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Risks of Large Portfolios.

Jianqing Fan1, Yuan Liao2, Xiaofeng Shi3

  • 1Department of Operations Research and Financial Engineering, Princeton University ; Bendheim Center for Finance, Princeton University.

Journal of Econometrics
|July 22, 2015
PubMed
Summary

This study introduces a high-confidence level upper bound (H-CLUB) for estimating portfolio risk using factor-based models. H-CLUB offers a more insightful and accurate risk assessment, especially in high-dimensional settings.

Keywords:
High dimensionalityfactor modelsprincipal componentssparse matrixvolatility

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Area of Science:

  • Quantitative Finance
  • Financial Risk Management
  • Econometrics

Background:

  • Estimating the risk of large investment portfolios relies on accurate volatility matrix estimation.
  • The precision of these risk estimators, particularly in high-dimensional scenarios, remains a significant challenge.
  • Factor-based risk models are increasingly used, but their estimation accuracy needs rigorous assessment.

Purpose of the Study:

  • To develop and assess a novel high-confidence level upper bound (H-CLUB) for factor-based risk estimators.
  • To analyze the asymptotic properties of risk estimators in high-dimensional settings.
  • To compare the performance of H-CLUB against traditional risk estimation bounds.

Main Methods:

  • Derivation of the limiting distribution for estimated risks in high dimensionality.
  • Construction of H-CLUB using confidence intervals for risk estimators with known and unknown factors.
  • Monte Carlo simulations to evaluate H-CLUB performance and quantify estimation errors.

Main Results:

  • Factor-based risk estimators exhibit the same asymptotic variance in high dimensions, regardless of factor knowledge.
  • This variance is marginally smaller than that of sample covariance-based estimators.
  • H-CLUB demonstrates superior performance over traditional bounds, offering enhanced risk assessment insights.

Conclusions:

  • H-CLUB provides a robust method for assessing the accuracy of factor-based risk estimations.
  • The relative error in risk estimation is minimal with typical 3-month daily data.
  • The study confirms the utility of factor models and H-CLUB for managing risk in large portfolios.