arXiv subjects

Revant Nayar

Publications and source records attributed to Revant Nayar.

4 recordsLinked to original sources

arXiv2026

Topological Risk Parity

We develop \emph{Topological Risk Parity} (TRP), a tree-based portfolio construction approach intended for long/short, market neutral, factor-aware portfolios. The method is motivated by the dominance of passive/factor flows that naturally create a tree-like structure in markets. We introduce two implementation variants: (i) a rooted minimum-spanning-tree allocator, and (ii) a market/sector-anchored variant referred to here as \emph{Semi-Supervised TRP}, which imposes SPY as the root node and the 11 sector ETFs as the second layer. In both cases, the key object is a sparse rooted topology extracted from a correlation-distance graph, together with a propagation law that maps signed signals into portfolio weights. Relative to classical Hierarchical Risk Parity (HRP), TRP is non-binary and designed for signed cross-sectional signals and hedged long-short portfolios: it preserves signal direction while using return-dependence geometry to shape exposures. It accounts for the fact that there is imperfect correlation between parent and child nodes, and thus does not propagate weights entirely to the children. We can also impose economically motivated hierarchy that involves industries, sub-industries or factors, etc. This makes it much more robust to macroeconomic shocks and crises, where within-cluster correlations might spike. These features make TRP well suited for market-neutral, equity stat-arb or L/S trend-type strategies, where enforcing neutrality or limiting exposures at the market, sector or factor level is extremely important.

q-fin.PM↗

arXiv2024

Multiscale Markowitz

Traditional Markowitz portfolio optimization constrains daily portfolio variance to a target value, optimising returns, Sharpe or variance within this constraint. However, this approach overlooks the relationship between variance at different time scales, typically described by $σ(Δt) \propto (Δt)^{H}$ where $H$ is the Hurst exponent, most of the time assumed to be $\frac{1}{2}$. This paper introduces a multifrequency optimization framework that allows investors to specify target portfolio variance across a range of frequencies, characterized by a target Hurst exponent $H_{target}$, or optimize the portfolio at multiple time scales. By incorporating this scaling behavior, we enable a more nuanced and comprehensive risk management strategy that aligns with investor preferences at various time scales. This approach effectively manages portfolio risk across multiple frequencies and adapts to different market conditions, providing a robust tool for dynamic asset allocation. This overcomes some of the traditional limitations of Markowitz, when it comes to dealing with crashes, regime changes, volatility clustering or multifractality in markets. We illustrate this concept with a toy example and discuss the practical implementation for assets with varying scaling behaviors.

q-fin.PM↗

arXiv2024

Endogenous Crashes as Phase Transitions

This paper explores the mechanisms behind extreme financial events, specifically market crashes, by employing the theoretical framework of phase transitions. We focus on endogenous crashes, driven by internal market dynamics, and model these events as first-order phase transitions critical, stochastic, and dynamic. Through a comparative analysis of early warning signals associated with each type of transition, we demonstrate that dynamic phase transitions (DPT) offer a more accurate representation of market crashes than critical (CPT) or stochastic phase transitions (SPT). Unlike existing models, such as the Log-Periodic Power Law (LPPL) model, which often suffers from overfitting and false positives, our approach grounded in DPT provides a more robust prediction framework. Empirical findings, based on an analysis of S&P 500 stocks from 2019 to 2024, reveal significant trends in volatility and anomalous dimensions before crashes, supporting the superiority of the DPT model. This work contributes to a deeper understanding of the predictive signals preceding market crashes and offers a novel perspective on their underlying dynamics.

q-fin.MF↗

arXiv2014

Strings and vortex rings

We treat string propagation and interaction in the presence of a background Neveu-Schwarz three-form field strength, suitable for describing vortex rings in a superfluid or low-viscosity normal fluid. A circular vortex ring exhibits instabilities which have been recognized for many years, but whose precise boundaries we determine for the first time analytically in the small core limit. Two circular vortices colliding head-on exhibit stronger instabilities which cause splitting into many small vortices at late times. We provide an approximate analytic treatment of these instabilities and show that the most unstable wavelength is parametrically larger than a dynamically generated length scale which in many hydrodynamic systems is close to the cutoff. We also summarize how the string construction we discuss can be derived from the Gross-Pitaevskii lagrangian, and also how it compares to the action for giant gravitons.

hep-th↗