Optimizing Portfolio Allocation in the Indian Defense Sector: A Python-Based Approach

We characterize the investor’s optimal portfolio allocation subject to a budget constraint and a probabilistic VaR constraint in complete markets environments with a finite number of states. The set of feasible portfolios might no longer be connected or convex, while the number of local optima increases exponentially with the number of states, implying computational complexity. The optimal constrained portfolio allocation may therefore not be monotonic in the state–price density. We propose a type of financial innovation, which splits states of nature, that is shown to weakly enhance welfare, restore monotonicity of the optimal portfolio allocation in the state-price density, and reduce computational complexity.

Markowitz’s portfolio theory is one of the most important theoretical developments in finance. Its elegance and theoretical appeal are illustrated by the fact that it is taught in virtually every undergraduate and MBA level course on portfolio management. Yet the Markowitz mean-variance (MV) optimization is not widely used by the investment community. In this book, Richard Michaud, a leading researcher in this area, explains why this is so. Based on his diagnosis of the problem, he advocates a “statistical view” of the MV optimization that leads to new procedures that can reduce or eliminate many practical deficiencies of the MV optimization. Using a simple global asset allocation example throughout the book, he illustrates the problems associated with a naïve implementation of the MV optimization procedure. He then describes how the new procedures can be applied, and shows how they improve the MV optimization results. The bottom line: the “statistical view” and the new procedures offer the potential of substantial improvements in the investment performance of the MV optimization. I agree with this assessment. I find this book a must-read for industry professionals and researchers who are interested in this area.

The 4 Percent Strategy Revisited: A Pre-Commitment Optimal Mean-Variance Approach to Wealth Management

Portfolio construction is an important practical problem in finance. In the traditional approach, introduced by Markowitz, one assumes normally distributed returns and constructs a portfolio with a minimum risk (measured by the standard deviation of portfolio returns) for a specified (and minimally acceptable) return.In practice, returns are not normally distributed and have heavy tails. As a result, the normality assumption severely underestimates risk. It has been long suggested that a more appropriate way is to model returns by using alpha-stable distributions.In this paper, we use elliptical stable distributions for optimal stable portfolio construction. We illustrate this by considering portfolios from S&P 500 sector exchange-traded funds (ETFs).Our main results indicate that stable portfolios are in general comparable with standard Markowitz portfolios. But we discovered a few properties of stable distributions that are promising for optimal portfolio selection problem. Stable risk estimation for next year is much closer to the actual portfolio risk, stable portfolios are more balanced, so they better handle maximum restriction on component weights, and stable portfolios are more resilient to extreme market conditions.Both stable and normal optimal portfolios outperform S&P 500 index and equally-weighted ETF portfolio in most years.We propose an investment strategy that uses both stable and normal distributions for building optimal portfolios. The return of this strategy exceeds the return of the strategies which use only stable or only normal distributions.

This thesis consists of three essays in financial economics, more precisely in the field of asset pricing and optimal portfolio choice. The first essay studies the asset pricing implications of heterogeneity in preferences coupled with long run risk in a dynamic general equilibrium pure exchange economy. It is concerned with the understanding of how risk sharing among different types of agents affects the assets returns moments in equilibrium and moreover, how these agents reacts dynamically to the long run risk that they perceive. The second and third essay approach the question of optimal portfolio with stochastic opportunity sets. The second essay proposes an approximation methodology for deriving approximate closed form solutions of dynamic optimal portfolio allocation problems. The third essay examines the optimal consumption, portfolio rule and life insurance purchase problem of a wage earner having uncertain lifetime when the market price of risk follows a mean-reverting stochastic process.

This study evaluates the benefits of portfolio diversification by examining the relationship between the returns of Sido Muncul Tbk (SIDO) and Indofood CBP Sukses Makmur Tbk (ICBP) using Modern Portfolio Theory (MPT). Daily closing prices from October 1, 2023, to September 30, 2024, were analyzed. Daily returns were calculated and assessed using descriptive statistics, Pearson correlation, and mean–variance optimization to construct the efficient frontier and identify the optimal allocation. The results show ICBP offers a lower return (6.25%) and lower risk (1.92), while SIDO provides a higher return (7.35%) with slightly higher risk (1.97). Portfolio optimization suggests a 50/50 allocation yields the most balanced outcome, minimizing risk (1.46) while maintaining a solid return (6.80%). The low correlation (0.13) between the two stocks highlights significant diversification benefits. Practical implications include providing Shariah-compliant investors with empirical guidance to build efficient portfolios that balance return and risk. The study is limited by its use of only two stocks and a one-year observation period, which may affect the generalizability of results to broader market conditions. Keywords: Modern Portfolio Theory, Portfolio Optimization, Efficient Frontier, Islamic Investment, Investment Decision-Making

While investors take investment decisions, they expect high returns at minimum risk, and they also do not want to block their entire investment in a single security. So, they aim at creating optimal portfolios through diversification. The present study examined the impact of a single market index on the different companies' stocks included in the index. By using Sharpe's single index model (SIM), analysis of risk and return is made easy. The study aimed at applying Sharpe's single index model for constructing an optimal portfolio and understanding the effect of diversification of investments. The study is empirical in nature and is based on secondary data. All the 30 companies listed in the BSE were included in the study. Sensex was used as the benchmark index. Data for a 7- year period (2005-2012) were used for portfolio construction. The study showed that by using this model, the investors can minimize their overall risk and maximize the returns over any period of time. It was found that even companies with high rates of return were not included in the portfolio as the risk involved in such companies was high. It was also proved that SIM has been useful to create an optimal portfolio by diversifying almost all the unsystematic risks.

Over the past two decades, a number of studies have examined the benefits of diversifying equity investments internationally, particularly into emerging markets. In the portfolio construction process, many researchers have criticised Markowitz's Portfolio Theory because of its inherent assumptions such as symmetric and constant correlations. In this study, we use a conditional copula model to estimate the time-varying asymmetric correlations of stock markets and construct optimal portfolios by using estimated correlations. We find that optimised portfolios provide significant benefits for both Australian and the US investors. Out-of-sample results show Copula model provides results closer to the in-sample-estimated benefits of diversification. The results have important implications for portfolio managers who seek to diversify into emerging markets.

Portfolio Analysis is one of the alternative alternative tools in making investment decisions in stocks. In investing, if it only depends on one type of stock, it is likely that many investors will bear the risk. This stage involves identifying which securities will be chosen to form a portfolio and what proportion of funds will be invested in each of these securities. The selection of these securities (in other words, investors diversify) is intended to minimize the risk borne. The selection of these securities will be influenced by risk preferences, cash needs patterns, and tax status. Investment decisions are decisions taken by investors to allocate the funds they have in the form of certain assets (financial assets) in the hope that they will get economic benefits in the future. If the decision taken is to buy a certain number of shares, then that is expected to get dividends and capital gains if the shares are resold. The main consideration for fund owners (investors) in optimizing investment decisions is to maximize the level of return on investment (risk) for certain investments (Saragih et al., 2006). The making of an investment decision framework largely determines the success of an investor in optimizing the level of investment returns and reducing as little as possible the risks faced (Markowitz, 1952). In connection with the above, the main problem in this study is how to design an optimal portfolio simulation which is a combination of LQ 45 liquid stocks listed on the Indonesia Stock Exchange (IDX). The research data was conducted on LQ 45 shares during the period March - June 2012. The variables of this study were stock prices, returns, standard deviations of returns. The statistical method used is the F-test for homogeneity of variants. The results showed that only 16 stocks had optimal portfolios. Optimal portfolio, characterized by high return and low risk.

Dynamic copulas provide a flexible framework for modelling time-varying dependencies between financial assets, overcoming the limitations of traditional correlation measures and DCC models. Their ability to capture non-linear relationships, tail dependence, and asymmetry makes them particularly useful for risk management and portfolio optimization. The main contributions of this paper are: first, by extending dynamic specifications to the Student’s t, Clayton, and Frank copulas, and second, by providing their implementation in the R environment through the “dynCopula” package, freely available for the research community. Our empirical application considers three major international stock markets (Euro Stoxx 50, S&P 500, Nikkei) and Bitcoin. The results reveal that the dependence between assets evolves over time and intensifies during periods of financial stress. We also show that diversification benefits increase as the degree of dependence decreases, provided that assets have similar risk levels. Finally, dynamic copulas yield more accurate estimates of market risk than static models. These results underscore the benefits of dynamic copulas for practitioners: they enable more reliable risk quantification, enhance hedging strategies, and support the construction of optimal or minimum-variance portfolios under changing market conditions, making them a valuable tool for both investment management and financial risk analysis.

What Investors Want! Behavioural Finance Implications in Optimal Portfolio Construction

This paper revisits the relationship between eigenvector asset centrality and optimal asset allocation in a minimum variance portfolio. We show that the standard definition of eigenvector centrality is misleading when the adjacency matrix in a network can take negative values. This is, for example, the case when the network topology is induced by the correlation matrix between assets in a portfolio. To correct for this, we introduce the concept of positive and negative eigenvector centrality. Our results show that the loss function associated to the minimum variance portfolio is positively/negatively related to the positive and negative eigenvector centrality under short-selling constraints but cannot be generalized beyond that. Furthermore, in contrast to what is claimed in the related literature, this relationship does not imply any monotonic relationship between the centrality of an asset and its optimal portfolio allocation. These theoretical insights are illustrated empirically in a portfolio allocation exercise with assets from U.S. and U.K. financial markets.

This research investigates whether optimizing stock portfolios aligns with prudence in Sharia-compliant stock investment. It compares the portfolio optimization analysis between Sharia-compliant securities and the Jakarta Islamic Index. Each group is structured with its optimal portfolio composition to achieve the highest expected return for various possible risks. Two efficient frontiers are derived from both optimal portfolios. A slight intersection is found in the efficient frontier between these two portfolio groups, justifying that taking high risks in one group results in a low-risk choice in the other portfolio group. The Sharia-compliant investment is realized by choosing an optimal portfolio with low risk while still tolerating investment selections with higher risk, as long as they are aligned with Islamic principles. The findings of this optimal portfolio offer practical guidance for investment decisions and significantly contribute to advancing the field of Islamic finance and investment practices.

In <b>Portfolio Optimization with Active, Passive, and Factors: <i>Removing the Ad Hoc Step</i></b>, from the March 2020 issue of <b><i>The Journal of Portfolio Management</i>, Roger Aliaga-Diaz, Giulio Renzi-Ricci, Ankul Daga</b>, and <b>Harshdeep Ahluwalia</b>, all with <b>The Vanguard Group</b>, discuss a more streamlined way to optimize portfolios. They present a quantitative asset-allocation framework that incorporates active, passive, and factor strategies—and propose a utility optimization model that concurrently allocates assets among investments in these three dimensions. Their approach condenses portfolio optimization into one step that integrates investors’ risk tolerance into asset allocation. The model incorporates investor risk preferences shaped by the uncertainties inherent with active, passive, and factor investment returns. By clarifying investors’ decision-making, this approach steers them away from ad hoc portfolio allocations and permits them to customize their portfolios more deliberately. The authors highlight practical applications, including how the approach can be used to substitute lower-cost factor strategies for higher-cost active strategies and to create factor-tilted portfolios aligned with investors’ varying risk thresholds. <b>TOPICS:</b>Analysis of individual factors/risk premia, factor-based models, portfolio theory, portfolio construction

In this article, the authors revisit a neglected paper written by Rubinstein in which he advocated a generalized logarithmic utility function. The profession has rather ignored his model in favor of the mean–variance approach, for reasons that are well known. The authors note that generalized logarithmic utility allows us to identify absolute risk aversion more directly and intuitively than the approaches adopted in mean–variance portfolio construction. They demonstrate that, for top-level asset allocation in which the conditions required by mean–variance are satisfied and mean–variance gives a good approximation to expected utility, generalized logarithmic utility gives essentially the same answer. In situations not suited to mean–variance, such as the inclusion of derivatives in portfolios or, more generally, when higher moments in return and utility probability distributions are unavoidable, Rubinstein’s model appears superior and seems particularly well suited to multi-asset investment. The authors’ simplified Bayesian model shows out-of-sample advantages for broad US asset allocation for the 2000 through mid-2020 period. <b>TOPICS:</b>Statistical methods, portfolio theory, portfolio construction <b>Key Findings</b> ▪ Maximizing the expected Rubinstein utility increases expected surplus growth for conservative investors and for those who do not rebalance frequently. Markowitz’s risk aversion parameter is replaced without requiring subjective judgement of aversion to return variance. ▪ Bayesian prediction can incorporate both scenario priors and observed return data in a simple grid form. This increases model flexibility and decreases sensitivity to errors in estimates of return probability distribution parameters. ▪ We demonstrate out-of-sample advantages for Rubinstein utility with simplified Bayesian prediction in broad US stock, bond, and cash allocation for the most recent decades. This is based on a prior inferred from earlier history, including the 1929 crash.