discussion of an ideal conventional financial system also centers on the concept of general equilibrium in neoclassical economics, which can be regarded as an attempt to provide a rigorous analytical conceptualization of Adam Smith's vision of competitive economy. The theoretical work by Kenneth Arrow, Gérard Debreu and Frank Hahn, including Arrow (1951, 1953), Arrow and Debreu (1954), Debreu (1959), and Arrow and Hahn (1971) elaborates the economy–finance nexus for risk sharing in an ideal market economy. The Arrow-Debreu-Hahn competitive equilibrium is derived from the concept of general equilibrium, which was formally rendered by Léon Walras (1874, 1877) with a mathematical modeling of competitive markets for individual commodities. Assuming that consumers and producers participate simultaneously in these commodities markets as price-takers, the price of a commodity in one market contributes to price determination in other markets. The model assumptions imply the existence of a set of prices that allows demand to equal supply for all markets. This equilibrium can be efficient under the conditions that economic agents maximize the utility derived from the purchase of commodities.
It is possible to extend the analysis of market equilibrium as proposed by John Hicks (1939) to the trading of commodities for future delivery. The optimal allocation remains conditional upon the existence of markets for future delivery for all individual commodities and on the formation of price expectations by economic agents. The existence of a pricing kernel that equalizes demand and supply in different markets for future delivery depends, however, on the conditions of homogenous expectations, where all economic agents hold the same expectations about forward prices. This calls for the strong assumption of perfect foresight, which implies in turn that economic agents are endowed with information about each others' utility and production functions. As noted by Arrow (2013), the realization that resources allocation is driven by forward-looking expectations leaves an important role for uncertainty to play in modeling competitive equilibrium. Uncertainty affects the trade-offs and relative prices that ensure that demand and supply are equal across all markets. Apart from its impact on current markets, uncertainty can also explain the limited availability of futures markets for future delivery, which are characterized by possible changes in tastes, which influence consumption and changes in technology as factor of production.
The incorporation of uncertainty into the general equilibrium model puts into perspective the importance of markets for risk sharing and risk allocation. The neoclassical or Walrasian model, advanced by the work of Arrow, Debreu, and Hahn, provides a competitive paradigm based on the interaction between profit-maximizing firms and utility-maximizing consumers. The Arrow-Debreu economy is characterized by the existence of a complete set of competitive markets. The completeness of markets implies the possibility of trading securities that span all goods under all states of nature. The price system allocates risk among economic agents based on payoffs that are contingent on different states of world. The concept of complete markets applies only to an environment of uncertainty, and should not be confused with imperfect or frictionless markets, which apply invariably under certainty or uncertainty. The completeness of markets under uncertainty implies that there is a market for insurance against risk associated with every contingency.1 The complete set of markets does not assume or presume that markets are also perfect and frictionless.
The efficient allocation of risk can be achieved theoretically through two approaches, as noted by Allen and Gale (2009). First, it is possible to ensure efficient risk allocation through a complete set of markets for contingent commodities, which are defined by the date and state of nature in which they are delivered. The complete markets allow each consumer to trade the optimal amounts of state-contingent commodities at prevailing prices subject to individual budget constraints. This approach assumes the existence of markets for an unlimited number of contingent commodities for delivery at different dates under different states of nature. The second approach to efficient allocation relies on the existence of Arrow securities, which provide payoffs of one unit of real wealth conditional on the realization of a particular state of nature, and zero in all remaining mutually exclusive states. The existence of Arrow-Debreu securities for all states of nature provides insurance against all contingencies, which implies in turn the possibility of smoothing consumption under all states of nature.
The rigorous analysis by Arrow, Hahn, and Debreu presents a conception of the decentralized competitive economy that Adam Smith envisioned based on the natural liberty to pursue individual interests. The morality and justice system is integral to Adam Smith's thinking, as it renders private actions interdependent. In his reflections on the limits of organization, Arrow (1974) himself acknowledges the importance of institutional structure to promote exchange, which is essential to the optimal allocation of risks and resources. It is argued that given the inevitable tension between the society and the individual due to competing claims, there remains a crucial role for interpersonal relations in the organization of society to (a) regulate the competition for resources and (b) achieve specialization of function. Arrow further argued that trust serves as an “important lubricant of a social system,” (1974, 23) but as with other similar values such as truthfulness and loyalty, trade of such a commodity on open markets is neither technically possible nor meaningful. More generally, Arrow (1975, 15) considers the significant role of virtues, including truth, trust, loyalty, and justice, in the operation of the economic system. Several values may be deemed indeed as the requisite or facilitator of the process of exchange. Thus, it may be further argued that these conditions also constitute the basis for complete contract. If both parties trust each other completely, it is possible to enter into a simple contract stipulating that parties “renegotiate” the terms and conditions of the contract should unforeseen contingencies arise.2 Even in the absence of a “complete contract” that stipulates all states of nature a priori, it is the institution of trust and similar virtues that has the potential of preserving the crucial property of state-contingent claims ex post basis.
The Pareto optimality conditions achieved under an Arrow-Hahn-Debreu economy with complete markets, under which every individual feels better according to one's own values, have two fundamental implications. First, the possibility arises for the resolution of uncertainty. It can be shown that uncertainty does not affect the equilibrium pricing of risky assets under certain conditions consistent with Arrow-Debreu economy. Following Ross (1987), these conditions are also consistent with the no-arbitrage arguments that underlie the Modigliani-Miller theorems about the irrelevance of the debt–equity ratio and dividend policy for the firm valuation. Second, given the absence of equilibrium under incomplete markets, it is also possible to improve Pareto optimality through the inception of markets for the trading of new financial securities. The development of markets for derivatives securities, which represent state-contingent claims, can thus be regarded as an attempt to gradually approach and converge toward the completeness of markets.
The theoretical advances in the analysis of general equilibrium by Arrow, Debreu, and Hahn provided the central argument that optimal risk allocation can be achieved through risk sharing. The subsequent development of finance theory provided useful insights into various areas of finance, including investment and financing decisions, portfolio risk diversification, equilibrium asset pricing, and derivatives pricing. But finance theory developed in the footsteps of the general equilibrium analysis relies also, to a large extent, on the assumption of the existence of a risk-free asset, which is arguably not included in the Arrow-Debreu model. The cornerstones of conventional finance are represented by modern portfolio theory by Markowitz (1952 and 1959), the Modigliani-Miller irrelevance theorems about the firm's capital structure, by Modigliani and Miller (1958a and 1958b), the capital asset pricing model by Sharpe (1964), Lintner (1965), and Mossin (1966), efficient markets hypothesis by Fama (1970), option pricing theory by Black and Scholes (1973), and arbitrage pricing theory by Ross (1976), among other theoretical propositions.
The Divide between an Ideal Image and the Reality
The optimal mechanism for risk allocation suggested by the Arrow-Hahn-Debreu model of general equilibrium is based on the concept of risk sharing, where predetermined interest rates are not explicitly included in the analysis. The existence of a risk-free asset in the competing theories of asset pricing results in an
The concepts of uncertainty and risk are used interchangeably in some parts of this chapter, but the important distinction is discussed in Chapter 3 about the analytics of finance.
It is noted that from the perspective of Islamic finance, which is discussed in following sections, there is also a clear command (
