arXiv subjects

Amita Sharma

Publications and source records attributed to Amita Sharma.

4 recordsLinked to original sources

arXiv2026

Shrinkage Estimators for Mean and Covariance: Evidence on Portfolio Efficiency Across Market Dimensions

The mean-variance model remains the most prevalent investment framework, built on diversification principles. However, it consistently struggles with estimation errors in expected returns and the covariance matrix, its core parameters. To address this concern, this research evaluates the performance of mean variance (MV) and global minimum-variance (GMV) models across various shrinkage estimators designed to improve these parameters. Specifically, we examine five shrinkage estimators for expected returns and eleven for the covariance matrix. To compare multiple portfolios, we employ a super efficient data envelopment analysis model to rank the portfolios according to investors risk-return preferences. Our comprehensive empirical investigation utilizes six real world datasets with different dimensional characteristics, applying a rolling window methodology across three out of sample testing periods. Following the ranking process, we examine the chosen shrinkage based MV or GMV portfolios against five traditional portfolio optimization techniques classical MV and GMV for sample estimates, MiniMax, conditional value at risk, and semi mean absolute deviation risk measures. Our empirical findings reveal that, in most scenarios, the GMV model combined with the Ledoit Wolf two parameter shrinkage covariance estimator (COV2) represents the optimal selection for a broad spectrum of investors. Meanwhile, the MV model utilizing COV2 alongside the sample mean (SM) proves more suitable for return oriented investors. These two identified models demonstrate superior performance compared to traditional benchmark approaches. Overall, this study lays the groundwork for a more comprehensive understanding of how specific shrinkage models perform across diverse investor profiles and market setups.

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arXiv2026

A comprehensive review and analysis of different modeling approaches for financial index tracking problem

Index tracking, also known as passive investing, has gained significant traction in financial markets due to its cost-effective and efficient approach to replicating the performance of a specific market index. This review paper provides a comprehensive overview of the various modeling approaches and strategies developed for index tracking, highlighting the strengths and limitations of each approach. We categorize the index tracking models into three broad frameworks: optimization-based models, statistical-based models and machine learning based data-driven approach. A comprehensive empirical study conducted on the S\&P 500 dataset demonstrates that the tracking error volatility model under the optimization-based framework delivers the most precise index tracking, the convex co-integration model, under the statistical-based framework achieves the strongest return-risk balance, and the deep neural network with fixed noise model within the data-driven framework provides a competitive performance with notably low turnover and high computational efficiency. By combining a critical review of the existing literature with comparative empirical analysis, this paper aims to provide insights into the evolving landscape of index tracking and its practical implications for investors and fund managers.

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arXiv2026

Class of topological portfolios: Are they better than classical portfolios?

Topological Data Analysis (TDA), an emerging field in investment sciences, harnesses mathematical methods to extract data features based on shape, offering a promising alternative to classical portfolio selection methodologies. We utilize persistence landscapes, a type of summary statistics for persistent homology, to capture the topological variation of returns, blossoming a novel concept of ``Topological Risk". Our proposed topological risk then quantifies portfolio risk by tracking time-varying topological properties of assets through the $L_p$ norm of the persistence landscape. Through optimization, we derive an optimal portfolio that minimizes this topological risk. Numerical experiments conducted using nearly a decade long S\&P 500 data demonstrate the superior performance of our TDA-based portfolios in comparison to the seven popular portfolio optimization models and two benchmark portfolio strategies, the naive $1/N$ portfolio and the S\&P 500 market index, in terms of excess mean return, and several financial ratios. The outcome remains consistent through out the computational analysis conducted for the varying size of holding and investment time horizon. These results underscore the potential of our TDA-based topological risk metric in providing a more comprehensive understanding of portfolio dynamics than traditional statistical measures. As such, it holds significant relevance for modern portfolio management practices.

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arXiv2021

Sectoral portfolio optimization by judicious selection of financial ratios via PCA

Embedding value investment in portfolio optimization models has always been a challenge. In this paper, we attempt to incorporate it by employing principal component analysis to filter out dominant financial ratios from each sector and thereafter, use the portfolio optimization model incorporating second-order stochastic dominance criteria to derive an optimal investment. We consider a total of $11$ financial ratios corresponding to each sector representing four categories of ratios, namely liquidity, solvency, profitability, and valuation. PCA is then applied over a period of 10 years to extract dominant ratios from each sector in two ways, one from the component solution and the other from each category on the basis of their communalities. The two-step Sectoral Portfolio Optimization (SPO) model is then utilized to build an optimal portfolio. The strategy formed using the formerly extracted ratios is termed PCA-SPO(A) and the latter PCA-SPO(B). The results obtained from the proposed strategies are compared with those from mean-variance, minimum variance, SPO, and nominal SSD models, with and without financial ratios. The empirical performance of proposed strategies is analyzed in two ways, viz., using a rolling window scheme and using market trend scenarios for S\&P BSE 500 (India) and S\&P 500 (U.S.) markets. We observe that the proposed strategy PCA-SPO(B) outperforms all other models in terms of downside deviation, CVaR, VaR, Sortino, Rachev, and STARR ratios over almost all out-of-sample periods. This highlights the importance of value investment where ratios are carefully selected and embedded quantitatively in portfolio selection process.

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