Paper: arXiv 2310.13511

Authors: Donggyu Kim, Minseog Oh

Abstract

This paper introduces a dynamic minimum variance portfolio (MVP) model using nonlinear volatility dynamic models, based on high-frequency financial data. Specifically, we impose an autoregressive dynamic structure on MVP processes, which helps capture the MVP dynamics directly. To evaluate the dynamic MVP model, we estimate the inverse volatility matrix using the constrained $\ell_1$-minimization for inverse matrix estimation (CLIME) and calculate daily realized non-normalized MVP weights. Based on the realized non-normalized MVP weight estimator, we propose the dynamic MVP model, which we call the dynamic realized minimum variance portfolio (DR-MVP) model. To estimate a large number of parameters, we employ the least absolute shrinkage and selection operator (LASSO) and predict the future MVP and establish its asymptotic properties. Using high-frequency trading data, we apply the proposed method to MVP prediction.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.0/10 (capped from 7.5: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically sophisticated approach combining high-frequency matrix estimation (CLIME), LASSO regularization, and asymptotic statistical proofs. Its empirical application to dynamic minimum variance portfolio optimization using high-frequency data provides strong practical relevance.

Research Flowchart

  flowchart TD
    A[Goal: Dynamic Minimum Variance Portfolio Prediction] --> B[Data: High-Frequency Financial Data]
    B --> C[Estimate Volatility & Weights via CLIME]
    C --> D[Formulate Dynamic Realized MVP Model]
    D --> E[Parameter Estimation & Selection via LASSO]
    E --> F[Outcomes: Out-of-Sample MVP Weight Prediction]