Portfolio Value-at-Risk Optimization for Asymmetrically Distributed Asset Returns

Joel  Goh; Kian Guan  Lim; Melvyn  Sim; Weina  Zhang

Article | European Journal of Operational Research

Portfolio Value-at-Risk Optimization for Asymmetrically Distributed Asset Returns

by Joel Goh, Kian Guan Lim, Melvyn Sim and Weina Zhang

Abstract

We propose a new approach to portfolio optimization by separating asset return distributions into positive and negative half-spaces. The approach minimizes a newly-defined Partitioned Value-at-Risk (PVaR) risk measure by using half-space statistical information. Using simulated data, the PVaR approach always generates better risk-return tradeoffs in the optimal portfolios when compared to traditional Markowitz mean–variance approach. When using real financial data, our approach also outperforms the Markowitz approach in the risk-return tradeoff. Given that the PVaR measure is also a robust risk measure, our new approach can be very useful for optimal portfolio allocations when asset return distributions are asymmetrical.

Keywords: robust optimization; portfolio management; value-at-risk; Mathematical Methods; Finance;

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Goh, Joel, Kian Guan Lim, Melvyn Sim, and Weina Zhang. "Portfolio Value-at-Risk Optimization for Asymmetrically Distributed Asset Returns." European Journal of Operational Research 221, no. 2 (September 1, 2012): 397–406.

Recent Medicare legislation seeks to improve patient care quality by financially penalizing providers for hospital-acquired infections (HAIs). However, Medicare cannot directly monitor HAI rates and instead relies on providers accurately self-reporting HAIs in claims to correctly assess penalties. Consequently, the incentives for providers to improve service quality may disappear if providers upcode, i.e., misreport HAIs (possibly unintentionally) in a manner that increases reimbursement or avoids financial penalties. Identifying upcoding in claims data is challenging due to unobservable confounders (e.g., patient risk). We leverage state-level variations in adverse event reporting regulations and instrumental variables to discover contradictions in HAI and present-on-admission (POA) infection reporting rates that are strongly suggestive of upcoding. We conservatively estimate that 10,000 out of 60,000 annual reimbursed claims for POA infections (18.5%) were upcoded HAIs, costing Medicare $200 million. Our findings suggest that self-reported quality metrics are unreliable and thus, recent legislation may result in unintended consequences.

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Article | Operations Research | May–June 2018

Data Uncertainty in Markov Chains: Application to Cost-Effectiveness Analyses of Medical Innovations

Joel Goh, Mohsen Bayati, Stefanos A. Zenios, Sundeep Singh and David Moore

Cost-effectiveness studies of medical innovations often suffer from data inadequacy. When Markov chains are used as a modeling framework for such studies, this data inadequacy can manifest itself as imprecision in the elements of the transition matrix. In this paper, we study how to compute maximal and minimal values for the discounted value of the chain (with respect to a vector of state-wise costs or rewards) as these uncertain transition parameters jointly vary within a given uncertainty set. We show that these problems are computationally tractable if the uncertainty set has a row-wise structure. Conversely, we prove that the row-wise structure is necessary for tractability. Without it, the problems become computationally intractable (strongly NP-hard). We apply our model to assess the cost effectiveness of fecal immunochemical testing (FIT), a new screening method for colorectal cancer. Our results show that despite the large uncertainty in FIT's performance, it could be cost-effective relative to the prevailing screening method of colonoscopy.

Keywords: Markov Chains; cost effectiveness; medical innovations; Colorectal Cancer; Health Care and Treatment; Cost vs Benefits; Innovation and Invention; Mathematical Methods; Health Industry;

Citation:

Goh, Joel, Mohsen Bayati, Stefanos A. Zenios, Sundeep Singh, and David Moore. "Data Uncertainty in Markov Chains: Application to Cost-Effectiveness Analyses of Medical Innovations." Operations Research 66, no. 3 (May–June 2018): 697–715. (Winner, 2014 INFORMS Health Applications Society Pierskalla Award & Finalist, 2014 INFORMS George E. Nicholson student paper competition.) View Details

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Portfolio Value-at-Risk Optimization for Asymmetrically Distributed Asset Returns

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