Psychological Approaches applied on Financial Markets

Contents

GRAPHICS

TABLES

EQUATIONS

LIST OF ABBREVIATIONS

1 INTRODUCTION
1.1 Task of the Paper
1.2 Methodology

2 FOUNDATIONS OF BUBBLE RESEARCH
2.1 Understanding Bubbles - A Crucial Point
2.1.1 Locusts and Financial Bubbles
2.1.2 Feedback cycles of financial markets
2.2 Bubbles in a historical Perspective

3 RATIONAL BUBBLES WITH CONVENTIONAL RATIONALITY AND PERFECT MARKETS
3.1 Perfect Financial Markets
3.1.1 Present Value Model
3.1.2 Efficient Market Hypothesis
3.2 Classical Rational Behavior under Risk and Uncertainty
3.2.1 Axioms of the EUM
3.2.2 Expected Utility and von Neumann - Morgenstern Utility Function
3.3 Rational Bubbles
3.3.1 Rational Expectations and Identical Information
3.3.2 Asymmetric Information
3.4 Anomalies and Deviations of the EUM
3.4.1 The Allais Paradox
3.4.2 The Disposition Effect
3.5 Conclusions for the Classical Model in Bubble Research
3.5.1 Imperfect Markets
3.5.2 Consequences for Rationality

4 THE DEVIATION FACTOR HYPOTHESIS
4.1 Bounded Rationality adjusted for Financial Bubbles
4.1.1 Non - optimal Decision Making
4.1.2 Detection of Decision Mistakes
4.2 Inherent Decision Mistakes
4.3 Exceeded Non - Rational Behavior
4.3.1 Over - Confidence and Euphoria
4.3.2 Fear
4.4 Indicators for Non - Rational Behavior and Difficulties in Observation
4.4.1 Leading Indicators of Confidence
4.4.2 Indices in Appliance and Limits of Measurement

5 CRITICAL ACCLAIM
5.1 Bubble- and Crisis Research
5.2 Psychological Approaches
5.3 Critique on the Deviation Factor Hypothesis

6 CONCLUSION

REFERENCES

Abstract

This Paper works out how psychological approaches can be applied on financial bubbles. The thesis shows that it is impossible to explain financial bubbles clearly and without flaws with classical rationality and perfect markets. Furthermore this paper tries to unite various behavioral approaches to explain financial bubbles in a more realistic way. Financial bubbles imagine a great importance for the entire economy, caused by their strong economic impact. Therefore an understanding of these bubbles is crucial to counteract them. To gain the aspired results the paper will present empirical studies and inconsistencies in classic economic theory. Additionally it will adjust alternative behavioral models for financial bubbles. It will be shown how human behavior leads to inherent mistakes at financial markets, which cause financial bubbles.

Diese Arbeit beschäftigt sich mit der Anwendung von psychologischen Verhaltensmodellen auf Finanzmärkte zur Erklärung von Finanzblasen. Es wird verdeutlicht werden, dass aus der klassischen Ökonomie stammende Theorien nicht in der Lage sind Finanzblasen fehlerfrei und eindeutig zu erklären. Daher bedient diese Arbeit sich psychologischer Modelle um Finanzblasen realitätsnäher zu erklären. Durch ihre immense Wirkungskraft beeinflussen Finanzblasen die gesamte Wirtschaft. Deswegen ist es außerordentlich wichtig diese zu verstehen um rechtzeitig Kontrollmaßnahmen einzuleiten. Um die angestrebten Resultate zu erreichen bedient sich diese Arbeit mehrerer empirischer Studien sowie Unregelmäßigkeiten in der klassisch ökonomischen Theorie. Weiterhin werden psychologische Modelle in einem einheitlichen Erklärungsmodell angepasst werden um Finanzblasen zu erklären. Dieses Modell wird verdeutlichen, dass es in der menschlichen Natur liegt Fehler zu machen. Diese Fehler führen auf den Finanzmärkten zu Finanzblasen.

Graphics

Graphic 1 Methodology of this Paper

Graphic 2 Post - Collapse Prices in Guilders

Graphic 3 von Neumann - Morgenstern utility function

Graphic 4 Principal Agency Theory

Graphic 5: Enrons decline in share price

Graphic 6 Value function according to prospect theory

Graphic 7 Decision heuristic for risk, time horizon and costs

Graphic 8 Illustration of the psychological chapters of a financial bubble

Graphic 9 Real Standard & Poor´s composite stock price index (solid line) and ex post rational PVM price (broken line)

Graphic 10 Illustration of the Confidence Multiplier

Tables

Table 1 Claims for market perfectness

Table 2 Phenomena inconsistent with the EUM

Table 3 Theoretical approaches to explain the independence axiom without violating other axioms of the EUM

Table 4 Variables influencing ࢽ

Table 5 Index Questions of the MMICC

Table 6 Index Questions of the ICC

Table 7 Index Questions of the MCSI

Equations

Equation 3.1 Asset return

Equation 3.2 Price of a financial asset for one period

Equation 3.3 Price of a financial asset for n pereiods with different periodic return

Equation 3.4 Present Value Model

Equation 3.5 Efficient Market Hypothesis (EMH)

Equation 3.6 Error Term of the EMH

Equation 3.7 On average value of the error term

Equation 3.8 Expected Utility Model

Equation 3.9 Price composition with a Bubble Term

Equation 3.10 Definition of the Bubble Term

Equation 3.11 Fundamental Value and Market Value

Equation 3.12 Expression of Rational Expectation

Equation 3.13 Consequences of Information Asymmetries

Equation 4.1 Deviation Factor Hypothesis

Equation 4.2 Composition of the Deviation Factor

Equation 4.3 Cummulated Weighted Impressions

List of Abbreviations

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“ Euphorion: Now I spring on solid earth,

but the earth retaliates,

throws me high up in the air: with a second spring, a third, throws me to the very roof.

Faust: Caution, caution, a fatal fall

would bring sorrow to us all.

Euphorion: I ´ ll stay no longer

here on land.

Let go my clothes, let go my hand. ” [ … ]

Euphorion: Nothing restrains

me - now, I have wings. Do not begrudge me this, But go I must.

Chorus: Icarus! Icarus!

Now he is dust.

Faust/Helen: All the earthly joy we know

by pain is quickly overthrown. ” ¹

1 Introduction

These lines are an extract of Goethe´s Faust II. In this scene Euphorion (the son of Faust and Helen) is born. The scene ends with his death in battle. The whole scene illustrates how euphoria could lead to devastating results. This is also a characteristic of financial bubbles. Therefore the whole scene can be seen as an analogy for financial bubbles. These bubbles are the topic of this thesis.

1.1 Task of the Paper

This work focusses on the explanation of bubbles from start to bust at financial markets in highly developed and developing countries. The aftermath of a financial bubble will not be part of explanation. It will be explained from start to bust how financial bubbles occur. Therefore this paper tries to answer the following question:

Can the process of financial bubbles from start to bust be explained and are there indicators based on psychological theories, which are influencing financial bubbles?

Hence the aftermath of financial bubble is not the task of this thesis. For answering this questions two major disciplines will be used. At first financial bubbles will be explained in the context of classic economic theory. Viz markets are perfect and economic agents are rational. The second discipline adds a psychological background to the assumption of classical theory. In this case agents have a bounded rationality and markets are imperfect.

1.2 Methodology

The methodology of this bachelor thesis deviates from given standards. Hence graphic

1 illustrates the steps of this work. This graphic will be explained in the following text.

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Graphic 1 Methodology of this Paper

The first step of this work is to define the problem which shall be explained. This already happened in the previous chapter. In the second chapter two questions will be asked to lay the foundations for further research: (I) why are financial bubbles relevant and (II) which components are relevant for analysis? When these questions are answered the thesis starts with its core tasks. Therefore this paper will decompose financial bubbles into interdependencies of market environment and behavior of market participants. Then it will try to explain these interdependencies, which create a financial bubble. Two different approaches will be proven for validity. Accordingly in chapter three classic economic theory (the first of two approaches) will be used to explain financial markets and financial bubbles. This will be done by explaining behavior under uncertainty and the information processing of financial markets. Flaws of these explanations will be revealed. The flaws and empirical findings, which contradict classical theory will be discussed and concluded. In graphic one the whole chapter three is represented by the left bracket. In chapter four additional theories from behavioral economics will be combined with the experiences gained from the conclusions of chapter three to synthesize a new idea of the explanation of financial bubbles (the second approach of two). This idea will be worked out in detail also in chapter four. Possible indicators for this idea will be shown, as well as the difficulties arising from these indicators. The whole forth chapter is represented by the right bracket of graphic one. As mentioned above chapter four only deals with a hypothesis, which thus is not empirically validated. Subsequently the work will mention major critiques on behavioral economics, crisis research and the idea mentioned in chapter four. Ultimately major findings will be concluded to solve the question of this thesis.

2 Foundations of Bubble Research

2.1 Understanding Bubbles - A Crucial Point

The task of the economy is to provide the society with goods to satisfy needs. In addition, the financial system tries to make the economy more efficient by facilitating funding, which leads to a more efficient allocation of resources.² Therefore, financial bubbles could be a great threat for a whole economy, because they can lead to huge deviations in the allocation of resources, through their influence on asset prices.

Funding is facilitated by the tasks of the financial system. Krugman notes three tasks of it.

- Reducing transaction costs
- Providing liquidity
- Reducing risk³

These improvements make it easier for lenders and borrowers to exchange money. In turn lenders and borrowers are now dependent from the financial system. Changes in asset prices can influence consumer and investment behavior through changes in aggregate wealth and company balance sheets. This in turn also affects government policy by performing anti-cyclical policy, if it’s necessary. So the overall real economy can be affected by price movements of the financial sector. Thus, a country´s economic performance largely depends on financial markets if a country uses a financial system to optimize its performance.

For instance in America Housing prices rose from 1997 to 2006 by 135% and slumped down in 2009 by 38% (without inflation). These price movements were part of the American housing bubble.⁴ During that crisis, subprime lending (lending money to people who struggle with repaying these loans) became famous and lead to the creation of poisonous securities. Holders of these securities defaulted as interest rates were raised to counter inflation. This led to a credit crunch, which later fueled the global financial crisis.⁵ Hence the aftermath of a bubble can affect the economy by triggering a crisis beside other exogenous shocks (e.g. war, natural disasters). A similar pattern can be seen in the Savings and Loans (S&L) crisis. Akerlof and Shiller (both received a Nobelprize in economics) pointed out that, “The S&L crisis was ultimately responsible for a considerable amount of the economic turmoil that disturbed the economy during the recession of 1990 - 91 and for slow recovery that followed it.”⁶

2.1.1 Locusts and Financial Bubbles

A famous example which illustrates the devastating outcome of bubbles is a swarm of locusts. As individuals locusts prefer a quiet solitary life. These insects are called Solitary locust. If they gather in great numbers they start to change color, even character and develop an insatiate hunger. They are then called Gregarious locusts and perform huge devastation in swarms, caused by one action, which is feeding.⁷ In March 27 2013 BBC News Africa announced that one of those swarms could cause hunger for 60% of the population in Madagascar. It was the worst plague since 1950.⁸ According to that, financial intermediaries have an insatiate hunger for capital by their profit - seeking motivation. As Minsky already notes, the profit - seeking motivation arises from the fact, that financial intermediaries are entrepreneurs.⁹ Besides changing behavior in groups, the insatiate hunger of every single financial intermediary causes feeding of capital due to speculation. Like locusts the scale of the single action exceeds if it happens in large groups. Mass - speculation leads to economic devastation, in this case an asset - price crash. These asset price crashes can be as bad for financial markets, as the incident in Madagascar for the population. If the economic consequences of the housing bubble are taken into account (e.g. credit crunch, economic slowdown) or the S&L crisis (drop in real estate prices, loss in confidence)¹⁰ they can even get worse due to a variety of effects (e.g. spill - over effects).

2.1.2 Feedback cycles of financial markets

As stated earlier, changes in financial markets can influence the economic performance of a country. Therefore GDP must change when asset prices fluctuate. One way to calculate GDP can be done with aggregate spending on final goods. Aggregate spending in turn is determined by consumption (C), Investment (I) and Government spending (G). For simplicity imports and exports are excluded. If G is fixed due to constant fiscal policy, only C and I can influence GDP. Four different effects are known to influence either C or I.

- wealth effect on consumption
- Tobin´s Q effect on investment
- effects of increasing asset prices on collaterals
- the confidence effect on private spending¹¹

The wealth effect on consumption indicates that changes in asset prices affect people´s consumption behavior by spending more for goods and services. If asset prices increase wealth of private households also increases, which triggers people to spend more. In the Euro zone for example a 10 % increase in financial wealth entails a change in consumption between 0,6 - 1,5%.¹² Thus, GDP changes if asset prices change, because overall consumption (C) changes.

Tobin´s Q measures valuation differences between a firm´s market value (stocks and bonds) and replacement costs value of capital of a firm.¹³ If it´s value is above one, the market value is higher than replacement costs. If this is the case a firm can sell shares or issue bonds and receives more for it than for company assets. This triggers investment, because the costs of capital are reduced. Statistical evidence indicates that the relation between a rise in Tobin´s Q and investment is relatively small. For example a 10% rise in average Q leads to a 2,5% rise in investment.¹⁴ Nevertheless, I alters, when asset prices do. Hence, GDP alters too.

Collaterals determine the availability of bank loans. Banks want borrowers to post collaterals to avoid moral hazards or adverse selection to get a certain amount of money. For instance, if a firm needs 1000 € for an investment, the firm wants to post a house, which is worth 1100€, as collateral. It only receives 900 € for that collateral. Thus, the investment is not realized. But if the value of the house increases to 1200€, the firm would get 1000€ from the bank. Hence the investment is realized. Therefore I increases due to an increase in asset prices, which are posted as collaterals.

The feedback cycles above focus on direct effects of asset price changes, which either change wealth or balance sheets of corporations or banks. The 4th feedback cycle influences the real economy indirectly with changes in confidence. Confidence has been identified as “important - if not leading - cause of the economic slowdown”¹⁵, of 1981 and 1982. When asset prices change, there is “a - price - to - earnings - to price feedback.”¹⁶ Rising stock prices feed confidence. Thus, people are likely to consume more. Corporate profits rise again, which also creates risings stock prices, et vice versa. Hence, C and I changes, because confidence changes, caused by asset price fluctuations. It is also assumed that confidence can change consumption and investment independently, through fear, due to public announcements.¹⁷ Connections to a confidence multiplier will be drawn later. Additionally, confidence as an economic concept will be explained later in more detail.

2.2 Bubbles in a historical Perspective

Speculation and financial bubbles have occurred in the past for many times. The Dutch tulip bulb bubble is a good example for the dimension of speculation. In 1635 a tulip bulb called Semper Augusts was worth $16000. However other variation of tulips had a relatively low price. In 1636 speculators entered the market and the prices for varieties of tulip bulb skyrocketed. Hence new market participants caused a rise in price. In 1637 the prices collapsed and a bulb was suddenly sold for 10% of its peak value. Until then the price even fell further. Graphic 2 shows the collapse in prices.

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Graphic 2 Post - Collapse Prices in Guilders¹⁸

Unfortunately the fundamental values for tulip bulbs in the 18th century were not recorded, but the rapid fall in price suggests that the bulbs were sold in these days above their fundamental value. A further famous bubble which happened in the recent past and caused devastating economic turmoil is the latest housing bubble of the USA. The origins of this bubble are hardly discussed. This paper will make no claim about the causes of the housing bubble. But a relevant aspect why this bubble could occur is a (how Akerlof and Shiller called it) financial miracle. The toxic papers (mortgage - backed securities packages with subprime mortgages) got a very high rating despite the fact that they had a very high risk. Thus nobody questioned the rating. Market participants just bought them for their return. Hence the failure of the rating agencies caused a distribution of these junk bonds across the whole world. This phenomenon is called an information asymmetry and will be examined later. The understanding of information asymmetries is an understanding of how the market process information. Thus the constitution of the market environment plays a role in the development of bubbles.

The Dutch tulip bulb bubble and the housing bubble in the USA were not unique events. Financial bubbles have been present variously in the past. Kindleberger and Aliber collected a list of the biggest ones of the past.

1. The Dutch Tulip Bulb Bubble 1636
2. The South Sea Bubble 1720
3. The Mississippi Bubble 1720
4. The late 1920s stock price bubble 1927 - 1929
5. The surge in bank loans to Mexico and other developing countries in the 1970s
6. The bubble in real estate and stocks in Japan 1985 - 1989
7. The 1985 - 1989 bubble in real estate and stocks in Finland, Norway and Sweden
8. The bubble in real estate and stocks in Thailand, Malaysia, Indonesia and several other Asian countries 1992 - 1997
9. The surge in foreign investment in Mexico 1990 - 1993
10. The bubble in over-the-counter stocks in the United States 1995 - 2000¹⁹

All these bubbles have in common that the asset price rises above the fundamental value. This is what is defined as a bubble. Hence this rise above the fundamental value must be explained to understand financial bubbles. In the case of the Dutch tulip bubble, entrances of new market participants seem to lead to a rise in price. Thus market participants are relevant for the explanation of financial bubbles. Furthermore if the US housing bubble is recalled, the market environment is also relevant for an explanation of financial bubbles, because without information asymmetries the bubble would not have developed. Therefore this work will define a bubble as a result of interdependencies of the market environment and market participants, which affect each other in a way that the price rises sharply above the fundamental value. The following chapters examine how market participants and the market environment can cause the necessary independencies. Two approaches will be presented and proven.

3 Rational Bubbles with Conventional Rationality and Perfect Markets

3.1 Perfect Financial Markets

In classical economic theory financial markets are assumed to be perfect. Two assumptions are necessary to guarantee perfectness. Both assumptions make the following claims.

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Table 1 Claims for market perfectness

How this is done will be shown in the following chapters.

3.1.1 Present Value Model

The present value model (PVM) says that an asset´s value is determined by its “present value of expected asset income.”²⁰ Thus, the value is determined as followed. A stock with a value of x ([illustration not visible in this excerpt]) in year t, annual dividends of 5€ paid at the beginning of the next year ([illustration not visible in this excerpt]) and a price of 110€ in the next year, ([illustration not visible in this excerpt]) has a return on invest of 15% ([illustration not visible in this excerpt]). It is assumed that future data is known based on all available information. The stock is sold at the end of the next period.

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3.1

Solving this equation to ܲ௧ to determine the current price:

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3.2

The current price of the stock mentioned above is thus.

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If this is performed for n periods the equation would change.

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It is assumed that ܲ[illustration not visible in this excerpt] grows at a lower rate than ܴ௧thus it converges to 0. Furthermore if [illustration not visible in this excerpt]emains constant it can be replaced by the relevant interest rate (‹), then the equation is changed further. The interest rate is assumed to be fixed over a given time period.

illustration not visible in this excerpt

The relevant interest rate ݅ consists of the safe interest rate ([illustration not visible in this excerpt] ) and a risk premium ([illustration not visible in this excerpt] Fluctuations in one of these components affect the value of the discounted asset income. These changes can happen directly due to raising the federal fund rate (this can be done by a central bank), thus[illustration not visible in this excerpt] changes. Or it can happen indirectly due to higher uncertainty at the markets (e.g. uncertainty can increase caused by lower annual growth rates), hence ߩ alters. Expectations about the future can also change, which also leads to a change in asset prices. Hence, interest rates and expectations can influence asset prices.

3.1.2 Efficient Market Hypothesis

The term “expected asset income” describes that the true value of future income is unknown. Hence, economists claim that the expected income is based on rational expectations. It characterizes all expectations as the best possible forecasts performed with all available information (ߛ). Hence market participants know all market mechanisms, which are responsible for price changes. Nobelprize winner Fama (1970) and Samuelson (1965) expanded this assumption with the Efficient Market Hypothesis (EMH). Fama claimed that market prices fully reflect all available information under the following conditions:

- No transaction costs when trading securities
- Information are available without costs for all market participants
- Information are utilized for pricing without exception²¹
- Price movements follow a random walk²²

Thus,

illustration not visible in this excerpt

where,

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Similarly on average:

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The equations above describe the following.

Equation 3.5 says that past and current information forms an expected asset price. Hence price changes can only occur if new information is revealed. Expected asset

price equals real asset price, when an error term (߳௧ାଵ) is added to the expected asset price. Forecast errors are independent from past or current information, because they are already reflected in price. This is known as orthogonality property.²³

Equation 3.6 states that the error term (߳௧ାଵ) is the difference between expected and real asset price.

Equation 3.7 expresses that on average the error term (߳௧ାଵ) is zero.²⁴ Thus the expected price can either be above or below the real price. But, generally it assumes that the future is known because on average correct predictions are made. It can be marked as one of the most critically discussed assumptions of the EMH. Further critical implications of this equation will be discussed in chapter 3.4.1.

Under these assumptions markets are confronted with three forms of efficiency.

- Weak efficiency - information of past prices and returns is used
- Semi - strong efficiency - all public available information and past information is used
- Strong efficiency - public, past and private information is used

Based on these forms of efficiency market information which are reflected in the price differ among several markets. Financial markets are assumed to follow the third form of efficiency and hence prices incorporate public, past and private information. Thus, no profits can be made by using information asymmetries.

3.2 Classical Rational Behavior under Risk and Uncertainty

If people are confronted with uncertain outcomes the outcome can either be risky or uncertain. Risky outcomes are outcomes where probabilities are known. They have a specific value and hence can be measured. In contrast uncertain outcomes are outcomes where the probability is unknown. Outcomes of stocks, bonds, mutual funds and many other financial instruments are uncertain. Thus models which describe behavior under uncertainty might be useful. Nevertheless economists tend to transform uncertainty into risk by just assuming an objective probability (in variations of the following model subjective probabilities also exist). Thus they apply models, which describe behavior under risk on uncertain outcomes. A reason why this can be done is not mentioned in standard economic textbooks.

A model which postulates behavior under risk is the expected utility model (EUM). The

EUM makes no statements concerning behavior under uncertainty. It was advanced by John von Neumann and Oskar Morgenstern with the implementation of the utility function. The model assumes that people choose opportunities with the highest expected utility. To illustrate utility for a certain level of wealth w, they invented a utility function denoted by u(w). It is assumed that the DM already has a certain amount of wealth and that the outcome of assets affect this wealth by the amount of [illustration not visible in this excerpt] . This function plays a crucial role in asset pricing. Its axioms are often criticized in terms of validity. A wide critique aiming at these axioms will follow in chapter 3.4.

In the following description of the EUM prospects are equal assets. This is done to avoid additional terminology and to make the description more consistent with the whole paper. Thus, it is defined that assets have an outcome [illustration not visible in this excerpt] and a probability of that outcome denoted by.[illustration not visible in this excerpt]²⁵

3.2.1 Axioms of the EUM

These axioms focus on preferences of decision makers on uncertain outcomes. I Completeness

For a portfolio p, with assets k, j a decision maker (DM) can either [illustration not visible in this excerpt] or ƒ̱„Ǥ This means in particular that a DM can fully identify his preferences over given opportunities.

II Transitivity

For assets[illustration not visible in this excerpt] then ƒ൐…Ǥ Thus hidden preferences of the DM can be derived through observable preferences. This axiom ensures consistency among choices.

III Continuous

For assets [illustration not visible in this excerpt] while ƒ[illustration not visible in this excerpt], there is a probability ’ such that, [illustration not visible in this excerpt] Thus a DM can be indifferent between getting 1 billion [illustration not visible in this excerpt] losing all his wealth [illustration not visible in this excerpt] and getting nothing[illustration not visible in this excerpt] if he faces a certain probability. Due to this axiom preferences can be visualized in a function.

IV Independence

If [illustration not visible in this excerpt] then [illustration not visible in this excerpt] More specifically, if asset ƒ is preferred over asset „ in the first state of nature, then asset ƒ[illustration not visible in this excerpt] will also be preferred over asset „[illustration not visible in this excerpt] in the second state of nature. This axiom claims that preferences are consistent among several rounds of choice.

V Monotonicity

Wilkinson claims the monotonicity axiom to be necessary in explanation.²⁶ Therefore this paper will also present it to guarantee correctness .This axiom is generally not mentioned in economic textbooks because it is treated as a very trivial one. It assumes that an asset ƒ can stochastically dominate another asset „Ǥ Let all[illustration not visible in this excerpt] Then[illustration not visible in this excerpt]

[illustration not visible in this excerpt]

3.2.2 Expected Utility and von Neumann - Morgenstern Utility Function

The following equation shows how to determine the expected utility. It is assumed, that decision makers (DMs) try to maximize expected utility. (I) DMs place objective probabilities to each outcome (no uncertainty is assumed, but risk). (II) They set certain amounts of utility to outcomes of assets according to the von Neumann - Morgenstern utility function. (III) DMs order assets according to the expected utility.²⁷

[illustration not visible in this excerpt]

Generally the von Neumann - Morgenstern utility function is assumed to be concave. Thus, [illustration not visible in this excerpt]. A crucial aspect of this function is the diminishing marginal utility. In particular: with every additional wealth the marginal utility [illustration not visible in this excerpt] declines. Hence an N., Wilkinson, 2008, p. 89 asset holder with wealth of 100.000€ will not gain the same utility from a 10€ increase, than someone with no wealth. Vice versa he will not suffer as much from a 10€ loss than someone with no wealth.²⁸

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Graphic 3 von Neumann - Morgenstern utility function²⁹

According to different asset pricing models and assumed behavior at financial markets the utility function differs in its shape. The quadratic form is used for the mean - variance model, which was developed by Markowitz.³⁰ The iso - elastic version (also called power utility function) is a major issue in consumption based approaches. Another popular form is also the constant absolute risk aversion utility function (CARA). Thus variations of the utility function are widely used among various econometric models of financial markets. A further implication is that people are in general risk - averse at overall levels of wealth. Beside this the model also states that people can be risk - neutral and risk - seeking. Among these claims the utility function also varies in its shape. In case of risk - neutrality the function is linear, in case of a risk - seeking person it is convex and thus exponential. Further mathematical explanations aiming at these variations are not relevant for the critique in chapter 3.4. Therefore they will be skipped.

Until now markets are described to be perfect, with full information about the future.

Additionally economic agents are completely rational in their behavior, which is defined by the axioms of the EUM. In this thesis the rationality defined by this model will be called conventional or classical rationality.

3.3 Rational Bubbles

A bubble occurs when the actual asset price exceeds the fundamental asset value. If this happens owners of financial assets think they can gain additional income from selling assets for a higher price in the future.³¹ Economists distinguish certain types of bubbles based on agent´s characteristics.

- agents have rational expectations and identical information
- agents have asymmetric information
- rational and behavioral agents trade with each other
- agents have heterogeneous believes

In this section bubbles with agents of the first and second form are presented. These bubbles fit into the so far developed framework described in the previous chapters.

3.3.1 Rational Expectations and Identical Information

As stated above it is assumed that agents behave rationally and have full information about the future (if EMH is taken literally). The presence of bubbles is known and all investors know how other investors would behave. Additionally they behave in the same way. Thus investors are representative agents. Furthermore these agents are risk - averse. Hence it is hard for economists to describe differences between actual and fundamental asset values without violating above stated theoretical frameworks. To avoid violations they invented a bubble term.

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The actual value can be decomposed into the fundamental value ݒ௧ and the bubble term ܾ௧. ݒ௧ equals equation 3.4, ܾ௧ is defined by equation 3.10.

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It is obvious that bubbles grow with the amount of ݎ, thus bubble´s growth rate is equal the discount rate in equation 3.3. A famous example of this bubble was performed by Watson and Blanchard (1982), where the bubble can burst or continue with probability π/ 1-π.

Controversies on Rational Bubbles with Identical Information

Empirical evidence for bubbles suggests that they occur. But the observed bubbles were relatively small and the observations took place in a very tiny time frame.³² Other tests also indicate that these bubbles exist. (See: Engsted, Nielsen (2010), Boucher (2003)). On the other hand economic literature often rejects rational bubbles. Diba and Grossmann claimed that positive rational bubbles can only start at the first day of trading. If it vanishes, it cannot be restarted. Hence rational bubbles are unique events.³³ Furthermore they are saying that bubbles cannot be negative, because this would imply negative asset prices.³⁴ Another strong argument against rational bubbles is the violation of the transversality condition. Brock argues that rational bubbles must be rejected due to the maximization problem of investors. If the actual price is above the fundamental value representative agents would sell asset, because the utility gain exceeds the utility from holding the asset forever. The decrease in demand leads to a fall in asset prices, thus the bubble is eliminated. The same can be applied if the actual value is less than the fundamental value. Demand would increase because the utility gain from holding it forever is higher than from selling it. Hence prices rise and the bubble is also eliminated.³⁵ The violation of the transversality condition is part of a lot of discussions in economic science. Economists also claim that this condition cannot rule out rational bubbles or that this condition can be avoided (See: Kamihigashi (2008, 2009), Zhou (2011)). Tirole also made two important remarks why rational bubbles cannot exist. The first one says that rational investors cannot expect to make speculative gains in perfect markets. The second says that a finite number of rational investors would never enter a bubble, because not every investor will find a buyer and thus some are worse of.³⁶ Hence, rational bubbles are not Pareto efficient and therefore they are avoided. Backward induction also shows the impossibility of rational bubbles. If an asset does not live infinitely (it is liquidated for its fair value at T) the bubble will burst at the end. If asset holders know that they will buy an asset for an inflated price at period T and get less for it when it is liquidated, why would they then buy it at Ǧͳ or Ǧʹ. This backward induction can be done up to the present value. Its conclusion: bubbles cannot exist due to the fact that buyers would know every time that they are buying an asset for an inflated price and that they would have a loss in utility when the asset is liquidated.³⁷ Thus the value of the stock must equal the present discounted value of its future dividends. Otherwise the asset would not be traded if the value is above the fundamental value because investors cannot get rid of it or they would hold it if the asset is below its fundamental value until the asset is liquidated to gain additional utility. Furthermore the bubble term ܾ௧seems to have no logical foundation. Economic literature does not tell what this term describes in reality. Hence the bubble term is a result of lacking explanatory power of the standard economic model (SEM). Deviations between actual and fundamental values cannot be explained clearly by this term, thus it more seems like a mathematical adjustment to prevent the SEM.

A further modification of rational bubbles with identical information is the intrinsic bubble. This type of bubble depends on real dividends and changes if fundamentals change.³⁸ Empirical observations neither support nor reject these bubbles. Cuthertson called evidences “inconclusive.”³⁹ Therefore these bubbles will not be discussed in this work.

[...]

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¹ Goethe, J., 1988: Faust: Part one and Two. pp. 178-179, 181

² Claus, I., Jacobsen, V., Jera, B., 2004: Financial systems and economic growth: An evaluation framework for policy. Wellington, p. 2

³ Krugman, P., Wells, R., 2009: Macroeconomics. 2nd Edition. New York, pp. 271

⁴ Levin, A., Wachter, S., 2012: Explaining the Housing Bubble. In: Georgetown Law Journal Vol 100 No. 4, http://georgetownlawjournal.org/files/2012/04/LevitinWachter.pdf (04.09.2013),pp. 1177-1258, here p. 1179,

⁵ Blackburn, R., 2008: The Subprime Crisis. In: New Left Review 50 (March/April 2008) http://faculty.washington.edu/sparke/blackburn.pdf (24.05.2013)

⁶ Akerlof, G., Shiller, R., 2009: Animal Spirits. p. 32

⁷ Hebblethwaite, C., 2013: Eating locusts: The crunchy, kosher snack taking Israel by swarm. In: BBC News Magazine. 21.03.2013. http://www.bbc.co.uk/news/magazine-21847517 (24.05.2012)

⁸ u.A., 2013: Madagascar hit by “severe” plague of locusts. BBC News Africa 27.03.2013. http://www.bbc.co.uk/news/world-africa-21955740 (24.05.2012)

⁹ Minsky, H., 1992: The Financial Instability Hypothesis. p. 6

¹⁰ Akerlof, G., Shiller, R., 2009. p. 32 - 33

¹¹ Sousa, R., 2009: Wealth effects on consumption - evidence from the euro area. In: European Central Bank Working Paper Series No 1050/ May 2009 http://www.ecb.europa.eu/pub/pdf/scpwps/ecbwp1050.pdf (25.05.2013) p. 5

¹² Sousa, R., 2009. p. 6

¹³ Blundell, R., Bond, S., et. al., 1992: Investment and Tobin´s Q - Evidence from company panel data. In: Journal of Econometrics 51. 1992,pp. 233-257, here p. 234

¹⁴ Blundell, R., Bonds, S., 1992, p. 251

¹⁵ Carroll, C., Fuhrer, J., 1994: Does Consumer Sentiment Forecast Houshold Spending ? If So, Why? In: The American Economic Review Vol. 84, No. 5 (Dec 1994),pp. 1397-1408, p. 1397

¹⁶ Aekerlof. G., Shiller, R., 2009, p. 135

¹⁷ Heim, J., u. Y. The Impact of Consumer Confidence on Consumption and Investment Spending. In: Journal of Applied Business and Economics. Vol. 11 No. 2 (Spring 2010), http://www.na-businesspress.com/JABE/Jabe112/HeimWeb.pdf (02.07.2013) , here p. 1

¹⁸ Graber, P., 2010: Famous First Bubbles. In: The Journal of Economic Perspectives, Vol. 4, No. 2 (Spring 1990), pp. 35-54, here p. 39

¹⁹ Kindleberger, C., Aliber, R., 2005: Manias, Panics and Crashes. Hoboken et. al., p. 9

²⁰ Ball, L., 2012: Money, Banking, and Financial Markets. New York, p. 57

²¹ Fama, E., 1970: Efficient Capital Markets: A Review of Theory and Empiciral Work. In: The Journal of Finance, Vol. 25, No. 2, p. 383-417, here p. 387

²² Further Reading: Gourieroux C., Jasiak, J., (2001); Bailey (2005)

²³ Cuthbertson, K., 1996: Quantitative Financial Economics: Stocks, Bonds and Foreign Exchange. Chichester, p.94

²⁴ Fama, E., 1970, p. 385

²⁵ N., Wilkinson, 2008: An Introduction to Behavioral Economics. London, p. 87ff

²⁶ N., Wilkinson, 2008 P.89

²⁷ Bailey, R., 2005: The Economics of Financial Markets. Cambridge et. al., p. 92

²⁸ Frank, R., 2008: Microeconomics and Behavior. New York, p. 183

²⁹ own illustration

³⁰ Bailey, R., 2005, p. 101

³¹ Brunnermeier, M., 2008: Bubbles: Entry in New Palgrave Dictionary of Economics. 2nd Edition, http://scholar.princeton.edu/markus/files/bubbles_survey.pdf (03.07.2013), pp. 1-2

³² Geiecke, F., Trede, M., 2010: A Direct Test of Rational Bubbles. In: Center for Quantitative Economics Working Paper 13 (2010) http://www1.wiwi.uni- muenster.de/cqe/forschung/publikationen/cqe-working-papers/CQE_WP_13_2010.pdf (09.07.2013), p. 14 - 15

³³ Diba, B., Grossman, H., 1988: The Theory of Rational Bubbles in Stock Prices. In: The Economic Journal Vol. 98, No. 392 (Sep 1988) pp. 746-754, here pp. 753-754

³⁴ Diba, B., Grossman, H., 1988, p. 750

³⁵ Flood, R., Hoderick, R. 1990: On Testing for Speculative Bubbles. In: The Journal of Economic Perspectives Vol. 4 No. 2 (Spring 1990), pp. 85-101, here p. 89

³⁶ Tirole, J., 1982: On the Possibility of Speculation under Rational Expectations. In: Econometrica, Vol. 50, No. 5 (Sep. 1982), pp. 1193 - 1182, here p. 1180

³⁷ Scherbina, A. 2013: Asset Price Bubbles: A Selective Survey. http://www.imf.org/external/pubs/ft/wp/2013/wp1345.pdf (10.07.2013), p. 9

³⁸ Cuthbertson, K., 1996, p. 163

³⁹ Cuthbertson, K., 1996, p. 168