Neoclassical Finance: 2 (Princeton Lectures in Finance) - Hardcover

Ross, Stephen A.

Hardcover

ISBN 10: 0691121389 ISBN 13: 9780691121383

Verlag: Princeton University Press, 2004

Inhaltsangabe

Neoclassical Finance provides a concise and powerful account of the underlying principles of modern finance, drawing on a generation of theoretical and empirical advances in the field. Stephen Ross developed the no arbitrage principle, tying asset pricing to the simple proposition that there are no free lunches in financial markets, and jointly with John Cox he developed the related concept of risk-neutral pricing. In this book Ross makes a strong case that these concepts are the fundamental pillars of modern finance and, in particular, of market efficiency. In an efficient market prices reflect the information possessed by the market and, as a consequence, trading schemes using commonly available information to beat the market are doomed to fail.


By stark contrast, the currently popular stance offered by behavioral finance, fueled by a number of apparent anomalies in the financial markets, regards market prices as subject to the psychological whims of investors. But without any appeal to psychology, Ross shows that neoclassical theory provides a simple and rich explanation that resolves many of the anomalies on which behavioral finance has been fixated.


Based on the inaugural Princeton Lectures in Finance, sponsored by the Bendheim Center for Finance of Princeton University, this elegant book represents a major contribution to the ongoing debate on market efficiency, and serves as a useful primer on the fundamentals of finance for both scholars and practitioners.

Über diesen Titel

Über die Autorin bzw. den Autor

Stephen A. Ross is the Franco Modigliani Professor of Finance and Economics at the Massachusetts Institute of Technology. Best known as the originator of arbitrage pricing theory and as the codiscoverer of risk-neutral pricing and the binomial model for pricing derivatives, he is the coauthor of the best-selling textbook series in finance, "Corporate Finance".

Von der hinteren Coverseite

"Stephen Ross, a pioneer of the field, surveys and integrates modern finance in this lovely book. Much of the analysis is strikingly novel. For example, Ross emphasizes how mild limits on risk aversion can extend no-arbitrage arguments to say a lot about asset prices; he derives discount factor bounds in a unified way from the principle that more choices make you happier; he presents the 'random walk' result in a compelling dynamic-trading environment; and he closes with a careful dynamic contingent-claims analysis of the closed-end fund discount. This chapter exemplifies the neoclassical philosophy that patient, scientific study can eventually solve the hardest empirical puzzles."--John Cochrane, University of Chicago Graduate School of Business, author of Asset Pricing

"Neoclassical Finance is a must-read--a masterly development of neoclassical asset pricing theory by one of its most original thinkers. Stephen Ross not only provides a rigorous yet intuitive synthesis of pricing fundamentals, but also shows how these fundamentals offer a powerful alternative to many of the claims of behavioral finance."--Hayne E. Leland, Arno Rayner Professor of Finance and Management, University of California, Berkeley

"This delightful volume of four edited lectures by Stephen Ross tells us about both his views and his tastes. The first chapter deals with no-arbitrage methods--as we might expect--and the remaining three with more contentious topics: bounds on the pricing kernel, market efficiency, and behavioural finance. As we have come to expect from Stephen Ross, the exposition is excellent and the range masterly. We also learn, from the choices that have been made in order to fit this material into a small space, what he thinks is important. This is an outstanding volume that will be read with profit and enjoyment both by Professor Ross's colleagues in the profession and by those outside finance seeking an introduction to these important and controversial questions."--Stephen M. Shaefer, Professor of Finance, London Business School

"Neoclassical Finance is a significant contribution to the field that deserves to be widely cited. Stephen Ross provides a clear and concise discussion of basic theory, a new and in some ways unique look at arbitrage and market efficiency, and resolves a long-standing empirical puzzle about closed-end funds."--Richard Roll, Japan Alumni Chair in Finance, Anderson School of Business, University of California, Los Angeles

"The battle between classical and behavioral economics is here to stay and will be a centerpiece of debate in the years to come, especially in the portfolio management arena. Stephen Ross contends that critics of neoclassical finance are all too willing to live with the proverbial $100 bill sitting unclaimed on the pavement, and underestimate the power of arbitrage. He does a marvelous job of establishing the basic foundations of neoclassical finance, and describing its tenets and results. And he does so with just the right mix of survey materials and new results."--Yacine Aït-Sahalia, Director, Bendheim Center for Finance, Princeton University

Aus dem Klappentext

"Stephen Ross, a pioneer of the field, surveys and integrates modern finance in this lovely book. Much of the analysis is strikingly novel. For example, Ross emphasizes how mild limits on risk aversion can extend no-arbitrage arguments to say a lot about asset prices; he derives discount factor bounds in a unified way from the principle that more choices make you happier; he presents the 'random walk' result in a compelling dynamic-trading environment; and he closes with a careful dynamic contingent-claims analysis of the closed-end fund discount. This chapter exemplifies the neoclassical philosophy that patient, scientific study can eventually solve the hardest empirical puzzles."--John Cochrane, University of Chicago Graduate School of Business, author of Asset Pricing

"Neoclassical Finance is a must-read--a masterly development of neoclassical asset pricing theory by one of its most original thinkers. Stephen Ross not only provides a rigorous yet intuitive synthesis of pricing fundamentals, but also shows how these fundamentals offer a powerful alternative to many of the claims of behavioral finance."--Hayne E. Leland, Arno Rayner Professor of Finance and Management, University of California, Berkeley

"This delightful volume of four edited lectures by Stephen Ross tells us about both his views and his tastes. The first chapter deals with no-arbitrage methods--as we might expect--and the remaining three with more contentious topics: bounds on the pricing kernel, market efficiency, and behavioural finance. As we have come to expect from Stephen Ross, the exposition is excellent and the range masterly. We also learn, from the choices that have been made in order to fit this material into a small space, what he thinks is important. This is an outstanding volume that will be read with profit and enjoyment both by Professor Ross's colleagues in the profession and by those outside finance seeking an introduction to these important and controversial questions."--Stephen M. Shaefer, Professor of Finance, London Business School

"Neoclassical Finance is a significant contribution to the field that deserves to be widely cited. Stephen Ross provides a clear and concise discussion of basic theory, a new and in some ways unique look at arbitrage and market efficiency, and resolves a long-standing empirical puzzle about closed-end funds."--Richard Roll, Japan Alumni Chair in Finance, Anderson School of Business, University of California, Los Angeles

"The battle between classical and behavioral economics is here to stay and will be a centerpiece of debate in the years to come, especially in the portfolio management arena. Stephen Ross contends that critics of neoclassical finance are all too willing to live with the proverbial $100 bill sitting unclaimed on the pavement, and underestimate the power of arbitrage. He does a marvelous job of establishing the basic foundations of neoclassical finance, and describing its tenets and results. And he does so with just the right mix of survey materials and new results."--Yacine Aït-Sahalia, Director, Bendheim Center for Finance, Princeton University

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NEOCLASSICAL FINANCE

By STEPHEN A. ROSS

PRINCETON UNIVERSITY PRESS

Copyright © 2005 Princeton University Press
All right reserved.
ISBN: 978-0-691-12138-3

Contents

Preface........................................................................................ixONE No Arbitrage: The Fundamental Theorem of Finance...........................................1TWO Bounding the Pricing Kernel, Asset Pricing, and Complete Markets...........................22THREE Efficient Markets........................................................................42FOUR A Neoclassical Look at Behavioral Finance: The Closed-End Fund Puzzle.....................66Bibliography...................................................................................95Index..........................................................................................101

Chapter One

NO ARBITRAGE: THE FUNDAMENTAL THEOREM OF FINANCE

Thirty years ago marked the publication of what has come to be known as the Fundamental Theorem of Finance and the discovery of risk-neutral pricing. The earlier option pricing results of Black and Scholes (1973) and Merton (1973) were the catalyst for much of this work, and certainly one of the central themes of this research has been an effort to understand option pricing. History alone, then, makes the topic of these monographs—the neoclassical theory of finance—particularly appropriate. But, history aside, the basic theorem and its attendant results have unified our understanding of asset pricing and the theory of derivatives, and have generated an enormous literature that has had a significant impact on the world of financial practice.

Finance is about the valuation of cash flows that extend over time and are usually uncertain. The basic intuition that underlies valuation is the absence of arbitrage. An arbitrage opportunity is an investment strategy that guarantees a positive payoff in some contingency with no possibility of a negative payoff and with no initial net investment. In simple terms, an arbitrage opportunity is a money pump, and the canonical example is the opportunity to borrow at one rate and lend at a higher rate. Clearly individuals would want to take advantage of such an opportunity and would do so at unlimited scale. Equally clearly, such a disparity between the two rates cannot persist: by borrowing at the low rate and lending at the high rate, arbitragers will drive the rates together. The Fundamental Theorem derives the implications of the absence of such arbitrage opportunities.

It's been said that you can teach a parrot to be an economist if it can learn to say "supply and demand." Supply, demand, and equilibrium are the catchwords of economics, but finance, or, if one is being fancy, financial economics, has its own distinct vocabulary. Unlike labor economics, for example, which specializes the methodology and econometrics of supply, demand, and economic theory to problems in labor markets, neoclassical finance is qualitatively different and methodologically distinct. With its emphasis on the absence of arbitrage, neoclassical finance takes a step back from the requirement that the markets be in full equilibrium. While, as a formal matter, the methodology of neoclassical finance can be fitted into the framework of supply and demand, depending on the issue, doing so can be awkward and may not be especially useful. In this chapter we will eschew supply and demand and develop the methodology of finance as the implication of the absence of arbitrage.

No Arbitrage Theory: The Fundamental Theorem

The assumption of no arbitrage (NA) is compelling because it appeals to the most basic beliefs about human behavior, namely that there is someone who prefers having more wealth to having less. Since, save for some anthropologically interesting societies, a preference for wealth appears to be a ubiquitous human characteristic, it is certainly a minimalist requirement. NA is also a necessary condition for an equilibrium in the financial markets. If there is an arbitrage opportunity, then demand and supply for the assets involved would be infinite, which is inconsistent with equilibrium. The study of the implications of NA is the meat and potatoes of modern finance.

The early observations of the implications of NA were more specific than the general theory we will describe. The law of one price (LOP) is the most important of the special cases of NA, and it is the basis of the parity theory of forward exchange. The LOP holds that two assets with identical payoffs must sell for the same price. We can illustrate the LOP with a traditional example drawn from the theory of international finance. If s denotes the current spot price of the Euro in terms of dollars, and f denotes the currently quoted forward price of Euros one year in the future, then the LOP implies that there is a lockstep relation between these rates and the domestic interest rates in Europe and in the United States.

Consider individuals who enter into the following series of transactions. First, they loan $1 out for one year at the domestic interest rate of r, resulting in a payment to them one year from now of (1 + r). Simultaneously, they can enter into a forward contract guaranteeing that they will deliver Euros in one year. With f as the current one-year forward price of Euros, they can guarantee the delivery of

(1+ r)f

Euros in one year's time. Since this is the amount they will have in Euros in one year, they can borrow against this amount in Europe: letting the Euro interest rate be r_e, the amount they will be able to borrow is

(1 + r)f/(1 + r_e).

Lastly, since the current spot price of Euros is s Euros per dollar, they can convert this amount into

(1 + r)f/(1 + r_e)s.

dollars to be paid to them today.

This circle of lending domestically and borrowing abroad and using the forward and spot markets to exchange the currencies will be an arbitrage if the above amount differs from the $1 with which the investor began. Hence, NA generally and the LOP in particular require that

(1+ r)f = (1+ r_e)s,

which is to say that having Euros a year from now by lending domestically and exchanging at the forward rate is equivalent to buying Euros in the current spot market and lending in the foreign bond market.

Not surprisingly, as a practical matter, the above parity equation holds nearly without exception in all of the foreign currency markets. In other words, at least for the outside observer, none of this kind of arbitrage is available. This lack of arbitrage is a consequence of the great liquidity and depth of these markets, which permit any perceived arbitrage opportunity to be exploited at arbitrary scale. It is, however, not unusual to come across apparent arbitrage opportunities of mispriced securities, typically when the securities themselves are only available in limited supply.

While the LOP is a nice illustration of the power of assuming NA, it is somewhat misleading in that it does not fully capture the implications of removing arbitrage opportunities. Not all arbitrage possibilities involve two different positions with identical cash flows. Arbitrage also arises if it is possible to establish two equally costly positions, one of which has a greater set of cash flows in all circumstances than the other. To accommodate this possibility, we adopt the following framework and definitions. While the results we obtain are quite general and apply in an intertemporal setting, for ease of exposition we will focus on a one-period model in which decisions are made today, at date 0, and payoffs are received in the future at date 1. By assumption, nothing happens in between these two dates, and all decisions are undertaken at the initial date, 0.

To capture uncertainty, we will assume that there is a state space, , and to keep the mathematics at a minimum, we will assume that there are only a finite number of possible states of nature:

ω = {θ₁, ..., θ_m}.

The state space, ω, lists the mutually exclusive states of the world that can occur, m. In other words, at time 1 the uncertainty is resolved and the world is in one and only one of the m states of nature in ω.

We will also assume that there are a finite number, n, of traded assets with a current price vector:

p = (p₁, ..., p_n).

Lastly, we will let

(η₁, ..., η_n)

denote an arbitrage portfolio formed by taking combinations of the n assets. Each element of η, say η_i, denotes the investment in asset i. Any such portfolio will have a cost,

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and we will refer to such a combination, η, as an arbitrage portfolio if it has no positive cost,

pη ≤ 0.

We represent the Arrow-Debreu tableau of possible security payoffs by

G = [g_ij] = [payoff of security j if state θ_ij occurs].

The rows of G are states of nature and the columns are securities. Each row of the matrix, G, lists the payoffs of the n securities in that particular state of nature, and each column lists the payoffs of that particular security in the different states of nature.

With the previous notation, we can define an arbitrage opportunity.

Definition: An arbitrage opportunity is an arbitrage portfolio with no negative payoffs and with a positive payoff in some state of nature. Formally, an arbitrage opportunity is a portfolio, η, such that

pη ≤ 0

and

Gη ≥ 0,

where at least one inequality for one component or the budget constraint is strict.

We can simplify this notation and our definition of NA by defining the stacked matrix:

A = [-p/G].

Definition: An arbitrage is a portfolio, , such that

Aη > 0.

Formally, then, the definition of no arbitrage is the following.

Definition: The principle of no arbitrage (NA):

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that is, there are no arbitrage portfolios.

The preceding mathematics captures our most basic intuitions about the absence of arbitrage possibilities in financial markets. Put simply, it says that there is no portfolio, that is, no way of buying and selling the traded assets in the market so as to make money for sure without spending some today. Any portfolio of the assets that has a positive return no matter what the state of nature for the world in the future, must cost something today. With this definition we can state and prove the Fundamental Theorem of Finance.

The Fundamental Theorem of Finance: The following three statements are equivalent:

1. No Arbitrage (NA).

2. The existence of a positive linear pricing rule that prices all assets.

3. The existence of a (finite) optimal demand for some agent who prefers more to less.

Proof: The reader is referred to Dybvig and Ross (1987) for a complete proof and for related references. For our purposes it is sufficient to outline the argument. A linear pricing rule, q, is a linear operator that prices an asset when applied to that asset's payoffs. In this finite dimensional setup, a linear pricing rule is simply a member of the dual space, R^m and the requirement that it is positive is just the requirement that q >> 0. The statement that q prices the assets means simply that q satisfies the system of equations:

p = qG.

It is easy to show that a positive linear pricing operator precludes arbitrage. To see this let η be an arbitrage opportunity. Clearly,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

But, since q >> 0, this can only be true if

Gη < 0,

which is inconsistent with arbitrage.

The converse result, that NA implies the existence of a positive linear pricing operator, q, is more sophisticated. Outlining the argument, we begin by observing that NA is equivalent to the statement that the set of net trades,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

does not intersect the positive orthant since any such common point would be an arbitrage. Since S is a convex set, this allows us to apply a separating hyperplane theorem to find a y that separates S from the positive orthant, R⁺. Since

yR⁺ > 0,

we have y >> 0. Similarly, for all η, we have

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(since if the inequality is strict, -η will violate it, i.e., S is a subspace.) Defining implies that

p = qG,

hence q is the desired positive linear pricing operator that prices the marketed assets.

Relating NA to the individual maximization problem is a bit more straightforward and constructive. Since any agent solving an optimization problem would want to take advantage of an arbitrage opportunity and would want to do so at arbitrary scale, the existence of an arbitrage is incompatible with a finite demand. Conversely, given NA, we can take the positive linear pricing rule, q, and use it to define the marginal utility for a von Neumann-Morgenstern expected utility maximizer and, thereby, construct a concave monotone utility function that achieves a finite maximum.

* * *

Much of modern finance takes place over time, a fact that is usually modeled with stochastic diffusion processes or with discrete processes such as the binomial. While our simplified statement of the Fundamental Theorem is inadequate for that setting, and while the theorem can be extended to infinite dimensional spaces, some problems do arise. However critical these difficulties are from a mathematical perspective, as a matter of economics their importance is not yet well understood. The nut of the difficulty appears to be that the operator that prices assets may not have a representation as a vector of prices for wealth in different states of nature, and that makes the usual economic analysis of trade-offs problematic.

A complete market is one in which for every state θ_i there is a combination of the traded assets that is equivalent to a pure contingent state claim, in other words, a security with a payoff of the unit vector: one unit if a particular state occurs, and nothing otherwise. In a complete market G is of full-row rank, and the equation

p = qG

has a unique solution,

q = pG^-1.

This determinancy is one reason why market completeness is an important property for a financial market, and we will later discuss it in more detail. By contrast, in an incomplete market, the positive pricing operator will be indeterminate and, in our setting with m states and n securities, if m > n, then the operator will be an element of a subspace of dimensionality m - n. This is illustrated in figure 1.1 for the m = 3 state, n = 2 security example. In figure 1.1, each of the two securities has been normalized so that R¹ and R² represent their respective gross payoffs in each of the three states per dollar of investment.

The Representation Theorem

The positive linear operator that values assets in the Fundamental Theorem has several important alternative representations that permit useful restatements of the theorem itself.

Definition: Martingale or risk-neutral probabilities are a set of probabilities, π^*, such that the value of any asset with payoffs of

z = (z₁, ..., z_m)

is given by the discounted expectation of its payoffs using the associated risk-less rate to discount the expectation,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Definition: A state price density, also known as a pricing kernel, is a vector,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

such that the value of any asset is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

These definitions provide alternative forms for the Fundamental Theorem.

(Continues...)

Excerpted from NEOCLASSICAL FINANCEby STEPHEN A. ROSS Copyright © 2005 by Princeton University Press. Excerpted by permission of PRINCETON UNIVERSITY PRESS. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Details zur Ausgabe

• Verlag: Princeton University Press
• Erscheinungsdatum: 2004
• Sprache: Englisch
• ISBN 10: 0691121389
• ISBN 13: 9780691121383
• Einband: Tapa dura
• Anzahl der Seiten: 118
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar