Risk Parity

Deep Declarative Risk Budgeting Portfolios ArXiv ID: 2504.19980 “View on arXiv” Authors: Manuel Parra-Diaz, Carlos Castro-Iragorri Abstract Recent advances in deep learning have spurred the development of end-to-end frameworks for portfolio optimization that utilize implicit layers. However, many such implementations are highly sensitive to neural network initialization, undermining performance consistency. This research introduces a robust end-to-end framework tailored for risk budgeting portfolios that effectively reduces sensitivity to initialization. Importantly, this enhanced stability does not compromise portfolio performance, as our framework consistently outperforms the risk parity benchmark. ...

Dynamic Investment Strategies Through Market Classification and Volatility: A Machine Learning Approach ArXiv ID: 2504.02841 “View on arXiv” Authors: Unknown Abstract This study introduces a dynamic investment framework to enhance portfolio management in volatile markets, offering clear advantages over traditional static strategies. Evaluates four conventional approaches : equal weighted, minimum variance, maximum diversification, and equal risk contribution under dynamic conditions. Using K means clustering, the market is segmented into ten volatility-based states, with transitions forecasted by a Bayesian Markov switching model employing Dirichlet priors and Gibbs sampling. This enables real-time asset allocation adjustments. Tested across two asset sets, the dynamic portfolio consistently achieves significantly higher risk-adjusted returns and substantially higher total returns, outperforming most static methods. By integrating classical optimization with machine learning and Bayesian techniques, this research provides a robust strategy for optimizing investment outcomes in unpredictable market environments. ...

A multi-factor market-neutral investment strategy for New York Stock Exchange equities ArXiv ID: 2412.12350 “View on arXiv” Authors: Unknown Abstract This report presents a systematic market-neutral, multi-factor investment strategy for New York Stock Exchange equities with the objective of delivering steady returns while minimizing correlation with the market. A robust feature set is integrated combining momentum-based indicators, fundamental factors, and analyst recommendations. Using various statistical tests for feature selection, the strategy identifies key drivers of equity performance and ranks stocks to build a balanced portfolio of long and short positions. Portfolio construction methods, including equally weighted, risk parity, and minimum variance beta-neutral approaches, were evaluated through rigorous backtesting. Risk parity demonstrated superior performance with a higher Sharpe ratio, lower beta, and smaller maximum drawdown compared to the Standard and Poor’s 500 index. Risk parity’s market neutrality, combined with its ability to maintain steady returns and mitigate large drawdowns, makes it a suitable approach for managing significant capital in equity markets. ...

Risk Analysis of Passive Portfolios ArXiv ID: 2407.08332 “View on arXiv” Authors: Unknown Abstract In this work, we present an alternative passive investment strategy. The passive investment philosophy comes from the Efficient Market Hypothesis (EMH), and its adoption is widespread. If EMH is true, one cannot outperform market by actively managing their portfolio for a long time. Also, it requires little to no intervention. People can buy an exchange-traded fund (ETF) with a long-term perspective. As the economy grows over time, one expects the ETF to grow. For example, in India, one can invest in NETF, which suppose to mimic the Nifty50 return. However, the weights of the Nifty 50 index are based on market capitalisation. These weights are not necessarily optimal for the investor. In this work, we present that volatility risk and extreme risk measures of the Nifty50 portfolio are uniformly larger than Markowitz’s optimal portfolio. However, common people can’t create an optimised portfolio. So we proposed an alternative passive investment strategy of an equal-weight portfolio. We show that if one pushes the maximum weight of the portfolio towards equal weight, the idiosyncratic risk of the portfolio would be minimal. The empirical evidence indicates that the risk profile of an equal-weight portfolio is similar to that of Markowitz’s optimal portfolio. Hence instead of buying Nifty50 ETFs, one should equally invest in the stocks of Nifty50 to achieve a uniformly better risk profile than the Nifty 50 ETF portfolio. We also present an analysis of how portfolios perform to idiosyncratic events like the Russian invasion of Ukraine. We found that the equal weight portfolio has a uniformly lower risk than the Nifty 50 portfolio before and during the Russia-Ukraine war. All codes are available on GitHub (\url{“https://github.com/sourish-cmi/quant/tree/main/Chap_Risk_Anal_of_Passive_Portfolio"}). ...

The Blockchain Risk Parity Line: Moving From The Efficient Frontier To The Final Frontier Of Investments ArXiv ID: 2407.09536 “View on arXiv” Authors: Unknown Abstract We engineer blockchain based risk managed portfolios by creating three funds with distinct risk and return profiles: 1) Alpha - high risk portfolio; 2) Beta - mimics the wider market; and 3) Gamma - represents the risk free rate adjusted to beat inflation. Each of the sub-funds (Alpha, Beta and Gamma) provides risk parity because the weight of each asset in the corresponding portfolio is set to be inversely proportional to the risk derived from investing in that asset. This can be equivalently stated as equal risk contributions from each asset towards the overall portfolio risk. We provide detailed mechanics of combining assets - including mathematical formulations - to obtain better risk managed portfolios. The descriptions are intended to show how a risk parity based efficient frontier portfolio management engine - that caters to different risk appetites of investors by letting each individual investor select their preferred risk-return combination - can be created seamlessly on blockchain. Any Investor - using decentralized ledger technology - can select their desired level of risk, or return, and allocate their wealth accordingly among the sub funds, which balance one another under different market conditions. This evolution of the risk parity principle - resulting in a mechanism that is geared to do well under all market cycles - brings more robust performance and can be termed as conceptual parity. We have given several numerical examples that illustrate the various scenarios that arise when combining Alpha, Beta and Gamma to obtain Parity. The final investment frontier is now possible - a modification to the efficient frontier, thus becoming more than a mere theoretical construct - on blockchain since anyone from anywhere can participate at anytime to obtain wealth appreciation based on their financial goals. ...

A return-diversification approach to portfolio selection ArXiv ID: 2312.09707 “View on arXiv” Authors: Unknown Abstract In this paper, we propose a general bi-objective model for portfolio selection, aiming to maximize both a diversification measure and the portfolio expected return. Within this general framework, we focus on maximizing a diversification measure recently proposed by Choueifaty and Coignard for the case of volatility as a risk measure. We first show that the maximum diversification approach is actually equivalent to the Risk Parity approach using volatility under the assumption of equicorrelated assets. Then, we extend the maximum diversification approach formulated for general risk measures. Finally, we provide explicit formulations of our bi-objective model for different risk measures, such as volatility, Mean Absolute Deviation, Conditional Value-at-Risk, and Expectiles, and we present extensive out-of-sample performance results for the portfolios obtained with our model. The empirical analysis, based on five real-world data sets, shows that the return-diversification approach provides portfolios that tend to outperform the strategies based only on a diversification method or on the classical risk-return approach. ...

Portfolio Optimization Rules beyond the Mean-Variance Approach ArXiv ID: 2305.08530 “View on arXiv” Authors: Unknown Abstract In this paper, we revisit the relationship between investors’ utility functions and portfolio allocation rules. We derive portfolio allocation rules for asymmetric Laplace distributed $ALD(μ,σ,κ)$ returns and compare them with the mean-variance approach, which is based on Gaussian returns. We reveal that in the limit of small $\fracμσ$, the Markowitz contribution is accompanied by a skewness term. We also obtain the allocation rules when the expected return is a random normal variable in an average and worst-case scenarios, which allows us to take into account uncertainty of the predicted returns. An optimal worst-case scenario solution smoothly approximates between equal weights and minimum variance portfolio, presenting an attractive convex alternative to the risk parity portfolio. We address the issue of handling singular covariance matrices by imposing conditional independence structure on the precision matrix directly. Finally, utilizing a microscopic portfolio model with random drift and analytical expression for the expected utility function with log-normal distributed cross-sectional returns, we demonstrate the influence of model parameters on portfolio construction. This comprehensive approach enhances allocation weight stability, mitigates instabilities associated with the mean-variance approach, and can prove valuable for both short-term traders and long-term investors. ...