همکاری سیاست های عملیاتی با ممانعت مالی برای ریسک گریزی شرکت ها  Coordinating operational policy with financial hedging for risk-averse firms

1. Introduction When making procurement, inventory, and production decisions, firms are usually exposed to uncertainties such as volatile commodity price, fluctuating foreign exchange rates, as well as uncertain customer demands. Such risk exposures are undesirable for risk-averse firms, but they could be controlled by financial hedging, typically using available hedging instruments like commodity futures, options, and currency swaps from the financial market. As reported by a recent empirical study (Bartran et al. 2009) on 7,319 nonfinancial firms across 50 countries, over half (60.3%) of the surveyed firms have implemented some form of hedging using financial derivatives. These hedging activities are found to have some significant implications on the operational decisions made in firms’ daily operations (see, e.g., Ding et al. 2007, Chod et al. 2010). In particular, financial hedging can reduce at least part of the risk exposure faced by a risk-averse firm. Such reductions in risk exposure, according to Eeckhoudt et al. (1995), will then lead to an increase or decrease in the optimal purchasing quantity of the firm. As a result, there is a need to investigate how to make the optimal operational decisions that are consistent with a risk-averse firm’s financial hedging activities. Our interest in studying the aforementioned hedging-consistent operational decisions was motivated by the increasing availability and widely use of financial hedging instruments nowadays. Nevertheless, how to quantify the economic implications of financial hedging on operational decisions remains a challenging problem despite the growing academic and research effort. To simplify the analysis, some researchers have resorted to the complete market assumption; that is, assuming that the risk exposure involved in the firm’s operations can be fully replicated by a “perfect” financial hedging portfolio in the market (Van Mieghem 2003). Given the existence of the replicating portfolio, the well-known risk-neutral valuation method in the finance literature can then be transplanted to “value” the operational decisions (Birge 2000). Consequently, the hedging-consistent operational decisions can be made via maximizing the expected value of the profit with the risk-neutral probability measure (Goel and Gutierrez 2011). Thus, this approach is referred to as the EV-based approach (expected-value-based approach) in this paper. The EV-based approach is appealing because it can help substantially reduce the number of decision variables when financial hedging is involved – the decision variables regarding the hedging positions are entirely eliminated from the Bellman equation. However, there is a major obstacle when applying this approach in practice – the complete market assumption may not be entirely justified. As Birge (2000, pp. 22-23) writes, “an investor might only be able to remove part of the market risk and then have some uncontrollable portion that still remain. This remainder would cause a limit to the extent that a market can value our decision.” To appropriately account for the “remainder risk”, the complete market assumption must be relaxed. By relaxing the complete market assumption, we develop a CE-based approach (the certainty-equivalent-based approach) for risk-averse firms to make the hedging-consistent operational decisions in dynamic settings. The CE-based approach is a novel extension of the EV-based approach because it allows for the existence of nonfinancial random factors in addition to financial random factors. For nonfinancial firms, the distinction between the financial random factors and nonfinancial random factors is the key to differentiate the financial risk that can be hedged using derivatives from the remainder risk that cannot. On the one hand, financial random factors refer to the risk factors associated with the price processes of some financial securities/indices, such as the fluctuating commodity price and volatile currency rates. On the other hand, nonfinancial random factors represent the idiosyncratic disturbances (e.g., uncertain customer demand, random production yield) that are unrelated to the financial market. Both types of random factors can disturb a firm’s operating profit in significant ways. For example, the operating profit of a multinational firm is exposed to both the volatile currency rates and uncertain global demand. The currency risk can usually be hedged using currency derivatives (Ding et al. 2007), so it should be recognized as a financial random factor. In contrast, the demand uncertainty is the remainder risk that cannot be hedged in the financial market, and thus should be treated as a nonfinancial random factor. When the nonfinancial random factor exists, the complete market assumption cannot apply, and the EV-based approach is no longer optimal. In this situation, the proposed CE-based approach can still be applied to simplify the procedure of making hedging-consistent operational decisions. The advantage is that the CE-based approach helps reduce the number of decision variables as the EV-based approach does. Moreover, we also investigate some structural properties of the CE-based value function, which allows us to prove that the commonly desired base-stock policy is optimal under a set of sufficient conditions. In addition, we present some straightforward numerical results to show that the CE-based approach dominates the EV-based approach in most of the cases.