More than a decade has passed since the publication of the first edition of this book. We are pleased by the reaction the book has received. Although it has not displaced John Grisham on booksellers' shelves, it has been adopted as a text in some leading economics departments, both in the US and abroad. We are also pleased that it is being used in finance classes in business schools.

As anyone who has spent the last decade on this planet knows, financial markets have in the past several years undergone the most severe convulsions since the Great Depression. Almost none of the major events that have occurred in financial markets – the boom and bust of subprime mortgage lending, the spread of the financial crisis from the US to the rest of the world, the transition from a liquidation in financial markets to a severe recession in the world economy – can be treated as a direct application of the ideas presented in this book. But it was never our intention to present all the theoretical tools used in applied work in finance – rather, the goal was to provide a highly stylized version of only the most basic ideas. As observed in the preface to the first edition of this book, this lack of direct descriptive realism does not mean that this material is useless.

Introduction

The fact that equilibrium exists in infinite-time security markets only when portfolio constraints are imposed implies that the concept of arbitrage in infinite-time security markets must reflect the presence of constraints on portfolio holdings. We follow the idea of Chapter 6 where we defined arbitrage under short-sales constraints in two-date security markets. As in the multidate model, event prices can be used to define the present value of future dividends of each security. We show that the absence of arbitrage under debt constraints implies the existence of strictly positive event prices.

A price bubble is the difference between the price of a security and the present value of dividends under some system of strictly positive event prices. We study the possibility of the existence of price bubbles in equilibrium in infinite-time security markets under debt constraints.

Arbitrage under Debt Constraints

The definition of an arbitrage under debt constraints is similar to the definition of an arbitrage under short-sales constraints in two-date security markets in Chapter 6. An arbitrage under debt constraints is a portfolio strategy (1) with positive payoff at every date (other than date 0, at which payoffs are not defined); (2) with negative date-0 price, with either the payoff being strictly positive in some event or the date-0 price being strictly negative; and (3) such that it can be added to any portfolio strategy satisfying debt constraints without violating the constraints.

Introduction

In Chapter 8 we defined agents as risk averse if they prefer the expectation of a consumption plan to the consumption plan itself. The consumption plan is obviously riskier than its expectation, and risk-averse agents prefer the latter.

A natural extension of this discussion is to consider a risk-averse agent who compares two consumption plans, neither of which is deterministic. In general, without more information about an agent's preferences, two risky consumption plans with the same expectation cannot be ranked: some risk-averse agents prefer one and some the other. However, in the spirit of the discussion of Chapter 9, it is appropriate to ask whether there is some condition on the distribution of two consumption plans with the same expectation such that all risk-averse agents whose preferences have expected utility representation do prefer one to the other. Section 10.2 defines an ordering of consumption plans that, as seen in Section 10.5, has the desired property.

In this chapter, we assume that date-0 consumption does not enter the utility functions.

Greater Risk

Let y and z be two (date-1) consumption plans. As in Chapter 9, these consumption plans can be viewed narrowly as random variables on the set of states S with given probabilities or broadly as arbitrary random variables (with finite expectations).

Financial economics plays a far more prominent role in the training of economists than it did even a few years ago. This change is generally attributed to the parallel transformation in financial markets that has occurred in recent years. Assets worth trillions of dollars are traded daily in markets for derivative securities, such as options and futures, that hardly existed a decade ago. However, the importance of these changes is less obvious than the changes themselves. Insofar as derivative securities can be valued by arbitrage, such securities only duplicate primary securities. For example, to the extent that the assumptions underlying the Black–Scholes model of option pricing (or any of its more recent extensions) are accurate, the entire options market is redundant because by assumption the payoff of an option can be duplicated using stocks and bonds. The same argument applies to other derivative securities markets. Thus it is arguable that the variables that matter most – consumption allocations – are not greatly affected by the change in financial markets. Along these lines one would no more infer the importance of financial markets from their volume of trade than one would make a similar argument for supermarket clerks or bank tellers based on the fact that they handle large quantities of cash.

Introduction

The analytical framework in the classical finance models discussed in this book is largely the same as in general equilibrium theory: agents, acting as price-takers, exchange claims on consumption to maximize their respective utilities. Because the focus in financial economics is somewhat different from that in mainstream economics, we will ask for greater generality in some directions while sacrificing generality in favor of simplification in other directions.

As an example of greater generality, it is assumed that uncertainty will always be explicitly incorporated in the analysis. We do not assert that there is any special merit in doing so; the point is simply that the area of economics that deals with the same concerns as finance but concentrates on production rather than uncertainty has a different name (capital theory). Another example is that markets are incomplete: the Arrow–Debreu assumption of complete markets is an important special case, but in general it will not be assumed that agents can purchase any imaginable payoff pattern on securities markets.

As an example of simplification, it is assumed that only one good is consumed and that there is no production. Again, the specialization to a single-good exchange economy is adopted only to focus attention on the concerns that are distinctive to finance rather than microeconomics, in which it is assumed that there are many goods (some produced), or capital theory, in which production economies are analyzed in an intertemporal setting.