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Essays On Prospect Theory And Asset Pricing

This article presents an overview of literature on behavioural and experimental asset pricing theory. We systematically review the evolution and current development of behavioural asset pricing models as an alternate approach to asset pricing in financial economics literature. A review and synthesis of research carried out in behavioural finance spreading across theoretical, empirical and experimental approaches are presented to understand the behavioural dimension of pricing of financial assets. From theoretical perspective, behavioural asset pricing models try to adopt additional behavioural variables into asset pricing process. In terms of empirical investigation perspective, it is documented that econometric and computational advancement takes its biggest place ever in financial literature when compared with the other field. Our review underlines the fact that the direction of advancing a methodology is changing from financial literature to economics due to the fact that there is huge account of raw data available to analyze. Future research direction should be judging the empirical power of the asset pricing models and their role in practice for incorporating a new dimension to the model. The distinctiveness of the study is that this is the first attempt to review literature written on behavioural asset pricing models in the form of structural empirical review. In doing so, the historical perspective of the concept and the place it will take in future are clarified and the way further researches will be conducted are explored.

JEL: E03, G02, G12

Table of content

1. Introduction

2. The CAPM and the Efficient Market Hypothesis

3. Evidence of CAPM Anomalies

4. Modern Finance: Alternative Asset Pricing Models
4.1 Inter-temporal Asset Pricing Model - ICAPM
4.2 International Asset Pricing Model - IAPM
4.3 Multifactor Asset Pricing Models: Fama-French and Carhart

5. Influence of Psychology on Risk and Return
5.1 Prospect Theory
5.2 Heuristics, Biases and Emotions
5.3 Irrationality and Overreaction

6. Behavioral Finance versus CAPM.

7. Conclusion

8. References

1. Introduction

“The chance to win is overestimated by all people. The chance to lose is underestimated by most people.” was already formulated by the moral philosopher and famous economist Adam Smith in his book “Wealth of Nations” in 1776. Two centuries later the behavioural economist Daniel Kahneman confirmed the notion that in situations with uncertainty people are inclined to biased decision-making.

Actual tests of the CAPM on stock data confirmed that the market premium as a single factor may be insufficient to explain stock returns completely. Stambough (1982) among many others found a positive relation between beta and average return, however, it was “too flat” and the intercept was greater than a risk-free bond1. Other effects were observed that could not be explained by the market premium alone; these “anomalies” such as the size factor2, book-to-market (“BTM”) factor3 and momentum factor4 among others led to the development of more extensive models. These models were in some respects more accurate than the CAPM in predicting future returns; however, it remained unclear why these factors actually matter.

So why may investors act irrationally? Do these effects arise from investors whose emotions, biases or believes affect their decision-making process? What additional factors should we add to our model to explain risk and return in real-life? The field of behavioural finance has tried to shed light on this issue by analyzing investor´s psychology and focusing less on which decisions are made but rather on how they are made. This paper will analyze the current research about the affect heuristic, biases and emotions and explore the explanatory power of these effects on future stock returns. As John Nash formulated it: Assuming people to be rational at all times may limit our thought; we cease to exist in the real world but live in a world ruled by theory, banks and money losing our “relation to the cosmos”, in other words the living things that surround us every day.

Although behavioural finance provides explanations why people make biased decisions in situations involving uncertainty, this qualitative knowledge is difficult to incorporate in models. Thus the question remains “ whether behavioural finance can provide better explanations than the CAPM ”.

In Section 1 the paper will start with a brief analysis of the traditional CAPM and its assumptions. Section 2 will depict the current state of research in regard to the validity of the CAPM by evaluating the evidence of anomalies. In section 3 several alternative models will be evaluated. Section 4 will present reasons why these anomalies exist in light of the behavioural finance view. In section 5 I will discuss both approaches and conclude in section 6 with my opinion and recommendations for further research.

2. The CAPM and the Efficient Market Hypothesis

Building on the work of Harry Markowitz and modern portfolio theory, the CAPM was independently developed by Treynor (1961), Sharpe (1964) and Lintner (1965). It built the foundation of modern finance assuming risk-free borrowing and lending as well as rational decision-making.

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In theory, the model combined risk-free assets with a tangency portfolio consisting of risky assets5 to form mean-variance efficient portfolios that would give the investor the optimal investment decision (Sharpe, 1964). Intuitively, beta (ßi), as a measure of sensitivity6, should exhibit a positive relation between the market premium R i, which equals the excess return over the risk-free rate R f, and a specified index return R m.

Probably CAPM´s greatest strength lies in its simplicity and intuitive logic. If the CAPM holds true, the systematic risk, i.e. beta, should explain the total deviation of cross-sectional returns from a stock to the market portfolio. A beta of one would imply that the stock moves one-to-one with the market portfolio, while a beta of two would imply that the stock moves twice as much as the market portfolio. However, if the beta is zero, the stock is not correlated at all to the market portfolio and stock returns will follow a random walk. Furthermore, if the CAPM shows to be valid, we expect

(i) the intercept to be equals zero, and
(ii) the market premium to be positive.

The CAPM and its assumptions are largely based on the efficient market hypothesis (EMH), and the validity of utility maximization. Now let us have a look at the origins of the theories of efficient markets and perfect rationality.

Efficient Markets

The term “homo oeconomicus” depicts a fictive individual whose sole interest lies in maximizing utility by exhibiting purely rational behavior. Her fixed preferences and perfect information set enables her to react immediately to changes in the environment. In finance, she would want to own traditional mean-variance efficient portfolios to maximize stock return, while minimizing volatility, following the Efficient Market Hypothesis (EMH) developed by Fama in the early 1960s. Since markets are efficient, stock prices should reflect all available information immediately.

The efficient market hypothesis was shown valid by researchers asserting that prices do follow a random walk, while incorporating all available information instantly (Samuelson, 1965). Furthermore, Fama (1970) and Sharpe (1964) among others have shown statistically significant results that not only depict a positive relationship between beta and the market premium, but also exhibit a strong internal consistency between the EMH and the CAPM.

Random Walk of Asset Prices

The random walk theory states that asset prices behave in an unpredictable way making arbitrage impossible. Malkiel (1973) argued that it is impossible to achieve consistent portfolio returns in excess of the market return7 by simulating a simple but clever game. Each student started with a stock worth $50, and the daily closing price was determined by a coin flip. While heads would move the stock price a half point higher, tails would move the stock price a half point lower. The evolving trend after a year was then analyzed by professional chartists making the recommendation to buy the stock because there was a recent up movement8.

After the chartists were told that the chance of movements was 50:50 letting prices fluctuate randomly, they found themselves fooled. Malkiel argued that the market and the movement of stock prices could just be as random as flipping a coin, and neither arbitrage nor excess returns are possible because of a random walk and efficient markets.

3. Evidence of CAPM Anomalies

Over time large numbers of researchers attempted to validate the traditional one- factor model and its assumptions. Fischer Black was among the first to question the assumption of risk-free borrowing and lending. Scholes and Black (1972) showed that low beta stocks may actually achieve higher returns than the CAPM would predict. During the last decades multiple studies have shown that beta as a single factor to measure risk fails to explain all cross-sectional variation in stock returns as certain “effects” were left unexplained.

Brav, Lehavy and Michaely (2005) found an extremely positive and significant intercept (alpha) of 20.3% contrary to the CAPM assumption of a zero alpha. An explanation may be that the data was biased by analyst´s overly optimistic forecasts to sell their products. In 1992 Fama and French not only showed that stocks with a low price-to-book and low P/E ratio outperformed the market significantly9, but also found beta to miss any predictive power in explaining stock returns.

During the last decades, researchers increasingly found anomalies questioning the usefulness of the CAPM in explaining stock returns. Prices on the first day of an initial public offering (IPO)10 were pushed up too far (Loughran and Ritter, 1995). Moreover, momentum strategies to buy recent winners were found to yield superior returns because of the noise in expert information (Crombez, 2001). The notion that stocks with a high market value tend to generate lower returns than stocks with low market value11 was shown using common stocks on the NYSE in the period from 1926 until 1975 (Banz, 1981). Fama and French provided further evidence of a BTM effect resulting in higher returns for value stocks than for growth stocks (1993). Overall, there had been increasing evidence that additional factors for stock returns existed that had been left unexplained by the CAPM.

However, the question remained whether these anomalies were due to a mispricing of risk or due to psychological factors. Fama and French were among the most prominent defenders of market efficiency and the precursors of multifactor models. They argued the anomalies to be risk factors that can be incorporated into and explained by more extensive models. The advocates of behavioral finance make biases, emotions and affects responsible for many anomalies. Before discussing and evaluating both theories, I will present the alternative asset pricing models that have been developed so far to capture unexplained variation in stock returns.

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1 one-month US T-Bill

2 Historically higher returns for small-cap than large-cap stocks

3 Historically higher returns for value than for growth stocks

4 Historically higher returns for recent winners than for recent losers

5 Based on Tobin´s Separation Theorem (1958)

6 Covariance = sensitivity of an asset´s return to the variation in the market return

7 Using technical (e.g. trends) or fundamental (e.g. economic data) analysis

8 Classical Momentum Strategy

9 US Stocks from 1963 - 1990

10 4,753 IPOs from 1970-1990

11 Size Effect