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India is the largest democracy in the world and has recently surpassed China to be the highest-populated country, with an estimated 1.425 billion (approximately 18% of the world population). Moreover, India's elderly population is projected to increase to 138 million by 2035. Indian economy is already reeling under the pressure of exorbitant pension liabilities of the government for existing pensioners. As such, India has introduced a National Pension System (NPS), which is a Defined Contribution Scheme for employees joining government service on or after 1st January 2004, bidding adieu to the age-old, tried and tested Old Pension System (OPS) which is a Direct Benefit Scheme, in vogue in India since the British Raj. This is an epoch-making move by the government as it seeks to inculcate Disciplined Saving among the people while significantly reducing the government burden by reducing the Pension Liabilities of the Central and State Governments. This paper aims to analyse various features and intricacies of the NPS and address the claims of various stakeholders like the Central Government, State Government, Employees, Pensioners, etc. In light of the above, and taking cognisance of the fact that many states such as Rajasthan, Chattisgarh, Jharkhand, etc, have exited the NPS scheme and have sought back their share of NPS employee and employer contribution, this study is relevant to address the current economic and fiscal issues of India to propel towards the ambitious goal of becoming a $ 5 trillion dollar economy by 2025. Keywords: Old Pension Scheme (OPS), National Pension System (NPS), Direct Benefit Scheme, Defined Contribution Scheme, Pension Liabilities.

We introduce new mathematical methods to study the optimal portfolio size of investment portfolios over time, considering investors with varying skill levels. First, we explore the benefit of portfolio diversification on an annual basis for poor, average and strong investors defined by the 10th, 50th and 90th percentiles of risk-adjusted returns, respectively. Second, we conduct a thorough regression experiment examining quantiles of risk-adjusted returns as a function of portfolio size across investor ability, testing for trends and curvature within these functions. Finally, we study the optimal portfolio size for poor, average and strong investors in a continuously temporal manner using more than 20 years of data. We show that strong investors should hold concentrated portfolios, poor investors should hold diversified portfolios; average investors have a less obvious distribution with the optimal number varying materially over time.

This article investigates a regime-switching investment strategy aimed at mitigating downside risk by reducing market exposure during anticipated unfavorable market regimes. We highlight the statistical jump model (JM) for market regime identification, a recently developed robust model that distinguishes itself from traditional Markov-switching models by enhancing regime persistence through a jump penalty applied at each state transition. Our JM utilizes a feature set comprising risk and return measures derived solely from the return series, with the optimal jump penalty selected through a time-series cross-validation method that directly optimizes strategy performance. Our empirical analysis evaluates the realistic out-of-sample performance of various strategies on major equity indices from the US, Germany, and Japan from 1990 to 2023, in the presence of transaction costs and trading delays. The results demonstrate the consistent outperformance of the JM-guided strategy in reducing risk metrics such as volatility and maximum drawdown, and enhancing risk-adjusted returns like the Sharpe ratio, when compared to both hidden Markov model-guided strategy and the buy-and-hold strategy. These findings underline the enhanced persistence, practicality, and versatility of strategies utilizing JMs for regime-switching signals.

The M6 Competition assessed the performance of competitors using a ranked probability score and an information ratio (IR). While these metrics do well at picking the winners in the competition, crucial questions remain for investors with longer-term incentives. To address these questions, we compare the competitors' performance to a number of conventional (long-only) and alternative indices using standard industry metrics. We apply factor models to measure the competitors' value-adds above industry-standard benchmarks and find that competitors with more extreme performance are less dependent on the benchmarks. We also uncover that most competitors could not generate significant out-performance compared to randomly selected long-only and long-short portfolios but did generate out-performance compared to short-only portfolios. We further introduce two new strategies by picking the competitors with the best (Superstars) and worst (Superlosers) recent performance and show that it is challenging to identify skill amongst investment managers. We also discuss the incentives of winning the competition compared to professional investors, where investors wish to maximize fees over an extended period of time.

For \\(n\\) assets and discrete-time rebalancing, the probability to complete a given schedule of investments and withdrawals is maximized over progressively measurable portfolio weight functions. Applications consider two assets, namely the S&P Composite Index and an inflation-protected bond. The maximum probability and optimal portfolio weight functions are computed for annually rebalanced schedules involving an arbitrary initial investment and then equal annual withdrawals over the remainder of the time period. Applications also consider annually rebalanced schedules that start with dollar cost averaging (equal annual investments) and then shift to equal annual withdrawals. Results indicate noticeable improvements in the probability to complete a given schedule when optimal portfolio weights are used instead of constant portfolio weights like the standard of keeping 90% in the S&P Composite Index and 10% in inflation-protected bonds.

The paper investigates quadratic hedging in a semimartingale market that does not necessarily contain a risk-free asset. An equivalence result for hedging with and without numeraire change is established (Proposition 3.16). This permits direct computation of the optimal strategy without choosing a reference asset and/or performing a numeraire change (Theorem 4.1). New explicit expressions for optimal strategies are obtained, featuring the use of oblique projections that provide unified treatment of the case with and without a risk-free asset (Theorem 4.3). The analysis yields a streamlined computation of the efficient frontier for the pure investment problem in terms of three easily interpreted processes (Equation~1.1). The main result advances our understanding of the efficient frontier formation in the most general case where a risk-free asset may not be present. Several illustrations of the numeraire-invariant approach are given.

Statistical arbitrage methods identify mispricings in securities with the goal of building portfolios which are weakly correlated with the market. In pairs trading, an arbitrage opportunity is identified by observing relative price movements between a pair of two securities. By simultaneously observing multiple pairs, one can exploit different arbitrage opportunities and increase the performance of such methods. However, the use of a large number of pairs is difficult due to the increased probability of contradictory trade signals among different pairs. In this paper, we propose a novel portfolio construction method based on preference relation graphs, which can reconcile contradictory pairs trading signals across multiple security pairs. The proposed approach enables joint exploitation of arbitrage opportunities among a large number of securities. Experimental results using three decades of historical returns of roughly 500 stocks from the S\\&P 500 index show that the portfolios based on preference relations exhibit robust returns even with high transaction costs, and that their performance improves with the number of securities considered.

We introduce a new framework for the mean-variance spanning (MVS) hypothesis testing. The procedure can be applied to any test-asset dimension and only requires stationary asset returns and the number of benchmark assets to be smaller than the number of time periods. It involves individually testing moment conditions using a robust Student-t statistic based on the batch-mean method and combining the p-values using the Cauchy combination test. Simulations demonstrate the superior performance of the test compared to state-of-the-art approaches. For the empirical application, we look at the problem of domestic versus international diversification in equities. We find that the advantages of diversification are influenced by economic conditions and exhibit cross-country variation. We also highlight that the rejection of the MVS hypothesis originates from the potential to reduce variance within the domestic global minimum-variance portfolio.

In this paper, we investigate the features and the performance of the Risk Parity (RP) portfolios using the Mean Absolute Deviation (MAD) as a risk measure. The RP model is a recent strategy for asset allocation that aims at equally sharing the global portfolio risk among all the assets of an investment universe. We discuss here some existing and new results about the properties of MAD that are useful for the RP approach. We propose several formulations for finding MAD-RP portfolios computationally, and compare them in terms of accuracy and efficiency. Furthermore, we provide extensive empirical analysis based on three real-world datasets, showing that the performances of the RP approaches generally tend to place both in terms of risk and profitability between those obtained from the minimum risk and the Equally Weighted strategies.