Integrated Risk Management for Newsvendors with VaR Constraints

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Author Information : Panos Kouvelis (Olin Business School, Washington University)
Rong Li (Whitman School of Management, Syracuse University)

Year of Publication : Manufacturing and Service Operations Management (2018)

Summary of Findings : We examine how the choice of different risk-management frameworks (Expected Utility, Mean-Variance, and Mean-VaR) affects the optimal operational hedge (inventory) and financial hedge (derivatives), and find that Mean-VaR (Mean profit maximization under a VaR constraint) is the only framework that allows the separation of inventory management from (operating) profit risk management (inventory is used to maximize mean profit, while financial hedge is used to control profit risk).

Research Questions : 1. How should managers and senior management interpret the VaR constraint when applied to a single-period operating profit? How does it affect the inventory decision?

2. Does VaR constraint always imply risk aversion? If not, how does it imply different risk attitudes through the inventory decision?

3. What are the jointly optimal operational (inventory) and financial hedging decisions, i.e., the optimal integrated risk management (IRM) solution, under Mean-VaR framework? How do these different types of hedging decisions interact?

4. Does the choice of different risk-management frameworks (Expected Utility, Mean-Variance, and Mean-VaR) affect the optimal operational hedge (inventory) and financial hedge (derivatives)? Why?

What we know : Profit risk management is essential to every business. Its methodology has evolved from the silo approach to the integrated approach (IRM). The existing risk-management frameworks, initially designed for the silo approach, are now used to analyze different types of risk simultaneously. We thus lack understanding of how these risk-management frameworks reflect multiple types of risk (operational and financial) and, more importantly, affect the operational and financial hedging decisions (cross-function decisions). In this paper, we offer an in-depth understanding of different risk-management frameworks and demonstrate the benefits of the Mean-VaR framework in a single-period decision-making context (newsvendor setting). We offer insights on how the use of this framework guides jointly optimal inventory and financial hedging decisions, and how these decisions differ in nature from more traditional frameworks, such as optimizing Expected Utility (EU) or Mean-Variance (MV).

Novel Findings : To the best of our knowledge, we are the first to study IRM in a single-period setting using the Mean-VaR framework. In practice, senior management often pre-set the VaR parameters, the profit target (V) and the confidence level of achieving that target (a). Managers, in turn, decide the inventory and financial hedging. Our results provide important guidance to senior management on the implications of different (V, a)-choices. Some choices result in inventory decisions exhibiting risk aversion (and risk neutrality), while others result in inventory decisions exhibiting risk seeking. We demonstrate that without financial hedging, under the risk-averse (V, a)-choices, the decision-maker has to sacrifice the mean profit for risk control by stocking below the risk-neutral inventory level. When financial hedging is available, however, the decision-maker does not need to rely on inventory decisions to control profit risk, and thus can focus them on profit maximization. Financial hedges alone can control profit risk, even when demand only partially correlates with the price of the financial asset used.

Our results also offer insights on how different risk management frameworks (Mean-VaR, EU, and MV) have a different effect on inventory management and risk management. We show that the Mean-VaR framework is the only one that, in the absence of financial hedging, calls for inventory increases (rather than inventory reduction) to help control the profit risk for some (V, a) parameters. We also show that only in the Mean-VaR framework, financial hedging is always effective (i.e., it completely controls profit risk by satisfying the VaR constraint) even in the presence of demand risks that cannot be hedged, and thus inventory is no longer needed to help control profit risk. Finally, we show that only in the Mean-VaR framework, inventory management is focused on profit maximization and is separable from risk management. Note that the finance literature on risk management also emphasizes the need for cross-functional coordination because of the correlation between operational and financial risks. Such a separation between inventory management and risk management resulting from the use of the Mean-VaR framework may reduce the need for cross-functional coordination, and thus provide convenience for IRM implementation. As a detailed implementation guideline, we provided the meaning of choice of the VaR parameters (V, a) and, more importantly, its impact on the decisions, implied risk attitude, and the firm's profit. As public companies are required to disclose their market risk via VaR, our findings may offer their managers effective ways to deal with profit risk management.

Novel Methodology : This research paper performed an analysis of the optimal integrated risk management (IRM) solution using the Mean-VaR framework and provided a comparison of how the choice of different risk-management frameworks affects the optimal IRM solution.

Implications for Practice : The findings suggest that risk-management practitioners should use the Mean-VaR framework for easy-to-implement IRM solutions which don’t require cross-functional coordination, and provides detailed guidelines of how to set parameters for this framework.

Implications for Policy: As public companies are required to disclose their market risk via VaR, our findings of the benefits of using Mean-VaR framework may give companies more incentive to comply with the policy and help the policy makers design more useful guidelines for risk management.

Implications on Research: This work lays the foundation for research on IRM, providing needed knowledge of the existing risk-management frameworks (which framework is appropriate to use in what situations).

Full Citations : Kouvelis P., R. Li. 2018. Integrated Risk Management for Newsvendors with VaR Constraints. Forthcoming at Manufacturing and Service Operations Management.

Abstract : We study a newsvendor problem with profit risk control using Value-at-Risk (VaR) constraints. When a firm's demand correlates with the price of a tradable financial asset, both financial tools (derivatives) and operational tools (inventory) can be used for profit risk management. Such integrated risk management (IRM) approaches have been studied using various optimization frameworks to reflect the risk aversion of decision-makers. To the best of our knowledge, we are the first to study IRM in a newsvendor setting using profit maximization under VaR constraints. The VaR constraints allow for flexibility in the choice of profit target, V, and confidence level of achieving it, a. It is important to understand the implications of different (V, a) choices: some choices result in inventory decisions exhibiting risk aversion (and risk neutrality), while others result in inventory decisions exhibiting risk seeking. We demonstrate that without financial hedging, under the risk-averse (V, a) choices, the decision-maker has to sacrifice mean profit for risk control by stocking below the profit-maximizing (or the risk-neutral) inventory level. When financial hedging is available, however, the decision-maker can use it alone to control the profit risk, even when demand only partially correlates with the price of the financial asset used. Thus, inventory is solely used for profit maximization, and financial hedging is solely used for profit control. Such a separation of inventory and financial hedging decisions simplifies the IRM implementation. This, however, is not the case under the Mean-Variance or Expected Utility frameworks. In these risk-averse frameworks, both inventory and financial hedging must combine to control risk control and thus these two types of decisions are often highly interdependent. VaR constraints, often preferred by regulators, may be helpful in implementing IRM in many regulated industrial settings.

Rong Li

Rong Li

Assistant Professor of Supply Chain Management at Martin J. Whitman School of Management
Rong Li is an assistant professor of supply chain management whose research interests include operations and finance interfaces, supply chain coordination and contracting, inventory management and maintenance with learning from real-time information. Dr. Li received a B.S. in mathematics from Nankai University, and M.S. and Ph.D. in industrial engineering from Purdue University.
Rong Li
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