# Advances In Quantitative Analysis Of Finance And Accounting Course

## Volume 6

## Chapter 1 – Collateral Constraints, Debt Management, and Investment Incentives

This chapter analyses the hedging decisions of an emerging economy which is exposed to market risks and whose debt contract is subject to collateral constraints. Within a sovereign debt model with default risk and endogenous collateral, the optimal choice of hedging instruments are studied when both futures and nonlinear derivatives are available. It is examined in which way the hedging policy is affected by the cost of default and the financial constraints of the economy and some implications are provided in terms of resource allocation.

### 1. Introduction

Emerging markets have been exposed to remarkable market risks and it is by now folk wisdom that, if given a choice, they should be endowed with instruments of hedging against downside risks (see Caballero, 2003; Caballero and Panageas, 2003; Shiller, 2003). Finding out which factors are the fundamental source of volatility for each country — for example, the prices of oil for Mexico, of coffee for Brazil, of semiconductors for Korea, of copper for Chile, and so on — is recognized as a crucial step in order to construct the appropriate hedging instruments, which will be contingent on observable variables (Caballero, 2003).

Yet, it remains to be answered the question concerning the proper application of derivative securities that can be used to construct hedging strategies and the optimal hedging policy. The purpose of this chapter is to examine the hedging decisions of an economy which is exposed to market risks and is subject to collateral constraints. The model considered here is a sovereign debt one, with default risk and endogenous collateral.

Collateral is typically used to secure loans. Since the article by Kiyotaki and Moore (1997), it has been pointed out that if collateral is endogenous, then the debt capacity of firms is altered, causing fluctuations in output (Krishnamurthy, 2003). In this chapter, a model is discussed where the use of hedging instruments may affect collateral values and thus, the debt capacity of the debtor.

In most literature relating to the 1980s debt crisis and following the Bulow and Rogoff models (1989, 1991), a given proportion of output or exports are assumed to be available for repayment of outstanding debt. This means that repayment is modeled as an output tax and actual repayment is the minimum of this amount and debt.

Alternatively, in other models (Eaton and Gersowitz, 1981; Eichengreen, 2003; Thomas, 2004) a fixed sanction is established in the case of default, which is not a direct claim on the country’s current resources and is not received by the creditors, but may represent the future losses due to diminished reputation.

In this chapter, a model is developed where the amount of repayment by the debtor country is determined endogenously by an optimizing choice of the debtor and where the two above mentioned aspects of the repayment contract are present.

Indeed, the debt contract is a collateralized one, where profits on internationally tradable goods can be used for repayment, constituting the endogenous collateral; additionally, in the case of default, a sanction is imposed which affects non-tradable goods, which represents the cost to the debtor of defaulting. Within this framework, hedging may be driven by the desirability to reduce expected default costs. As Smith and Stulz (1985) have shown, by hedging a debtor is able to reduce the likelihood of default by increasing the income it gets in the downside.

The present chapter is most related to the literature on risk management. Recently, a few articles have studied the optimal choice of hedging instruments of a firm when either futures or options are available. It has been shown that in the model of competitive firms with output price uncertainty, where all input decisions are made simultaneously prior to resolution of uncertainty, hedging with futures does provide a perfect hedge and there is no scope for nonlinear instruments such as options as pure hedging instruments.

Albuquerque (2003) characterizes optimal currency hedging in three cases, namely in the presence of bankruptcy costs, with a convex tax schedule, and in the case of a loss-averse manager. In all these cases, he shows that futures dominate options as hedging instruments against downside risk. Batterman et al. (2000) study the optimal choice of hedging instruments of an exporting firm exposed to exchange rate risk, when both currency futures and standard options are available. They show that the hedge effectiveness of futures is larger than that of options.

Wong (2003) studies the optimal hedging decision of an exporting firm which faces hedgeable exchange rate risk and non-hedgeable price risk, when price and exchange rate risk have a multiplicative nature. This source of non- linearity creates a hedging demand for nonlinear payoff currency options distinct from that for linear payoff currency futures. Moschini and Lapan (1992) analyze the problem of hedging price risk under production flexibility, yielding nonlinearity of profits in output price, and show that there is a role for options even when the use of futures is allowed.

In Froot et al. (1993) it is shown that firms may decide not to hedge fully, if there is correlation between investment opportunities and the availability of funds; moreover, options may be needed in addition to futures to implement the optimal hedge when there are state-dependent financing opportunities.

In this chapter optimal investment and hedging decisions are characterized. It is shown that the decision to use nonlinear hedging strategies in addition to futures contracts can be optimal in relation to market conditions and financial constraint of the economy. In particular, it is shown in which way the optimal hedging decision is affected by the cost of default.

In addition to a short position in futures, either concave or convex hedging with options is optimal, depending on the size of default costs. In particular, it is found that if default costs are sufficiently large, options are used for financing purposes, that is, to increase financial resources when these are needed for investment purposes.

If default costs are sufficiently low, options are employed for speculative motives, i.e., financial resources are reduced when they are needed for investment purposes. The present results are thus closely related to those of Adam (2002, 2004) who shows how firms employ nonlinear hedging strategies to match financial resources against financial needs at different time periods.

The remainder of the chapter is organized as follows. Section 2 describes the model and the hedging problem of the economy. Section 3 contains the optimal hedging choices of a futures and straddles. Section 4 concludes. All proofs are in the Appendix.

## Chapter 2 – A Concave Quadratic Programming Marketing Strategy Model with Product Life Cycles

As a more general approach, the authors formulate a concave quadratic programming model of the marketing strategy (QPMS) problem. Due to some built-in limitations of its corresponding linear programming version, the development of the QPMS model is necessary to further improve the research effort of evaluating the profit and sales impact of alternative marketing strategies.

It is the desire of the authors that this study will increase the utilization of programming models in marketing strategy decisions by removing artificially restrictive limitations necessary for linear programming solutions, which preclude the study of interaction effects of quantity and price in the objective function. The simulation analysis of the QPMS and its linear counterpart LPMS indicates that the solutions of the QPMS model are considerably more consistent with a priori expectations of theory and real world conditions.

### 1. Introduction

One of the marketing strategic decisions may involve the optimal allocation of sales force and advertising effort in such a way that a firm maximizes its profit or sales. Efforts designed to evaluate the profit and sales impact of alternative sales force and advertising effort are particularly useful in today’s highly competitive marketing environment. The purpose of this chapter is three-fold.

First, the conventional linear programming marketing strategy (LPMS) model is examined to identify several limitations in marketing strategy problems. Second, a quadratic programming model was formulated to extend and complement the LPMS model of the existing literature in marketing strategy.

Finally, results obtained from both models were compared and critical evaluations are made to highlight the difficulty embedded in the marketing strategy problem. A brief review of the well-known linear programming marketing strategy model is provided prior to describing the quadratic programming model of marketing strategy problem.

In the wake of growing globalization and bubbling electronic commerce, how to match products to market is of primary importance, especially in terms of gaining greater dominance in a market. For example, the Coca-Cola Company attempted to increase its market share from 42% to 50% of the US soft drink market by 2000. The mix of marketing strategies includes lower prices, expanding distribution capacity, and heavier promotional efforts in extolling the products (Frank, 1996).

Needless to say, positioning strategies are intended to deliver the value proposition of a product or group of products in the eyes and minds of the targeted buyers. The value requirements are exclusively derived from the buyers. It is said that the success of Dell Computer Corporation can be traced to Michael Dell’s strategic vision of high-performance, low-priced personal computers marketed directly to end-users (Kerwin and Peterson, 2001).

Another important marketing strategy is the development and management of product life cycle. In the stage of introduction and growth, the emphasis is on trial purchasers and price is typically higher. As the product moves into maturity-saturation stage, the focus is on repeat purchasers with lower prices as sales volume reaches its peak. Regardless of the reasons, be it a market niche or product life cycle, pricing of a product holds the key to the success of a business organization.