arXiv subjects

Nolan Alexander

Publications and source records attributed to Nolan Alexander.

6 recordsLinked to original sources

arXiv2026

A Mathematical Optimization Approach for Expert-Informed Bayesian Best Subset Selection

A central challenge in statistical modeling is identifying the subset of features that belong in the true regression model. The classical best subset selection problem, recently made tractable via mixed-integer optimization (MIO), finds the globally optimal sparse solution. It does not, however, make use of any information beyond the observed data. In many applied settings, domain experts can meaningfully rank or score the relevance of candidate predictors, yet no existing framework integrates such probabilistic expert assessments directly into the best-subsets objective. This paper presents Expert-Implied Bayesian Best Subsets (EBBS), a method that incorporates domain-expert probability estimates of feature relevance into the MIO best-subsets problem through a maximum a posteriori (MAP) framework. Expert views from multiple respondents are aggregated into a single prior probability per feature using the Poisson binomial distribution for marginal probability estimates, the pairwise win rate for pairwise comparisons, or the normalized mean rank for ordinal rankings. This probability enters the objective function as a log-odds penalty term that smoothly encourages or discourages the selection of each feature consistent with the expert consensus. This paper provides analytic derivations of the MAP formulation and characterizes its theoretical properties. The proposed model reduces to Best Subsets when experts all have no views. Empirical results on synthetic and real datasets are forthcoming.

cs.LG↗

arXiv2026

On the Structure of Risk Contribution: A Leave-One-Out Decomposition into Inherent and Correlation Risk

This paper develops a decomposition of standard Risk Contribution (RC) into two economically interpretable components: inherent risk and correlation risk. Using a leave-one-out representation, each position's RC separates into a term reflecting its own volatility contribution independent of the portfolio and a term capturing its covariance with the remainder of the portfolio. The inherent component is always positive, arising from the intrinsic volatility of the position, while the correlation component may amplify or mitigate total portfolio risk depending on how the position moves relative to other holdings. Because the decomposition operates within standard RC, it preserves the property of strict additivity. This separation provides diagnostic insight not visible from aggregate risk contributions alone. It distinguishes whether a position contributes risk because it is volatile in isolation or because it is highly correlated with the rest of the portfolio, and it clarifies when a negatively correlated position functions as an effective hedge. Two approaches to time-series analysis are presented to track how inherent and correlation risk evolve across market regimes, revealing whether changes in portfolio risk during stress periods are driven by volatility shocks, correlation shifts, or both. Empirical illustrations suggest that the decomposition provides stable, transparent, and easily implementable risk diagnostics that can support portfolio risk reporting, stress testing, and performance attribution.

q-fin.RM↗

arXiv2026

Measuring Strategy-Decay Risk: Minimum Regime Performance and the Durability of Systematic Investing

Systematic investment strategies are exposed to a subtle but pervasive vulnerability: the progressive erosion of their effectiveness as market regimes change. Traditional risk measures, designed to capture volatility or drawdowns, overlook this form of structural fragility. This article introduces a quantitative framework for assessing the durability of systematic strategies through minimum regime performance (MRP), defined as the lowest realized risk-adjusted return across distinct historical regimes. MRP serves as a lower bound on a strategy's robustness, capturing how performance deteriorates when underlying relationships weaken or competitive pressures compress alpha. Applied to a broad universe of established factor strategies, the measure reveals a consistent trade-off between efficiency and resilience -- strategies with higher long-term Sharpe ratios do not always exhibit higher MRPs. By translating the persistence of investment efficacy into a measurable quantity, the framework provides investors with a practical diagnostic for identifying and managing strategy-decay risk, a novel dimension of portfolio fragility that complements traditional measures of market and liquidity risk.

q-fin.RM↗

arXiv2026

Asset allocation using a Markov process of clustered efficient frontier coefficients states

We propose a novel asset allocation model using a Markov process of states defined by clustered efficient frontier coefficients. While most research in Markov models of the market characterize regimes using return and volatility, we instead propose characterizing these states using efficient frontiers, which provide more information on the interactions of underlying assets that comprise the market. Efficient frontiers can be decomposed to their functional form, a square-root second-order polynomial defined by three coefficients, to provide a dimensionality reduction of the return vector and covariance matrix. Each month, the proposed model hierarchically clusters the monthly coefficients data up to the current month, to characterize the market states, then defines a Markov process on the sequence of states. To incorporate these states into portfolio optimization, for each state, we calculate the tangency portfolio using only return data in that state. We then take the expectation of these weights for each state, weighted by the probability of transitioning from the current state to each state. To empirically validate our proposed model, we employ three sets of assets that span the market, and show that our proposed model significantly outperforms benchmark portfolios.

q-fin.PM↗

arXiv2026

Forecasting Tangency Portfolios and Investing in the Minimum Euclidean Distance Portfolio to Maximize Out-of-Sample Sharpe Ratios

We propose a novel model to achieve superior out-of-sample Sharpe ratios. While most research in asset allocation focuses on estimating the return vector and covariance matrix, the first component of our novel model instead forecasts the future tangency portfolio, and the second component then determines the optimal investment portfolio. First, to forecast the tangency portfolio, we forecast the efficient frontier by decomposing its functional form, a square root second-order polynomial, into three interpretable coefficients, which can then be used to calculate a forecasted tangency portfolio. These coefficients can be forecasted using vector autoregressions. Second, the model invests in the portfolio on the efficient frontier that is the minimum Euclidean distance from this forecasted tangency portfolio. A motivation for our approach is to address the limitation that the tangency portfolio only maximizes the Sharpe ratio when future returns and covariances are stationary, and can be directly estimated with historical data, which often does not hold in out-of-sample data. Our approach addresses this shortcoming in a novel way by forecasting the tangency portfolio, rather than estimating return and covariance. For empirical testing, we employ two sets of assets that span the market to demonstrate and validate the performance of this novel method.

q-fin.PM↗

arXiv2024

Using Machine Learning to Forecast Market Direction with Efficient Frontier Coefficients

We propose a novel method to improve estimation of asset returns for portfolio optimization. This approach first performs a monthly directional market forecast using an online decision tree. The decision tree is trained on a novel set of features engineered from portfolio theory: the efficient frontier functional coefficients. Efficient frontiers can be decomposed to their functional form, a square-root second-order polynomial, and the coefficients of this function captures the information of all the constituents that compose the market in the current time period. To make these forecasts actionable, these directional forecasts are integrated to a portfolio optimization framework using expected returns conditional on the market forecast as an estimate for the return vector. This conditional expectation is calculated using the inverse Mills ratio, and the Capital Asset Pricing Model is used to translate the market forecast to individual asset forecasts. This novel method outperforms baseline portfolios, as well as other feature sets including technical indicators and the Fama-French factors. To empirically validate the proposed model, we employ a set of market sector ETFs.

q-fin.PM↗