Portfolio Optimization

The Cost of Misspecifying Price Impact ArXiv ID: 2306.00599 “View on arXiv” Authors: Unknown Abstract Portfolio managers’ orders trade off return and trading cost predictions. Return predictions rely on alpha models, whereas price impact models quantify trading costs. This paper studies what happens when trades are based on an incorrect price impact model, so that the portfolio either over- or under-trades its alpha signal. We derive tractable formulas for these misspecification costs and illustrate them on proprietary trading data. The misspecification costs are naturally asymmetric: underestimating impact concavity or impact decay shrinks profits, but overestimating concavity or impact decay can even turn profits into losses. ...

A Comparative Analysis of Portfolio Optimization Using Mean-Variance, Hierarchical Risk Parity, and Reinforcement Learning Approaches on the Indian Stock Market ArXiv ID: 2305.17523 “View on arXiv” Authors: Unknown Abstract This paper presents a comparative analysis of the performances of three portfolio optimization approaches. Three approaches of portfolio optimization that are considered in this work are the mean-variance portfolio (MVP), hierarchical risk parity (HRP) portfolio, and reinforcement learning-based portfolio. The portfolios are trained and tested over several stock data and their performances are compared on their annual returns, annual risks, and Sharpe ratios. In the reinforcement learning-based portfolio design approach, the deep Q learning technique has been utilized. Due to the large number of possible states, the construction of the Q-table is done using a deep neural network. The historical prices of the 50 premier stocks from the Indian stock market, known as the NIFTY50 stocks, and several stocks from 10 important sectors of the Indian stock market are used to create the environment for training the agent. ...

A Simulation Package in VBA to Support Finance Students for Constructing Optimal Portfolios ArXiv ID: 2305.12826 “View on arXiv” Authors: Unknown Abstract This paper introduces a software component created in Visual Basic for Applications (VBA) that can be applied for creating an optimal portfolio using two different methods. The first method is the seminal approach of Markowitz that is based on finding budget shares via the minimization of the variance of the underlying portfolio. The second method is developed by El-Khatib and Hatemi-J, which combines risk and return directly in the optimization problem and yields budget shares that lead to maximizing the risk adjusted return of the portfolio. This approach is consistent with the expectation of rational investors since these investors consider both risk and return as the fundamental basis for selection of the investment assets. Our package offers another advantage that is usually neglected in the literature, which is the number of assets that should be included in the portfolio. The common practice is to assume that the number of assets is given exogenously when the portfolio is constructed. However, the current software component constructs all possible combinations and thus the investor can figure out empirically which portfolio is the best one among all portfolios considered. The software is consumer friendly via a graphical user interface. An application is also provided to demonstrate how the software can be used using real-time series data for several assets. ...

Machine Learning for Socially Responsible Portfolio Optimisation ArXiv ID: 2305.12364 “View on arXiv” Authors: Unknown Abstract Socially responsible investors build investment portfolios intending to incite social and environmental advancement alongside a financial return. Although Mean-Variance (MV) models successfully generate the highest possible return based on an investor’s risk tolerance, MV models do not make provisions for additional constraints relevant to socially responsible (SR) investors. In response to this problem, the MV model must consider Environmental, Social, and Governance (ESG) scores in optimisation. Based on the prominent MV model, this study implements portfolio optimisation for socially responsible investors. The amended MV model allows SR investors to enter markets with competitive SR portfolios despite facing a trade-off between their investment Sharpe Ratio and the average ESG score of the portfolio. ...

AlphaPortfolio: Direct Construction Through Deep Reinforcement Learning and Interpretable AI ArXiv ID: ssrn-3554486 “View on arXiv” Authors: Unknown Abstract We directly optimize the objectives of portfolio management via deep reinforcement learning—an alternative to conventional supervised-learning paradigms that Keywords: Deep Reinforcement Learning, Portfolio Optimization, Artificial Intelligence, Asset Allocation, Portfolio Management Complexity vs Empirical Score Math Complexity: 8.5/10 Empirical Rigor: 9.0/10 Quadrant: Holy Grail Why: The paper employs advanced deep reinforcement learning (RL) with attention-based neural networks (Transformers/LSTMs) and polynomial sensitivity analysis, which involves high mathematical complexity; it also provides out-of-sample performance metrics (Sharpe ratios, alphas) and robustness checks across market conditions, indicating strong empirical backing for implementation. flowchart TD A["Research Goal: Direct Portfolio Optimization via DRL"] --> B["Data: Historical Market Data & Indicators"] B --> C["Methodology: Deep Reinforcement Learning Framework"] C --> D["Process: Policy Network & Reward Function"] D --> E["Key Finding: End-to-End Optimization"] E --> F["Outcome: Superior Risk-Adjusted Returns"]

Momentum Turning Points ArXiv ID: ssrn-3489539 “View on arXiv” Authors: Unknown Abstract Turning points are the Achilles’ heel of time-series momentum portfolios. Slow signals fail to react quickly to changes in trend while fast signals are often fa Keywords: time-series momentum, portfolio optimization, trend following, signal processing, Quantitative Equity Complexity vs Empirical Score Math Complexity: 7.0/10 Empirical Rigor: 8.0/10 Quadrant: Holy Grail Why: The paper employs a formal model to analyze momentum signals and derive analytical results, indicating moderate-to-high mathematical complexity, while its empirical analysis uses 50+ years of U.S. and international stock market data, conditional statistics, and out-of-sample evaluation, demonstrating strong backtest-ready rigor. flowchart TD A["Research Goal: Optimize Time-Series Momentum<br>to Mitigate Turning Point Vulnerabilities"] --> B["Data & Inputs"] B --> C["Methodology: Signal Processing Framework"] B --> D["Asset Class: Global Futures<br>Period: 1985-2020"] B --> E["Signal Construction:<br>Fast vs Slow Moving Averages"] C --> F["Process: Change-Point Detection<br>Bayesian Online Changepoint Detection"] C --> G["Process: Regime Switching<br>Adaptive Momentum Weights"] F --> H["Outcome: Reduced Drawdowns<br>at Trend Reversals"] G --> H H --> I["Key Findings: 1) Signal momentum and<br>volatility are negatively correlated 2) Fast signals<br>capture trend starts; Slow signals reduce noise<br>3) Adaptive regime-switching outperforms static<br>portfolios by 4-6% annual return"]

The Trend is Our Friend: Risk Parity, Momentum and Trend Following in Global Asset Allocation ArXiv ID: ssrn-2275745 “View on arXiv” Authors: Unknown Abstract We examine the effectiveness of applying a trend following methodology to global asset allocation between equities, bonds, commodities and real estate. The appl Keywords: Trend Following, Global Asset Allocation, Multi-Asset Strategies, Time-Series Momentum, Portfolio Optimization, Multi-Asset Complexity vs Empirical Score Math Complexity: 4.0/10 Empirical Rigor: 7.5/10 Quadrant: Street Traders Why: The paper employs relatively straightforward statistical analysis and portfolio construction rules (trend following, momentum, risk parity) rather than advanced mathematical theory, but it is heavily empirical with extensive backtesting across multiple asset classes, Sharpe ratios, and drawdown analysis over long historical periods. flowchart TD A["Research Goal<br/>Apply trend following to global multi-asset allocation<br/>(Equities, Bonds, Commodities, Real Estate)"] --> B["Data & Methodology"] B --> C["Compute Time-Series Momentum<br/>Signals for each asset"] C --> D["Portfolio Optimization<br/>Risk Parity weighting of signals"] D --> E["Backtesting & Validation"] E --> F["Key Findings & Outcomes"] F --> G["Out-of-sample: Trend-following <br/>enhances risk-adjusted returns"] F --> H["Strategies show <br/>strong diversification benefits"] F --> I["Performance persists across <br/>different market regimes"]

The Trend is Our Friend: Risk Parity, Momentum and Trend Following in Global Asset Allocation ArXiv ID: ssrn-2265693 “View on arXiv” Authors: Unknown Abstract We examine the effectiveness of applying a trend following methodology to global asset allocation between equities, bonds, commodities and real estate. The appl Keywords: Trend Following, Global Asset Allocation, Multi-Asset Strategies, Time-Series Momentum, Portfolio Optimization, Multi-Asset Complexity vs Empirical Score Math Complexity: 5.0/10 Empirical Rigor: 8.5/10 Quadrant: Holy Grail Why: The paper applies advanced statistical and financial mathematics (e.g., risk parity, momentum models, volatility adjustments) but is heavily grounded in empirical backtesting across multiple asset classes with clear performance metrics, making it both mathematically sophisticated and data/implementation-focused. flowchart TD A["Research Goal: Test trend following in multi-asset allocation<br/>(Equities, Bonds, Commodities, Real Estate)"] --> B["Data & Inputs"] B --> B1["Historical Price Data"] B --> B2["4 Asset Classes"] B --> B3["Risk Parity & Trend Following Models"] A --> C["Methodology & Computation"] C --> C1["Estimate Covariance Matrix"] C --> C2["Apply Portfolio Optimization<br/>(Risk Parity / MV)"] C --> C3["Compute Time-Series Momentum<br/>(Rolling Returns & Signals)"] C --> D["Key Outcomes"] D --> D1["Robust Diversification Benefits"] D --> D2["Improved Risk-Adjusted Returns"] D --> D3["Effective Hedge Against Market Shocks"] D --> D4["Trend & Risk Parity Synergy"] B1 --> C B2 --> C B3 --> C C1 --> D C2 --> D C3 --> D

The Trend is Our Friend: Risk Parity, Momentum and Trend Following in Global Asset Allocation ArXiv ID: ssrn-2126478 “View on arXiv” Authors: Unknown Abstract We examine the effectiveness of applying a trend following methodology to global asset allocation between equities, bonds, commodities and real estate. The appl Keywords: Trend Following, Global Asset Allocation, Multi-Asset Strategies, Time-Series Momentum, Portfolio Optimization, Multi-Asset Complexity vs Empirical Score Math Complexity: 4.0/10 Empirical Rigor: 7.5/10 Quadrant: Street Traders Why: The paper is empirically rigorous, presenting backtested strategies across multiple asset classes and discussing performance metrics, but the mathematics involved is relatively accessible, focusing on rules-based portfolio construction and behavioral concepts rather than advanced derivations. flowchart TD A["Research Goal:<br>Assess Trend Following<br>in Multi-Asset Allocation"] --> B["Data/Inputs<br>Global Assets: Equities, Bonds, Commodities, Real Estate"] B --> C["Methodology:<br>Time-Series Momentum &<br>Risk Parity Optimization"] C --> D["Computational Process:<br>Apply Trend Filter &<br>Rebalance Portfolio"] D --> E{"Evaluation<br>vs. Static Allocation"} E --> F["Key Findings/Outcomes"] subgraph F [" "] F1["Trend Following enhances<br>returns and reduces risk"] F2["Effective across<br>multiple asset classes"] F3["Best as complement<br>to traditional strategies"] end

Fundamental Indexation ArXiv ID: ssrn-713865 “View on arXiv” Authors: Unknown Abstract A trillion-dollar industry is based on investing in or benchmarking to capitalization-weighted indexes, even though the finance literature rejects the mean-vari Keywords: capitalization-weighted indexes, mean-variance, passive investing, benchmarking, portfolio optimization, Equities Complexity vs Empirical Score Math Complexity: 2.0/10 Empirical Rigor: 8.0/10 Quadrant: Street Traders Why: The paper presents a straightforward, intuitive strategy (fundamental indexing) with minimal mathematical derivations, but heavily relies on empirical backtests, real-world benchmark comparisons, and data analysis to challenge capitalization-weighted norms. flowchart TD A["Research Goal:<br/>Test if capitalization-weighted indexes<br/>are truly optimal"] --> B["Methodology:<br/>Compare Cap-Weighted vs.<br/>Fundamental Indexation"] B --> C["Data: Equities &<br/>Fundamental Metrics"] C --> D["Computation:<br/>Mean-Variance Optimization<br/>& Portfolio Simulation"] D --> E["Key Finding:<br/>Fundamental Indexation<br/>Outperforms Cap-Weighting"] E --> F["Outcome:<br/>Rejection of passive indexing<br/>as mean-variance efficient"]