Portfolio Risks under Estimation Uncertainty and Price Movement

25 Pages Posted: 7 Apr 2021 Last revised: 12 Jul 2021

See all articles by Anish Shah

Anish Shah

Investment Grade Modeling; Brown University - Division of Applied Mathematics

Date Written: September 9, 2020


Risk decomposition is a standard tool for analyzing investment portfolio risk. The portfolio is divided into notional parts—e.g., individual securities, holdings by sector or region, factor exposures—whose contributions to net risk are estimated and reported. Convention regards the inputs—portfolio weights and covariance—as fixed and known, but portfolio composition changes with price movement and estimates have errors. Since behavior only in the direction of net risk is counted, hedged effects are invisible regardless of size. What if numbers aren’t exact? Hedge instability manifests in proportion to underlying gross (not net) exposure, akin to leverage. For example, in a market-neutral portfolio, market is the largest risk in each side, conventionally uncounted since hedged, and extremely consequential under small deviations. To solve the problem, this paper models weights and parameters as uncertain. Evaluating a portfolio across the range of possibility measures risks better and surfaces latent fragility. No longer point-estimated, contributions are reported with a center and spread.

Keywords: Covariance, Estimation Error, Multi-factor Models, Risk Contributions, Risk Decomposition, Uncertainty

JEL Classification: G11, C00

Suggested Citation

Shah, Anish, Portfolio Risks under Estimation Uncertainty and Price Movement (September 9, 2020). Available at SSRN: https://ssrn.com/abstract=3774239 or http://dx.doi.org/10.2139/ssrn.3774239

Anish Shah (Contact Author)

Investment Grade Modeling ( email )

Cambridge, MA 02139
United States

HOME PAGE: http://www.linkedin.com/in/anishrshah

Brown University - Division of Applied Mathematics

182 George St
Providence, RI 02912
United States

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