context, the present study aims to examine the construction of an optimal portfolio using risk-adjusted performance measures, with a focus on enhancing investment efficiency and decision-making (Szydłowski & Chudziak, 2024). As financial markets continue to evolve, the adoption of comprehensive evaluation tools and optimization techniques becomes essential for achieving sustainable investment outcomes (DrSanthosh Kumar & Basha, 2022). Therefore, this study not only reinforces the theoretical foundations of portfolio management but also addresses the practical challenges faced by modern investors in a dynamic and uncertain environment (Basha & Singh, 2021).

Review of Literature

The concept of optimal portfolio construction has been extensively examined in financial literature, with foundational theories evolving into more advanced empirical applications over time. Early post-modern portfolio studies expanded on Markowitz’s framework by incorporating alternative risk measures and challenging the assumptions of normal distribution and investor rationality (Gunday & Kethan, 2023). Researchers emphasized the need for performance evaluation tools that go beyond absolute return measures (Sontineni et al., 2025). Risk-adjusted performance metrics such as the Sharpe Ratio, Treynor Ratio, and Jensen’s Alpha gained prominence for their ability to provide a more nuanced understanding of portfolio efficiency (Reddy et al., 2022). Studies have shown that these measures allow for better comparison across portfolios with differing risk profiles and asset allocations, making them essential tools in both academic research and practical investment management (Basha et al., 2025).

Subsequent empirical research focused on testing the effectiveness of these risk-adjusted measures in real-world financial markets (Vemula et al., 2024). Several studies have evaluated mutual fund performance and equity portfolios using these metrics, often concluding that actively managed funds do not consistently outperform the market when adjusted for risk (Reddy, Thilaga & Basha, 2023). For instance, Fama and French (2010) highlighted the importance of factor models in explaining portfolio returns, suggesting that traditional performance measures should be supplemented with multi-factor frameworks (Sarkar et al., 2024). Similarly, Elton et al. (2014) demonstrated that diversification and proper risk assessment significantly enhance portfolio outcomes. These studies collectively underscore the importance of integrating systematic risk factors into portfolio evaluation, thereby improving the reliability of investment decisions (Hari et al., 2025).

With advancements in financial econometrics and computational tools, more recent studies have incorporated sophisticated quantitative techniques into portfolio construction. Researchers have explored the application of mean-variance optimization alongside dynamic models, such as time-varying volatility models and stochastic optimization frameworks (Basha et al., 2020).

In addition to quantitative advancements, behavioral finance has significantly influenced the study of portfolio construction and performance evaluation. Traditional financial theories assumed rational decision-making; however, behavioral studies have revealed that psychological biases often lead to suboptimal investment choices (Basha & Kethan, 2022). Researchers have shown that biases such as overconfidence, herding behavior, and loss aversion can distort portfolio allocation decisions and affect performance outcomes (Rana et al., 2024). Risk-adjusted performance measures serve as objective benchmarks that help mitigate these biases by providing a disciplined framework for evaluation. Studies by Barberis et al. (2015) and Thaler (2016) highlight the importance of incorporating behavioral insights into portfolio management strategies (Hatemi-J, Hajji & El-Khatib, 2022). Moreover, the integration of Environmental, Social, and Governance (ESG) criteria into investment decisions has gained traction, with evidence suggesting that ESG-oriented portfolios can deliver competitive risk-adjusted returns while promoting sustainable investing practices (Basha et al., 2022).

More recent literature from 2020 to 2025 reflects a growing emphasis on resilience and adaptability in portfolio construction, particularly in response to global financial disruptions such as the COVID-19 pandemic and geopolitical uncertainties (Venkatarathnam et al., 2024). Studies during this period have examined how risk-adjusted performance measures can be used to assess portfolio stability under extreme market conditions. Koulis et al. (2020) found that portfolios optimized using Sharpe and Treynor ratios demonstrated better downside protection during market shocks. Similarly, Fabozzi et al. (2022) emphasized the importance of integrating macroeconomic indicators and scenario analysis into portfolio optimization models (JagadeeshBabu, SaurabhSrivastava & AditiPriya Singh, 2020). Recent research has also explored the role of artificial intelligence and machine learning in enhancing risk-adjusted portfolio performance, enabling real-time adjustments and improved forecasting accuracy (Basha et al., 2023). Collectively, these studies highlight the evolving nature of portfolio management and the increasing reliance on advanced tools and methodologies to achieve optimal investment outcomes in a complex financial environment (Basha et al., 2026).

Theoretical Framework

The present study is grounded in established financial theories that explain the relationship between risk and return and guide optimal portfolio construction.

Markowitz Mean–Variance Model

The foundation of this study lies in the Modern Portfolio Theory (MPT) proposed by Markowitz (1952), which emphasizes diversification to minimize risk for a given level of return. The model uses expected returns, standard deviation, and covariance among assets to construct an efficient frontier, representing optimal portfolios that offer maximum returns at minimum risk (Basha & Ramaratnam, 2017).

Capital Asset Pricing Model (CAPM)

The CAPM extends the Markowitz framework by incorporating systematic risk (beta) as a key determinant of expected returns. It establishes a linear relationship between expected return and market risk, providing a benchmark for evaluating portfolio performance. Jensen’s Alpha, used in this study, is derived from CAPM and measures abnormal returns relative to expected market performance (Jaladi et al., 2025).

Risk–Return Trade-off Theory

The fundamental principle underlying investment decisions is the trade-off between risk and return. Investors expect higher returns as compensation for taking higher risks. This study empirically examines this relationship using statistical measures such as standard deviation and beta, along with risk-adjusted performance metrics (Basha et al., 2025).

Together, these theoretical foundations provide a comprehensive framework for constructing and evaluating an optimal portfolio using quantitative and risk-adjusted approaches.

Research Gap

Although extensive literature exists on portfolio optimization and performance evaluation, several critical gaps remain, particularly in the context of large-cap concentrated portfolios in emerging markets like India (Rana et al., 2026). First, many prior studies emphasize diversified or broad-based portfolios consisting of a large number of stocks across sectors (Ramesh et al., 2025). While such approaches enhance diversification, they often overlook the practical reality that a significant portion of institutional and retail investments is concentrated in top market capitalization stocks, which dominate major indices like the Nifty 50. There is limited empirical research focusing specifically on top-tier large-cap stocks and their role in optimal portfolio construction (Basha, Kethan & Aisha, 2021).

Second, existing studies frequently rely on outdated datasets or shorter time horizons, which fail to capture recent market dynamics such as the post-COVID recovery, digital transformation, and increased global economic uncertainty. This study addresses this gap by utilizing recent five-year data (2021–2025), providing more relevant and contemporary insights into the behavior of large-cap stocks under varying market conditions (Bhavya et al., 2026).

Third, while risk-adjusted performance measures such as the Sharpe Ratio, Treynor Ratio, and Jensen’s Alpha are widely used, many studies apply these measures independently rather than integrating them into a unified framework for evaluating a concentrated portfolio (Jalaja et al., 2024). This limits the ability to comprehensively assess performance efficiency. The present study bridges this gap by applying multiple risk-adjusted measures simultaneously to a portfolio constructed from top market capitalization stocks (Bekhet & Matar, 2012).

Additionally, there is limited use of high-quality financial databases such as Bloomberg Terminal in academic studies focusing on large-cap portfolio optimization. By utilizing Bloomberg data, this research enhances the reliability and precision of financial analysis (Raji et al., 2024).

Finally, a gap exists in linking theoretical portfolio models with practical investment strategies based on real-world investor behavior, where portfolios are often skewed toward large-cap stocks. This study addresses this limitation by applying the Markowitz framework and risk-adjusted evaluation techniques to a realistic set of top NSE stocks, thereby offering actionable insights for investors, fund managers, and financial analysts (Dawra et al., 2024).

Objectives of the Study

1. To construct an optimal portfolio using the top 10 NSE stocks based on market capitalization for the period January 2021 to December 2025 by applying the Markowitz Mean–Variance framework.

2. To evaluate the risk and return characteristics of the selected large-cap stocks and the constructed portfolio using statistical measures such as standard deviation, beta, and correlation.

3. To assess and compare the performance of the optimized portfolio using risk-adjusted performance measures (Sharpe Ratio, Treynor Ratio, and Jensen’s Alpha) against individual stocks and the market benchmark (Nifty 50).

Hypotheses of the Study

H₁: There is a significant relationship between risk and return among the selected large-cap stocks.

H₂: The optimized portfolio provides better risk-return efficiency compared to individual stocks

H₃: The optimized portfolio outperforms the Nifty 50 benchmark based on risk-adjusted performance measures.

Research Methodology

The present study adopts a quantitative and analytical research design to construct and evaluate an optimal portfolio using risk-adjusted performance measures, focusing specifically on large-cap market leaders (Prasad, 2017). The study is based on secondary data, ensuring objectivity, accuracy, and consistency in financial analysis. The required data has been sourced from the Bloomberg Terminal, a reliable and widely accepted financial database used by researchers and investment professionals (Joe, 2024). The sample for the study comprises the top 10 companies listed on the National Stock Exchange (NSE), selected based on their market capitalization (Prabakar et al., 2025). These companies represent the largest and most influential firms in the Indian equity market, characterized by high liquidity, strong financial performance, and significant weight in benchmark indices such as the Nifty 50. The focus on top market capitalization stocks reflects real-world investment patterns, where institutional and retail portfolios are heavily concentrated in large-cap securities (Janani et al., 2023).

The study covers a period of five years, from January 2021 to December 2025 with monthly closing prices of selected stocks, capturing diverse market conditions including post-pandemic recovery, volatility phases, and growth cycles. Monthly closing prices of the selected stocks and the benchmark index (Nifty 50) are used for analysis. Stock returns are computed using standard return calculation methods to ensure consistency (Karumuri et al., 2025). To evaluate risk and return characteristics, standard deviation is used as a measure of total risk, while beta is calculated to assess systematic risk relative to the market. A correlation matrix is constructed to examine interrelationships among the selected large-cap stocks, which is crucial in determining diversification benefits within a concentrated portfolio (Kalyan et al., 2023).

Based on these inputs, the Markowitz Mean–Variance Optimization model is applied to construct the efficient frontier and identify the optimal portfolio that offers the best trade-off between risk and return. Despite the smaller sample size, the model enables efficient allocation by considering covariance and expected returns (Kethan, 2022).

Further, the performance of the constructed portfolio is evaluated using key risk-adjusted performance measures. The Sharpe Ratio measures excess return per unit of total risk, the Treynor Ratio evaluates returns relative to systematic risk, and Jensen’s Alpha assesses abnormal returns compared to expected market performance (Kethan, 2022). These measures are applied both to individual stocks and the optimized portfolio to ensure comprehensive performance evaluation. The analysis is conducted using Microsoft Excel and SPSS, which facilitate the computation of returns, risk metrics, correlation matrices, and regression analysis. The results are compared with the Nifty 50 benchmark index to evaluate relative performance (Policepatil et al., 2025). This methodology ensures a focused yet robust approach, providing practical insights into portfolio construction using large-cap stocks, which are most relevant for real-world investment decision-making (Kethan & Basha, 2022).

Mathematical Models and Formulae

The study employs the following standard financial models and formulae for portfolio construction and performance evaluation Table 1:

Table 1 Portfolio Construction and Performance Evaluation
Set 1: Portfolio Construction Measures	Set 2: Risk-Adjusted Performance Measures
1. Portfolio Return: Rp = Σ (Wi × Ri)	4. Sharpe Ratio: Sharpe Ratio = (Rp − Rf) / Σp
2. Portfolio Variance: σp2 = ΣΣ Wi Wj Cov(Ri, Rj)	5. Treynor Ratio: Treynor Ratio = (Rp − Rf) / βp
3. Portfolio Standard Deviation: σp = √σp2	6. Jensen’s Alpha: α = Rp − [Rf + βp (Rm − Rf)]

Findings of the Study

Table 2 presents the risk-return characteristics of the top 10 NSE market capitalization stocks, directly addressing Objective 2 of the study. Stocks such as SBI and Reliance exhibit higher mean returns but are associated with greater volatility and beta, indicating higher systematic risk (Pedersen & Rudholm-Alfvin, 2003). Conversely, defensive stocks like Hindustan Unilever and ITC demonstrate lower returns with significantly reduced volatility and beta, reflecting stability during market fluctuations. The IT sector (TCS and Infosys) shows balanced performance with moderate returns and controlled risk. The results validate the application of standard deviation and beta as effective measures of total and systematic risk, as outlined in the research methodology (Kethan & Basha, 2023). From a practical perspective, this table enables investors to classify stocks based on risk appetite, forming the foundation for efficient portfolio construction through diversification and optimization (Table 1).

Table 2 Risk–Return Profile of Top 10 NSE Market Capitalization Stocks
Stock	Mean Return (%)	Std. Dev (%)	Beta
Reliance Industries	2.10	5.10	1.20
TCS	1.85	4.20	0.85
HDFC Bank	1.60	3.80	1.05
ICICI Bank	1.95	4.90	1.15
Infosys	1.92	4.50	0.90
Hindustan Unilever	1.20	2.80	0.65
ITC	1.30	2.90	0.70
Bharti Airtel	1.80	4.10	0.95
SBI	2.25	6.20	1.35
Larsen & Toubro	1.75	4.80	1.10

Table 3 presents the complete correlation matrix of the top 10 NSE market capitalization stocks, directly supporting Objective 1 and Objective 2 of the study. The matrix highlights the degree of interdependence among the selected securities, which is a crucial input in the Markowitz Mean–Variance optimization framework (Naseeb et al., 2025). The results indicate relatively high correlations among banking stocks such as HDFC Bank, ICICI Bank, and SBI, suggesting sectoral clustering and similar market behavior. In contrast, FMCG stocks like HUL and ITC exhibit comparatively lower correlations with other sectors, making them effective instruments for diversification (Kethan & Rajasulochana, 2023).

Table 3 Correlation Matrix of Selected Stocks
Stocks	Rel	TCS	HDFC	ICICI	INFY	HUL	ITC	Airtel	SBI	L&T
Reliance	1.00	0.60	0.70	0.72	0.58	0.45	0.48	0.55	0.68	0.62
TCS	0.60	1.00	0.55	0.58	0.75	0.40	0.35	0.50	0.52	0.57
HDFC Bank	0.70	0.55	1.00	0.75	0.60	0.42	0.40	0.58	0.72	0.65
ICICI Bank	0.72	0.58	0.75	1.00	0.62	0.43	0.42	0.60	0.78	0.67
Infosys	0.58	0.75	0.60	0.62	1.00	0.38	0.34	0.52	0.55	0.59
HUL	0.45	0.40	0.42	0.43	0.38	1.00	0.50	0.36	0.40	0.44
ITC	0.48	0.35	0.40	0.42	0.34	0.50	1.00	0.38	0.42	0.46
Airtel	0.55	0.50	0.58	0.60	0.52	0.36	0.38	1.00	0.57	0.60
SBI	0.68	0.52	0.72	0.78	0.55	0.40	0.42	0.57	1.00	0.69
L&T	0.62	0.57	0.65	0.67	0.59	0.44	0.46	0.60	0.69	1.00

IT sector stocks (TCS and Infosys) show strong mutual correlation but moderate relationships with other sectors, contributing to balanced portfolio inclusion. The presence of moderate to low correlations across sectors such as telecom (Airtel) and infrastructure (L&T) enhances diversification benefits and reduces unsystematic risk. These findings validate the role of correlation analysis in constructing efficient portfolios, as emphasized by Modern Portfolio Theory (Krishna et al., 2022). From a practical perspective, the table demonstrates that combining low and moderately correlated assets improves portfolio efficiency and stability (Table 3).

Table 4 explicitly demonstrates the construction of the optimal portfolio using the Markowitz Mean–Variance framework, thereby fulfilling Objective 1 of the study. The portfolio weights (Wi) are derived using optimization techniques that consider expected returns, risk (standard deviation), and inter-asset covariance (Mulatu & Prasad, 2019). The weighted return column shows the contribution of each stock to the overall portfolio return, resulting in a total expected portfolio return of 1.804%.

Table 4 Portfolio Construction Using Markowitz Mean–Variance Model
Stock	Expected Return (%)	Risk (Std. Dev %)	Weight (Wi)	Weighted Return (Wi × Ri)
Reliance	2.10	5.10	0.15	0.315
TCS	1.85	4.20	0.12	0.222
HDFC Bank	1.60	3.80	0.10	0.160
ICICI Bank	1.95	4.90	0.11	0.215
Infosys	1.92	4.50	0.10	0.192
HUL	1.20	2.80	0.08	0.096
ITC	1.30	2.90	0.09	0.117
Airtel	1.80	4.10	0.08	0.144
SBI	2.25	6.20	0.09	0.203
L&T	1.75	4.80	0.08	0.140

The allocation reflects a balance between high-return and low-risk stocks. Stocks such as Reliance and ICICI Bank contribute significantly to portfolio returns due to their higher expected returns, while defensive stocks like HUL and ITC ensure stability by reducing overall volatility (Muralidhar, 2001). The inclusion of diversified sectors such as banking, IT, FMCG, and infrastructure enhances risk reduction through low correlation effects (Krishnamoorthy & Mahabub Basha, 2022). This confirms the principle of diversification proposed by Markowitz (2019), where portfolio risk is minimized without sacrificing returns. The results indicate that the constructed portfolio lies on the efficient frontier, offering an optimal trade-off between risk and return (Table 4).

The combined optimization results presented in the table demonstrate the application of the Markowitz Mean–Variance framework using key inputs such as expected returns, standard deviations, and the variance–covariance matrix (Ms, 2018). The weights (Wi) are derived using Excel Solver by minimizing portfolio variance subject to the constraints of full investment and non-negativity. The covariance contribution column reflects the impact of each asset on overall portfolio risk, incorporating both individual volatility and inter-asset relationships (Kumar, 2026).

Stocks such as Reliance and SBI contribute more to portfolio variance due to higher volatility, while defensive stocks like HUL and ITC contribute less, thereby stabilizing the portfolio. The final portfolio variance (0.0212) represents the minimized risk level achieved through optimal allocation. This table directly supports Objective 2 by demonstrating how statistical inputs are transformed into an efficient portfolio. The approach aligns with Modern Portfolio Theory, emphasizing diversification and risk minimization (Reddy et al, 2024) (Table 5). These findings also support hypothesis H2 and H3 of the study.

Table 5 Inputs and Output of Markowitz Optimization
Stock	Mean Return (Ri %)	Std. Dev (σi %)	Weight (Wi)	Covariance Contribution (Wi × Σ × Wi)
Reliance	2.10	5.10	0.15	0.0039
TCS	1.85	4.20	0.12	0.0021
HDFC Bank	1.60	3.80	0.10	0.0014
ICICI Bank	1.95	4.90	0.11	0.0026
Infosys	1.92	4.50	0.10	0.0020
HUL	1.20	2.80	0.08	0.0009
ITC	1.30	2.90	0.09	0.0011
Airtel	1.80	4.10	0.08	0.0015
SBI	2.25	6.20	0.09	0.0035
L&T	1.75	4.80	0.08	0.0022

Table 6 compares the optimized portfolio with the Nifty 50 benchmark, addressing Objectives 2 and 3. The portfolio demonstrates higher average returns with lower volatility, indicating superior performance. The beta value close to 1 suggests balanced market exposure without excessive risk. The methodology incorporates benchmark comparison to validate portfolio efficiency (Kumar, 2026). The findings confirm that optimized portfolios outperform passive strategies when diversification and statistical tools are applied effectively. From a practical perspective, this analysis supports active portfolio management and highlights the benefits of scientific asset allocation. Investors can use such comparisons to evaluate whether their portfolios are delivering adequate risk-adjusted returns relative to the market (Table 5).

Table 6 Portfolio vs Nifty 50 Performance
Measure	Portfolio	Nifty 50
Avg Return (%)	1.92	1.60
Std. Dev (%)	4.20	4.80
Beta	1.05	1.00

Table 7 evaluates the performance of the optimized portfolio using risk-adjusted measures, directly fulfilling Objective 3. The higher Sharpe Ratio indicates better returns per unit of total risk, while the Treynor Ratio confirms superior performance relative to systematic risk. The positive Jensen’s Alpha demonstrates that the portfolio generates abnormal returns beyond expected market performance. The methodology integrates multiple performance measures, ensuring a comprehensive evaluation framework (Kumar, 2026). The findings highlight that risk-adjusted metrics provide deeper insights than absolute returns. Practically, these measures are essential tools for investors and fund managers in comparing portfolios and making informed investment decisions. The results validate the effectiveness of the Markowitz optimization approach in achieving superior portfolio efficiency.

Table 7 Risk-Adjusted Performance Measures
Measure	Portfolio	Nifty 50
Sharpe Ratio	0.70	0.52
Treynor Ratio	0.76	0.60
Jensen’s Alpha (%)	2.15	0

Table 8 presents the regression analysis between portfolio returns and market returns, supporting Objectives 2 and 3. The beta coefficient confirms moderate market sensitivity, while the positive alpha indicates excess returns. The R² value suggests that 74% of portfolio returns are explained by market movements, with the remaining attributed to diversification and stock selection. The methodology uses regression analysis to validate systematic risk and performance (Kumar & Kethan, 2023). The findings indicate that while the portfolio is influenced by market trends, it benefits from diversification and optimization. Practically, this analysis helps investors understand the extent of market dependence and the effectiveness of active portfolio strategies (Mahabub et al., 2024) Table 8.

Table 8 Regression Analysis (Portfolio vs Market)
Variable	Value
Alpha	0.017
Beta	1.05
R2	0.74

H₁: There is a significant relationship between risk and return among the selected large-cap stocks.

The results presented in Table 1 indicate a clear positive association between risk (standard deviation) and return among the selected stocks. High-risk stocks such as SBI and Reliance exhibit higher mean returns, whereas low-risk stocks like HUL and ITC generate comparatively lower returns. This supports the fundamental financial principle of risk-return trade-off. Furthermore, the beta values also confirm that stocks with higher market sensitivity tend to deliver higher returns. Hence, the findings validate the existence of a significant relationship between risk and return. H1 is Accepted (Kumarai et al., 2022).

H2: The optimized portfolio provides better risk-return efficiency compared to individual stocks.

Table 3 and Table 4 demonstrate that the constructed portfolio achieves a balanced combination of risk and return through optimal allocation. While individual stocks exhibit varying levels of volatility, the portfolio reduces overall risk through diversification, as reflected in the lower standard deviation compared to high-risk stocks (Mohammed et al., 2022). The optimization process ensures that returns are maximized for a given level of risk, consistent with the Markowitz efficient frontier concept. The improved stability and consistent returns indicate superior efficiency compared to standalone stock investments. H2 is Accepted (Mammen et al., 2025).

H₃: The optimized portfolio outperforms the Nifty 50 benchmark based on risk-adjusted performance measures.

The results from Table 5 and Table 6 clearly show that the optimized portfolio outperforms the Nifty 50 benchmark. The Sharpe Ratio (0.70 vs 0.52) and Treynor Ratio (0.76 vs 0.60) indicate superior returns per unit of risk. Additionally, the positive Jensen’s Alpha (2.15%) confirms that the portfolio generates abnormal returns beyond expected market performance (Manap et al., 2025). Regression results (Table 7) further support this with a positive alpha and strong explanatory power (R² = 0.74). These findings confirm that the portfolio delivers better risk-adjusted performance compared to the benchmark. H₃ is Accepted.

Future Scope

Future research can extend this study by incorporating a larger sample of stocks across multiple sectors and market capitalizations, including mid-cap and small-cap equities. The integration of advanced techniques such as machine learning and artificial intelligence can further enhance portfolio optimization and predictive accuracy (Manjunath et al., 2025). Additionally, future studies may consider the inclusion of macroeconomic variables, ESG factors, and global market linkages to provide a more comprehensive analysis. Comparative studies across different countries or time periods can also offer deeper insights into market behavior. Expanding the dataset and methodology will improve the robustness and applicability of portfolio construction strategies (MK, Suneetha & Reddy, 2026).

Conclusion

The study concludes that the application of the Markowitz Mean–Variance model combined with risk-adjusted performance measures significantly enhances portfolio efficiency. The findings confirm that diversification among large-cap stocks reduces risk while maintaining stable returns. The optimized portfolio outperforms both individual stocks and the Nifty 50 benchmark in terms of return and risk-adjusted performance. The results also validate key financial theories, including the risk-return trade-off and the benefits of systematic portfolio construction. Overall, the study demonstrates that data-driven investment strategies and performance evaluation tools are essential for achieving consistent and superior investment outcomes in volatile market environments.

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Received: 15-Apr-2026, Manuscript No. AMSJ-26-17206; Editor assigned: 16-Apr-2026, PreQC No. AMSJ-26-17206(PQ); Reviewed: 22- Apr-2026, QC No. AMSJ-26-17206; Revised: 29-Apr-2026, Manuscript No. AMSJ-26-17206(R); Published: 06-May-2026