Bubbles and Crashes II: A Survey of the Efficient Market Hypothesis, Part I

“A study of economics usually reveals that the best time to buy anything is last year.”

-Marty Allen

1. Introduction

A thorough study of asset price bubbles and market crashes necessitates the study of the efficient market hypothesis, one of the most controversial theories in modern finance and economics. In the wake of the 2008-2009 financial crisis, the efficient market hypothesis (EMH) has faced both opprobrium and found defense. In various editorials and journal articles, economists have criticized the financial community for what they argue was unreasonable and nearsighted adherence to the pronouncements of the hypothesis (Thaler, 2008). Others, however, hold that government interference, specifically its attempts to manage inefficiencies, have created the conditions necessary to promote price bubbles (Thompson, 2006).

In an ideal capital market, prices incorporate all available information necessary for the proper allocation of resources. However, the existence of asset bubbles and crashes may suggest that the allocation of resources is often improper. Indeed much of the discussion about the current financial crisis implies that efficient markets preclude asset price bubbles. However, definitions of the EMH vary and are implicitly based on general equilibrium principles that may be consistent with asset price bubbles. Therefore one must determine the extent to which the forms of the efficient market hypothesis preclude various assertions about bubbles. Of related importance are the relationships between financial efficiency, loosely defined as the absence of arbitrage opportunities, and other standards of efficiency (e.g. informational and welfare efficiency) as they may have some bearing on the existence of price bubbles.

Bubbles and Crashes I: Motivation and Initial Reading List

“I can calculate the motions of the heavenly bodies, but not the madness of people.”

– Sir Isaac Newton after losing £20,000 in the South Sea Bubble

Bubbles and their subsequent crashes have confounded historians, economists, financiers and the general populous throughout history.  Examples, often categorized as bubbles, include Tulip Mania, the South Seas bubble, the Dot Com bubble, and the recent housing bubble.  The importance of bubbles and crashes cannot be overlooked in the macroeconomic sense.  The housing bubble is a prime example of this; where, as a consequence of the crash, global GDP (cumulative GDP of every country) was severely affected. Much of the literature in macroeconomics ignored the consequences of bubbles by ignoring financial intermediation and associated frictions.  In light of the recent crises, the literature is now shifting toward an approach that brings together financial economics, monetary economics, and standard macroeconomic techniques.

An asset bubble is formed when an asset’s price is significantly different from its fundamental value, also known as its intrinsic value. In practice it is sometimes calculated as the discounted sum of expected future income; however, this may not be a good estimate to the actual fundamental value. In order to calculate the true fundamental value, we must first construct a general equilibrium model such as Milgrom & Stokey 1982 or Tirole 1982.

246A: Complex Analysis, Notes 1 – Analytic functions, Cauchy’s formula and singularities.

The following series of posts comprises our introduction to complex analysis as taught by Professor Rowan Killip at the University of California, Los Angeles, during the Fall quarter of 2009. Where necessary, course notes have been supplemented with details written by the authors of this website using assistance from Complex Analysis by Elias Stein and Rami Shakarchi. The basic properties of complex numbers will be assumed allowing us to begin with the definition of a holomorphic (or complex-differentiable) function, the central notion in our study of complex analysis.

The basic properties of complex numbers will be assumed, allowing us to begin with the definition of a holomorphic (or complex-differentiable) function, the central notion in our study of complex analysis.

Definition 1.1 Suppose is an open set and . We say is holomorphic (or complex-differentiable) at if there exists We say is holomorphic on if it has this property for all .