Mathematics and Economics

Bubbles and Crashes: Motivation and Initial Reading List

In Asset Pricing Reading Group, Bubbles and Crashes, Economics, Finance on November 10, 2009 at 3:57 pm

“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, and the housing bubble is a prime example: as a consequence of the crash, global GDP (the 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. This construction will be discussed in more detail in some future posts. Unfortunately, the theoretical definition of bubbles is not easily applied since the fundamental value is difficult or impossible to observe.  For this reason, some alternative operational definitions have been proposed.  Jeremy J. Siegal, proposed an operational definition of a bubble as “any time the realized asset return over a given future period is more than two standard deviations from its expected return” (Siegel 2003).  Though this  definition implicitly implies that asset returns are normally distributed, or Gaussian,  so that virtually all returns should lie in the range of two standard deviations from the mean.  Notable authors such as Benoît Mandelbrot and Nassim Taleb have argued against using normal distributions for assets since fat tails are often observed in many assets. Along these lines, Didier Sornette offers another operational definition; bubbles are “caused by the slow build-up of long-range correlations leading to a global cooperative behavior of  the market and eventually ending in a collapse in a short critical time interval.” (Sornette 2001). Note that this definition concerns asset market bubbles which occur, in theory, when an underlying process inflates all of the assets in that particular market above their fundamental value.  We will discuss this definition, whether it coincides with the theoretical definition, and Sornette’s work further in future posts.

In order to address the existence of asset bubbles, as theoretically defined, we must first examine the fundamental properties of prices.  More specifically, we must discuss the validity of the Efficient Markets Hypothesis.  The definition provided by Fama (Fama 1990): “I take the market efficiency hypothesis to be the simple statement that security prices fully reflect all available information. A precondition for this strong version of the hypothesis is that information and trading costs, the costs of getting prices to reflect information, are always 0 (Grossman and Stiglitz (1980)). A weaker and more economically sensible version of the efficiency hypothesis says that prices reflect information to the point where the marginal benefits of acting on information (i.e. the potential profits to be made) do not exceed marginal costs (Jensen (1978)).” We will take Jensen’s more sensible definition and additionally consider the the three different forms of the efficient markets hypothesis: weak, semi-strong, and strong.  Each form is designated by the specification of  the information that is reflected by prices.  A rigorous definition of the EMH and its forms will be given in the next installment of this series. Moreover, we will discuss whether any of the forms of the EMH permit the existence of bubbles as theoretically defined.

Once we have discussed the efficient markets hypothesis, we will then tackle the problem of defining the notion of fundamental values and bubbles in the theoretical frameworks of general equilibrium models such as Milgrom and Stokey (1982), Postlewaite et al., and Tirole (1982). In addition, we will also look at the fundamental formation of  prices in divisible good markets through various continuous auction formats with the eventual goal of analyzing bubbles in those formats.

In our future posts, we will review and analyze the following papers:

  1. Efficient Capital Markets: A Review of Theory and Empirical Work” by EF Fama – Journal of Finance, 1970
  2. Efficient Capital Markets: II” by EF Fama – The Journal of Finance, 1991.
  3. Efficient Capital Markets and Martingales” by SF Leroy – Journal of Economic Literature, 1989.
  4. Information, Trade and Common Knowledge” by P Milgrom and M Stokey.
  5. On the possibility of speculation under rational expectations” by J Tirole – Econometrica, 1982.
  6. Finite bubbles with short sale constraints and asymmetric information” by F Allen, S Morris, and A Postlewaite – Journal of Economic Theory.
  1. […] Asset Pricing Reading Group General Announcement In Asset Pricing Reading Group, Economics, Finance on October 29, 2009 at 9:20 am Update (11/17/09): The Asset Pricing Reading Group will be meeting today at 5:15 in the 9th floor conference room of Bunche (Bunche 9383). We will be discussing the papers listed in Bubbles and Crashes I. […]

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