How to hedge if the payment date is uncertain?

• Author: Olaf Korn,Alexander Merz
• Date: 01 April 2019
• DOI: http://doi.org/10.1002/fut.21987
• Published date: 01 April 2019

Received: 10 February 2017

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Revised: 26 November 2018

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Accepted: 30 November 2018

DOI: 10.1002/fut.21987

RESEARCH ARTICLE

How to hedge if the payment date is uncertain?

Olaf Korn

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Alexander Merz

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1

Faculty of Business and Economics,

University of Goettingen, Goettingen,

Germany

2

Centre for Financial Research Cologne

(CFR), Cologne, Germany

Correspondence

Olaf Korn, University of Goettingen,

Goettingen D-37073, Germany.

Email: okorn@uni-goettingen.de

Funding information

Deutsche Forschungsgemeinschaft,

Grant/Award Number: KO 2285/1

Abstract

This paper investigates how firms should hedge price risk when payment dates

are uncertain. We derive variance‐minimizing strategies and show that the

instrument choice is essential for this problem, similar to the choice between a

strip and a stack hedge. The first setting concentrates on futures hedges,

whereas the second allows for nonlinear derivatives. In both settings, firms

should take positions in derivatives with different maturities simultaneously.

We present an empirical analysis for commodities and exchange rates, showing

that in both settings the optimal strategy clearly outperforms the commonly

used heuristic strategies which consider only one hedging instrument at a time.

KEYWORDS

exotic derivatives, futures, hedging, uncertain payment dates

JEL CLASSIFICATION

G32, D81

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INTRODUCTION

Derivatives markets offer hedging opportunities for a variety of different risks, such as commodity price risk, interest

rate risk, or foreign exchange risk. The design of a firm’s hedging strategy, however, is often complicated by another

source of risk: the uncertainty about the timing of cash flows to be hedged. This kind of uncertainty arises, for example,

if a firm produces for stock but does not know exactly when its products will be sold, technological problems or weather

conditions lead to uncertain production times, a claim of recourse in foreign currency is decided in a lawsuit that may

take more or less time, or ongoing negotiations about an order make it uncertain when raw materials will be required

by a producing firm.

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In this paper, we study the corresponding problem of hedging price risk when the payment date is uncertain and

show that this hedging problem raises interesting issues about the instrument choice.

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In particular, we investigate two

research questions. (a) When the payment date is uncertain and the hedging period exceeds the remaining time to

maturity of the nearby derivatives contract, should hedging strategies use a mix of different derivative contracts with

different maturities or is it sufficient to use one maturity at a time? This question is akin to the common problem of

hedgers to choose between using a strip hedge or stack hedge, where the stack hedge is frequently preferred because of

the illiquidity in the back months contracts.

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(b) Is hedging with linear contracts such as forwards or futures sufficient

J Futures Markets. 2019;39:481–498. wileyonlinelibrary.com/journal/fut © 2019 Wiley Periodicals, Inc.

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A concrete example of uncertainty about the timing of cash flows to be hedged are the firm‐flexible contracts sold by Metallgesellschaft’s American subsidiary, MG Corp (Mello & Parsons, 1995;

Pirrong, 1997). Under firm‐flexible contracts, buyers were allowed to defer or accelerate purchases, but had to buy all quantities deferred by the end of the contract. This feature was one of the issues

MG Corp’s hedging strategy had to face, which finally ended in a disaster for the firm.

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The timing option provided to the holder of a short position in futures contracts (Boyle, 1989) is a means to deal with such uncertain payment dates. However, a timing option can usually be exercised

only during the maturity month. If uncertainty regarding the timing of cash flows refers to longer periods, the problem remains that it is unclear which maturities to choose.

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As an example, consider the MG case again. The illiquidity in the back months of crude oil futures was an important aspect in MG Corp’s decision to use a stack hedge. Although our model does not

consider any differences in liquidity between short‐term and long‐term futures, we briefly discuss a corresponding model extension and its implications in Section 2.1.

when the payment date is uncertain or should firms use options, possibly even exotic ones? These research questions

are studied both theoretically and empirically.

First, we analyze the variance‐minimizing hedging strategies in two settings. The first setting considers hedging with

futures contracts only and the second one allows for exotic options written on futures, leading to tailor‐made payoff

functions. Our main result for the first setting is that under perfectly liquid futures markets firms should

simultaneously hold futures contracts of different maturities if the last potential payment date exceeds the remaining

maturity of the shortest‐maturity derivative contract. Over time the hedge is adjusted to account for new information

about the payment date. Simultaneous coverage of different maturities is also required in the second setting. Nonlinear

derivatives written on the prices of multiple futures are optimal if uncertainty about the payment date and price risk are

correlated, since such correlation leads to profits being nonlinearly related to price. If the two sources of risk are

independent, linear contracts are optimal.

Next, we offer empirical support for our analytical results by comparing the performance of different hedging

strategies in the presence of uncertain payment dates. The empirical study is based on the prices of oil, copper, and gold

as well as the US dollar (USD) to euro exchange rate. It compares the optimal strategy in each setting with various

alternatives, including heuristic strategies that hold only positions in a single futures contract at a time. Our empirical

results show that the optimal hedging strategy clearly outperforms such heuristic alternatives often used in practice. For

short hedge horizons and a weak dependence between price and payment date, linear hedging instruments are

sufficient. If price and payment date are strongly dependent, however, nonlinear derivatives lead to a significant

improvement in terms of risk reduction.

Our paper contributes to the vast body of literature on corporate hedging decisions. This literature includes very

general dynamic models (e.g., Bolton, Chen, & Wang, 2011; Rampini, Sufi, & Viswanathan, 2014) of the investment,

financing, and risk management policies of financially constrained firms. We focus on one specific aspect: a firm’s

hedging policy with derivatives. Moreover, we abstract from liquidity constraints that might restrict the firm’s usage of

derivatives (see also Adam‐Müller & Panaretou, 2009; Lien, 2003). However, our model is more general than the models

by Bolton et al. (2011) and Rampini et al. (2014) with respect to two aspects that are essential for our research questions.

First, our model treats the payment date of the firm’s cash flows from operations as a stochastic state variable. Second,

our model allows for the use of derivative contracts with different maturity dates, that is, it is less restrictive with

respect to the instrument choice.

The issue of uncertain payment dates is closely related to two other problems that have been studied in the literature

on corporate hedging, namely, basis risk and quantity risk. Basis risk may occur for different reasons.

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For example, the

grade of a commodity may differ from the grade a futures contract relates to or a futures contract with the desired

maturity date may just not be available. The latter problem was termed an “imperfect time hedge”in the literature

(Batlin, 1983; Karp, 1988). The imperfect time hedge is similar to our hedging problem in the sense that an unknown

(stochastic) payment date of the cash flows to be hedged introduces a potential mismatch between the payment date

and the maturity dates of hedging instruments, that is, leads to basis risk. However, the reasons why basis risk occurs

are different. In the imperfect time hedging problem the payment date is known but no derivative contract is available

that matures at that date. In our problem, the payment date is unknown (stochastic) but multiple derivatives contracts

exist whose maturity dates cover all potential payment dates. These differences in setting have important consequences:

The hedging problem we study mandates an analysis of multiple periods and it turns out that the optimal strategy uses

multiple hedging instruments with different maturity dates simultaneously. This is not the case for the imperfect time

hedging problem, as studied by Batlin (1983) and Karp (1988).

Another way of looking at our hedging problem is that, at any potential payment date, a promised cash flow may or

may not occur, which means that the quantity to be hedged is either that promised or zero. Thus, we have to deal with a

certain kind of quantity risk. Such quantity risk could result either from demand uncertainty (Leland, 1972) or

production risk.

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What is specific about the hedging problem when payment dates are uncertain, however, is again the

specific dynamic setting. In this setting a variance‐minimizing hedging strategy requires to hold derivatives with

different maturities simultaneously, an issue of the instrument choice that has not been investigated in the literature on

basis risk or quantity risk so far. For this reason, our analysis extends this strand of literature.

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The effects of basis risk on hedging strategies with futures have been analyzed by, for example, Rolfo (1980), Anderson and Danthine (1980, 1981), Benninga, Eldor, and Zilcha (1984), Briys,

Crouhy, and Schlesinger (1993), and Adam‐Müller and Nolte (2011).

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Hedging problems with futures contracts under both price risk and quantity risk have been analyzed by, for example, Benninga, Eldor, and Zilcha (1985), Eaker and Grant (1985), Kerkvliet and

Moffett (1991), Lapan and Moschini (1994), Chowdhry (1995), Adam‐Müller (1997), and Brown and Toft (2002).

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KORN AND MERZ