Thomas S. Y. Ho

Optimal dealer pricing under transactions and return uncertainty

Abstract The paper examines the optimal behavior of a single dealer who is faced with a stochastic demand to trade (modeled by a continuous time Poisson jump process) and facing return risk on his stock and on the rest of his portfolio (modeled by diffusion processes). Using stochastic dynamic programming, we derive the optimal bid and ask prices that maximize the dealers expected utility of terminal wealth as a function of the state in which he finds himself. The relationship of the bid and ask prices to inventory of the dealer, instantaneous variance of return, stochastic arrival of transactions and other variables is examined.

The Determinants of Bank Interest Margins: Theory and Empirical Evidence

This paper has developed a model of bank margins or spreads in which the bank is viewed as a risk-averse dealer. It was demonstrated that an interest spread or margin would always exist, and that this was the result of transactions uncertainty faced by the bank. Moreover, it was shown that this pure spread depended on four factors: the degree of managerial risk aversion; the size of transactions undertaken by the bank; bank market structure; and the variance of interest rates. The model implied that liability and asset structures had to be analyzed together since they were directly interrelated through transactions uncertainty. It was shown that because of this transactions uncertainty, hedging behavior was perfectly rational within an expected utility maximizing framework. Extending the model from a structure with one kind of loan and deposit to loans and deposits with many maturities should lead to further interesting insights into margin determination especially as “portfolio†effects may become apparent.

Bond indenture provisions and the risk of corporate debt

Abstract This paper examines the effect of alternative bond indenture provisions on the allocation of risk among the firms claimants. The approach taken here differs from that of earlier studies in that risk allocation is examined while the firms leverage (in market value terms) is held constant. In this context, four indenture provisions are examined: (1) the time to maturity, (2) the promised payment schedule, (3) financing restrictions and (4) priority rules. It is concluded that risk is transferred from stockholders to bondholders as the time to maturity and promised payment increase appropriately. Furthermore substitution of longer-term debt for an equal amount of shorter-term debt also increases the risk to bondholders while decreasing the risk to stockholders. The analysis shows that a coupon bond can be represented by a unique discount bond with the same risk and value. This permits the characterization of the effective maturity of a risky debt issue, a concept analogous to the stochastic duration of a default-free coupon bond. These results are shown to be independent of the means used to finance the debt issue. Finally, it is concluded that the relative risk associated with different bonds issued by the same firm cannot be determined by the structure of priority rules alone. It is also necessary to consider the timing of the promised payments compared to that of the other debt issues in the firms capital structure.

The Value of Corporate Debt with a Sinking-Fund Provision

A systematic investigation into the effects of sinking-fund provisions is important considering the preponderance of these provisions in corporate bond indentures. Approximately 80% of all publicly traded corporate issues contain a sinking-fund feature amortizing on average more than 50% of the principal amount of these issues. Thompson and Norgaard (1967) find these proportions to be stable over the 1960-67 period. McKeon (1980) reports 78.6% of all industrial bonds outstanding in 1979 contained a sinkingfund provision. Furthermore, sinking-fund provisions are a particularly common occurrence in mediumand low-grade issues but are less prevalent in high-grade issues. This relationship is most striking in utility issues. Thompson and Norgaard report that only 30% of Aa rated utilities issued in 1963 contained sinking-fund provisions whereas 100% of Baa rated new issues contained such a provision. A sinking-fund provision obligates the firm to amortize a portion of the debt prior to maturity. It gives the firm the option to satisfy this amortization requirement by either purchasing the bonds to be redeemed from the market or calling the bonds by means of a sinking-fund call. Thus, Most corporate debt issues contain a sinkingfund provision which provides for periodic retirement of a proportion of the issue prior to maturity. Retirement may be achieved either through a call at a specified price or through market purchases. This paper considers the value of a sinking-fund provision in the context of a contingent claims valuation model. It is concluded that the value of the sinking fund is determined by the risk of the underlying firm, the initial yield to maturity of the issue, and the sinking funds redemption rate. The value of sinking-fund debt is calculated over a range of parameter values, and the conditions under which the sinking-fund provision is valueless are determined.

Dynamic Financial System: Complexity, Fragility and Regulatory Principles

A financial system improves the allocation of real resources and enhances the performance of the production economy, but these benefits are offset in part by the risk of financial distress and the associated deadweight loss resulting from bankruptcy costs. We argue that “tiers” of financial claims increase complexity and fragility of the financial network. In equilibrium, the financial system grows relative to the real economy as the allocation of funds and risks becomes more sophisticated and as more financial claims are tiered. Growth is limited by the risk of a tiered, complex financial network and by the need to set aside additional capital as the financial sector grows. We discuss several sources of fragility in the financial system. We propose that regulators should limit the breaks in the system and do more to improve the resiliency of the network and less on individual issues that are only symptoms of fundamental problems of a network. We advocate a market based system of regulation in which market participants regulate each other, to a degree. In order for this to be feasible, the financial network must be organized according to three principles: trading transparency, competitive markets and competitive regulators, and incentive alignment of participants. Insofar as these regulatory approaches are successful in limiting network fragility, capital requirements can be reduced. Regulators should keep in mind this tradeoff between capital and regulation. With regard to regulatory policy, regulators should let the three principles be their guide in adapting to the evolving financial system rather than implementing narrowly conceived regulations that are quickly outmoded.

Regulatory Principles for the Financial System

Ho, Palacios, and Stoll consider the regulatory structure for derivatives and suggest several principles that an improved system should embody: transparency, competition, and incentive compatibility. The primary objectives of regulation should be maintaining the integrity of the financial network against systemic risks and protection of customers (with the former more in need of formal regulation than the latter). A general theme is that attempts to regulate the fine details of the financial system are not likely to be as effective as setting forth general principles that can be applied in a dynamically evolving environment. Competition is highlydesirable, among both financial institutions and regulators. Sharing responsibility across multiple regulators would promote innovation and reduce the chance of “regulatory capture” by the industry.

Allocate Capital and Measure Performances in a Financial Institution

This paper provides a model for allocating capital and measuring performances for financial institutions. The methodology relates the economic valuation of the balance sheet to the market value of the firm. In so doing, each business unit is evaluated on an economic basis, and the capital allocated to these units is related to the risk premiums that the market demands. The papers results have broad applications for corporate managers, risk managers, and other market participants in managing financial institutions to increase shareholders’ value.

Primitive Securities: Portfolio Building Blocks

A fixed-income instrument may be valued by treating its stream ofpromised cash flows os a package o f bullet payments, and pricing each one like a zero-coupon bond. Yet this provides only limited information about option feutures that are present in many bonds. ? l i s article describes a poweful new approach to understanding and valuing bonds as packages o f contingent cash flows that may depend on the interest rate path over time. There are 2” distinct paths through an n-period binomial interest rate tree, but the ,“bond space,” containing all possible distinct bonds of maturity up to n is o f larger dimension. We show how to form Q set of ‘

Catastrophe Theory in Banking and Finance

rimitive” bonds, o f which 2” have value and the remainder are valueless. These primitive bonds constitute a basis for the bond space and can be used to value, and replicate, any bond or bond portfolio. By examining the weight a bond places on each primitive, it is possible to see clearly how optionality afects bond value and what interest rate scenarios are most important to it. We show how the technique can be implemented as a tool f o r analyzing all types offixed-income: securities, and describe the use ofthe ‘)primitive projile,” i.e., the pattern o f weights on dijierent interest rate scenarios. TI show applications o f the primitive profile, we illustrate t,he efect o f the callfeature f o r a callable bond, and show how two CMO instruments dijier in their exposure to prepayrnent risk.

Term structure movements and pricing interest rate contingent claims

Publisher Summary This chapter discusses the applications of catastrophe theory in banking and finance. Catastrophe theory investigates the qualitative aspects of discontinuity in natural phenomena. Thoms classification theorem for stable universal unfoldings, the main result in catastrophe theory, provides a better understanding of causes and effects of catastrophic phenomena in many disciplines, including biology, physics, and engineering. The catastrophic phenomena discussed in the chapter have three properties. The first property is that of divergence whereby small, continuous changes in initial conditions (or parameters) can lead to large, discontinuous (catastrophic) changes in state variables. This type of behavior contrasts with traditional, Hamiltonian, dynamic systems in which small changes in initial conditions result in only small changes in the state variable. The second property is that of bifurcation (or asymmetries) in the behavior of a state variable x as certain parameters increase or decrease; bifurcation implies that there will be a discontinuous jump in x at some value of a control variable when it is increasing that is different from the behavior of x when the control variable is decreasing. As a result, x will be multivalued over a certain range of the control variable. The third property is that of stability—the catastrophe condition is robust to marginal changes in the structural relationships underlying the system.