Modern Portfolio Theory

Dissertation - Literature Review

This chapter is a detailed exploration of the behavioural finance literature relevant to the research objectives. The author will explore the beginnings and the development of the framework and will critically analyse the points of the literature which are essential for the research conducted in this study.

1.0 Introduction

The financial theory based on Modern Portfolio Theory (Markowitz, 1952) and the Capital Asset Pricing Model (Sharpe, 1964), has long shaped the way in which academics and practitioners analyse investment performance. The theory is based on the notion that all investors act rationally and consider all available information in the decision-making process and that therefore investment markets are efficient, reflecting all available information. According to Baberis and Thaler (2002), rationality is defined thus :

“Rationality means two things. First, when they receive new information, agents update their beliefs correctly, in the manner described in Bayes Law¹. Second, given their beliefs, agents make choices that are normatively acceptable, in the sense that they are consistent with Savage's notion of subjective expected utility²”

Therefore, when an investor learns something new about a future cash flow concerning a particular security, they should respond in an efficient manner to this new information, in turn pushing up the price when the news is good and bringing prices down when news is bad. As a consequence, security prices should fully incorporate all available information almost immediately.

During the 1980's and 1990's, contradictory evidence began to emerge that led many academics to reconsider the foundations of traditional finance. Empirical studies discovered anomalies and excess volatility in the stock markets that could not be explained by traditional finance models and suggested that academics should look to other fields of research to explain these discrepancies.

In response to the growing number of problems, a new area of research emerged which offered an alternative explanation to the essential question of why prices deviate from their fundamental values. In the 1990's, a lot of the focus of academic discussions moved away from the rigid models of traditional finance towards developing theories on human behaviour and how it relates to financial markets. Behavioural Finance is the integration of traditional finance and economics with the psychological and decision making sciences. Its main argument is based on the claim that human behaviour and perceptions represent two crucial elements of financial decision making (Hirshleifer, 2001). Behavioural Finance scholars started the search for new models and ideas to help explain and predict investor behaviour. They assumed that investors may be irrational in their reactions to new information and make wrong investment decisions. As a result markets will not always be efficient and asset pricing may deviate from predications of traditional market models. There are a number of behavioural finance models which try to suggest that agents fail to update their beliefs correctly (Kahneman & Tversky, 1979).

This review will evaluate the literature in the field of behavioural finance and will focus on the two main building blocks - the limits of arbitrage and investor psychology. In the first section, the limits of arbitrage will be explored, with the main focus on market efficiency and noise traders. In the following section, the focus will be on the psychological aspect of behavioural finance, focusing on the extensive experimental evidence which illustrates how people form their beliefs and make decisions.

2.0 Traditional Framework

In the period between the early 1950's and late 1960's, instrumental research in the area of traditional finance was conducted. This was a very productive time for financial thought with many theorists putting together complex mathematical models to try and explain price behaviour. In these models, human behaviour and reasoning were over-simplified as researchers tried to invent practical empirical models. The most influential model which emerged from this period was the Efficient Markets hypothesis (EMH) (Fama, 1970), a theory which, even in today's changing environment, still represents a cornerstone of academic finance. This theory states that markets are considered to be efficient relative to a given information set, providing there are no abnormal profit opportunities for investors trading on the basis of information (Fama, 1970). The EMH implies that it is virtually impossible for investors to consistently beat the market, unless by luck.

The EMH theoretical foundations are based on three underlying principles (Fama, 1970). The first assumption is that investors are fully rational. Therefore, when an investor learns something new about a future cash flow concerning a particular security, they should respond in an efficient manner to this new information, in turn pushing up the price when the news is good and bringing prices down when news is bad. As a consequence, security prices should fully incorporate all available information almost immediately.

Secondly, as irrational investors' transactions are conducted in a random manner, their irrationalities will offset each other, with the result that stock price will not be affected in any way. Subsequently the market may remain efficient even if not all investors are acting rationally. Their investment decisions are conducted in a random way and every trade made is likely to cancel the others out. Therefore an irrational investor will not be able to gain sufficient momentum to influence fundamental asset prices.

The final assumption believes that the rational investor will arbitrage away the irrational investors' influences on the underlying stock price. When a large group of irrational investors trade in a similar style and together they manage to move prices away from their equilibrium value, it is presumed that rational arbitrageurs will quickly notice the mispricing and act accordingly to return the prices to normal. If these three underlying principles hold and people are rational, then markets in turn will be efficient.

There are a number of other quantitative models which emerged out of this traditional school of thought. The modern Portfolio Theory, the Capital Asset Pricing Model and the Arbitrage Pricing Theory are models which underpin the rational expectations based theory. However, there is a large amount of data and research which contradicts their foundations. For example, Fama and French (1993) have shown that the basic facts about the aggregate stock market, the cross-section average returns and individual trading behaviour are not easily understood in this framework.

3.0 Background of Behavioural Finance

As cited by Shiller (2002) :

“Finance from a broader social science perspective including psychology and sociology is now one of the most vital research programmes and it stands in sharp contradiction to much of the efficient markets theory”

In the early 1990's, a lot of the focus of academic discussion moved away from the neoclassical frameworks of stock valuation towards developing models of human psychology and its relation to financial markets. As such, the Behavioural Finance paradigm has emerged in response to the difficulties faced by the traditional framework in explaining …. and in essence it argues that investment choices are not always made on the basis of full rationality. It also attempts to understand the investment market phenomena by relaxing the two doctrines of the traditional framework, that is, firstly, that agents fail to update their beliefs correctly and, secondly, that there is a systematic deviation from the normative process in making investment choice. Bowman and Buchanan (1995) acknowledge that -

“The knowledge on human behaviour should be used in order to help us understand how investors may misperceive the results of their actions and by extension, the functioning of the share market.”

The expectations-based models argue that the irrationality exhibited by investors will be undone through the process of arbitrage (Freidman, 1953). Behavioural Finance argues that there are ‘limits to arbitrage', which allow investor irrationality to be substantial and to be able to have a long-term impact on prices. To explain investor irrationality and their decision making processes, Behavioural Finance draws upon the experimental evidence of the cognitive psychology discipline and the biases which arise when people form their beliefs and preferences (Baberis & Thaler, 2002). Therefore, limits to arbitrage and psychology are seen as the two major building blocks of behavioural finance.

3.1 Limits of Arbitrage

Behavioural Finance does not negate the arbitrage mechanism per se and its price correcting ability. However, it argues that not every deviation from fundamental value created by actions of irrational traders will be an attractive investment opportunity for rational arbitrageurs (Szyszka, 2008). Even when an asset is highly mispriced, many arbitrage strategies, which are designed to correct and eliminate the fundamental mispricing, are ultimately risky and costly for the arbitrageur. Therefore many strategies are perceived to be unattractive and this results in the mispricing remaining unchallenged for a comparatively long period of time.

The theory of arbitrage can be traced back to Friedman (1953), who stated that rational traders will quickly undo any mispricing caused by irrational traders. Friedman's argument is based on two underlying assumptions. Firstly, as soon as an asset deviates from its fundamental value, an attractive investment opportunity will arise from this mispricing. Secondly, rational traders will immediately react to the situation by purchasing the asset, thereby correcting the mispricing. Behavioural Finance doesn't dispute the fact that an attractive investment opportunity will be exploited - it argues that arbitrage strategies developed to correct the mispricing can be both risky and costly, resulting in the mispricing remaining unchallenged.

3.2 Fundamental Risk

When an arbitrageur observes a mispriced asset on the market, he needs to find a similar asset which is priced correctly on another market, to enable him to correct this mispricing, thus taking an opposite arbitrage position. If the trader is unable to take up this position, he faces fundamental risk, that is, the risk that new information comes to the market and changes the fundamental value of the asset in the wrong direction. Even when arbitrageurs are able to hedge the fundamental risk that they face and take a long position in the asset where it is cheaper and a short position in the same asset on another market where it is more expensive, the trader is still exposed to Noise Trader Risk.

3.3 Noise Trader Risk

Noise trader risk can be defined as the risk that irrationality on the market may become stronger and may drive mispricing to an even greater extent (Shleifer & Vishny, 1997). As the mispricing increases, the gap between long and short positions increases which in turn goes against the belief of rational arbitrageurs. If this trend continues, an arbitrageur whose investment horizon is usually relatively short and who often borrows money to fund his trades, may be forced to close his positions before the mispricing is corrected, ultimately resulting in him suffering significant losses. Shleifer (2000) has argued that noise trader risk, the risk from traders who are attempting to buy into rising markets and sell into declining markets, limits the extent to which one should expect arbitrage to bring prices quickly back to rational values, even in the presence of an apparent bubble. Even the most rational arbitrageurs will regret selling a share short which may collect a greater price in the future, even if that price is unreasonably high.

Rational arbitrageurs cannot entirely eliminate the effects of noise traders on the market if the size and the ability of the former group to trade are very limited (Camerer, 1989). Consequently, a single arbitrageur who notices a mispricing in the market faces not only the noise trader risk, but also the risk of synchronization of actions of other rational traders (Abreu & Brunnermeier (2002). Typically, a single arbitrageur does not have the momentum to correct the mispricing on his own. The individual needs other arbitrageurs to follow his strategy. However, the individual does not know if and how quickly other rational traders will react to the same arbitrage opportunity and take up a similar positions. Also, the risk aversion of arbitrageurs by itself limits their ability to cancel noise traders, even if arbitrageurs have infinite buy-and-hold horizons (Shiller, 1984). As stated by Black (1986), if noise traders undervalue or overvalue stocks for a long period of time, the short horizon under which arbitrageurs' performance is evaluated, limits their ability to force asset prices back to their fundamental values. As a result, due to the limitations of arbitrage, noise traders are able to force asset prices away from their equilibrium value for extended periods of time.

Rational arbitrageurs also have to realise that noise trader strategies may become even more extreme and unpredictable, resulting in increased risk for the arbitrageur. This additional risk is referred to as ‘noise investor risk'. Noise investor risk is systematic and non-diversifiable which in turn creates additional volatility on the stock markets. Rational arbitrageurs would not bear this risk unless compensated with higher expected returns (De Long et al., 1990). This once again limits the successfulness of rational arbitrageurs.

3.4 Implementation Barriers

Arbitrage can become a costly activity for a number of reasons. Firstly, transaction costs, which include bid-ask spreads, commissions and price impact, can limit the arbitrageur in exploiting an obvious mispricing. Secondly, the fees charged for borrowing stocks to take a short position can often be off-putting. As cited by Baberis and Thaler (2002), D'Avolie (2002) finds -

“That for most stocks, they range between ten and fifteen basis points but they can be much larger; in some cases, arbitrageurs may not be able to find shares to borrow at any price.”

A further barrier they may face is legal constraints. For example, in many large pension funds, short-selling is prohibited altogether. Finally, the vast amount of research and learning required to exploit a mispricing in a further deterrent. Shiller (1984) found that even if noise trader demand causes a persistent mispricing, it may not be detectable for arbitrageurs unless they expend large amounts of time and resources.

3.5 Evidence

Limits of arbitrage have been confirmed empirically by cases of evident mispricing that remain unchallenged in the market for long periods of time.

An example of this is the case of ‘twin shares'. In 1907, Royal Dutch and Shell merged their interests on a 60:40 basis while both remained separate entities. The stocks of Royal Dutch traded mostly on the US and Dutch Stock Exchange and were to claim 60 percent of the total cash flow, while shares in Shell, which traded in the UK, were to claim 40 percent of the total cash flow of the two firms. Theoretically, the market value of Royal Dutch equity should always be 1.5 times greater than the market value of Shell. Empirical evidence shows that Royal Dutch was sometimes 35 percent underpriced relative to Shell and at times they were 15 percent overpriced. It took until 2001 for the shares to finally sell at their correct values. This is a key example where two shares which are perfect substitutes for each other, would allow the opportunity of easy arbitrage profits. The main risk in this situation is noise trader risk and there is the fear that the share will become even more undervalued in the near future.

A further example of the limits of arbitragecomes from the inclusion of a new stock on the S&P 500. Schleifer (1986) discovered that when a stock is added to the index, the price jumps on average by 3.5 percent and much of this increase remains. A prime example of this is when Yahoo was added to the index, its share price rocketed 24 percent in a single day. Arbitrage is limited in this case due to the fundamental risk and noise trader risk faced by traders. They may find it is very difficult to find a substitute stock and also there is the risk that the price will continue to rise in the short run. In the case of yahoo, its share price was $115 before its addition in the index and it had risen to $214 a month later.

Behavioural theorists show that the strategies required to correct the mispricing can be both costly and risky, thus rendering the mispricing opportunity unattractive and allowing them to continue. The examples of Yahoo and Royal Dutch outlined above confirm this point perfectly.

4.0 Psychology aspect of Behavioural Finance

The theory of limited arbitrage shows that if irrational traders cause deviations from fundamental value, rational traders will often be powerless to do anything about it (Baberis & Thaler, 2002). In order to explain the various investor behaviours in financial markets, behavioural analysts draw on the knowledge of human cognitive behavioural theories and analyse extensive experimental evidence which shows the systematic biases which arise when people form beliefs or preferences.

4.1 Judgement Under Uncertainty

4.1.1 Overconfidence

Behavioural finance assumes that agents may be irrational in their reactions to new information and investment decisions. One of the observations of behavioural theorists has been the overconfidence phenomena. Overconfidence allows many of the anomalies and price deviations in traditional finance to be explained, something which standard economic theory struggles to do.

People can make mistakes when they receive information and form their beliefs. Extensive evidence shows that individuals tend to be overconfident in their own beliefs and judgements (Odean and Barber, 2000). These individuals also tend to be over-optimistic and perceive things to be far better than they actually are. In general terms, overconfidence and over-optimism make investors trade at far too high a volume and sometimes at far too high a price. Research also shows that when an individual has formed an opinion, he often adheres to it and inadequately updates his beliefs in the line of new information. As a result of the above behaviours, people tend to take too many risks and fail to change their beliefs even after occurring heavy losses. This is turn could cause the stock market to overreact.

4.1.2 Representativeness and Conservatism

Conservatism can be defined as the condition where investors are subconsciously reluctant to alter their beliefs in the face of new evidence (Edwards, 1968). This bias affects an investor's decision-making process, as even if an investor changes his beliefs in the light of new information, the extent of that change is relatively small in terms of what it should be under strictly rational conditions.

Edwards (1968) conducted an experiment which tested a subject's ability to revise probabilities in the light of new evidence. This experiment was constructed so that there was only one correct answer to the probability revision problem given to the subject. It found that people tended to revise their probabilities in the correct direction, but tended not to revise them enough. It was found that people respond insufficiently to new information and this has been replicated in a number of papers such as Beach and Braun (1994) and is now referred to as conservatism bias.

Representativeness Heuristic

The representativeness heuristic as documented by Kahneman & Tversky (1974) can also play an important role in driving overconfidence. They recognised that in forming subjective judgments, people have a tendency to disregard base rate probabilities, and to make judgements based solely in terms of observed similarities to familiar patterns (Shiller, 2001). For example, when people try to determine the probability that a data set A was generated by a model B, or that an object A belongs to a class B, they often use the representativeness heuristic. This means that they evaluate the probability by the degree to which A reflects the essential characteristics of B (Baberis & Thaler, 2002).

Under the representativeness heuristic, investors will consider a number of positive company performances as a representative of continuous growth potential and ignore the possibility that this performance is of a random nature. This can encourage the investor to expect instinctively that past price changes will continue, even if his professional training tells him that this should not happen (Shiller, 2001).

4.1.3 Anchoring

Kahneman and Tversky (1974) argue that when forming estimates, people often start with some initial, possibly arbitrary value, and then adjust away from it. Experimental evidence shows that the adjustment is often insufficient, resulting in the tendency to ‘anchor' too much on the initial value. Anchoring is a term used in psychology to describe the common human tendency to rely too heavily or ‘anchor' on one trait or piece of information when making decisions. During the normal decision making process, individuals anchor, or rely too heavily, on specific information or a specific value and then adjust to that value to account for other elements of the circumstances.

In Kahneman and Tversky's empirical study, subjects were asked to estimate the percentage of United Nations countries which are African. In each case, a number between zero and one-hundred was assigned as an initial value and the subject was asked if this was too high or too low, and what adjustment was needed to be made. Despite the fact that each of the subjects knew that the initial value had been determined randomly, by spinning a wheel in the subjects presence, there still was a tendency to be biased towards the initial value.

This phenomenon can be related to the financial markets by looking at how investors pay too much attention to the past prices of securities. Studies have found that the two most common numbers to which investors appear to anchor, are the fifty-two week high and the fifty-two week low for a stock. There is a market tendency for people to assume that a stock has the potential to get back to its fifty-two week high but not breech its fifty-two week low. The problem with this thought process is that it assumes that those numbers are an indication of value and are not just random outcomes based on the fads that can be witnessed in the market.

4.1.4 Mood and Emotion

Judgments based on mood and emotion, rather than rational valuation, can play an important part in investor decision making. A number of recent studies have used environmental factors to investigate whether mood and emotion influence investor choices and stock market prices. Kamstra, Kramner and Levi (2003) investigated Seasonal Affective Disorder (SAD), which tries to find a link between depression and the lack of winter sunlight. Their findings indicate that in markets where SAD is prominent, there is a high amount of seasonal variation in returns. They conclude that the variation is due to the changing risk aversion of SAD investors. Further studies have linked variations in returns to lunar cycles and weather related optimism and pessimism. Stock Markets in the United States of America are slightly more prone to more positive returns on days with less cloud cover (Elton and Gruber, 2007). Additional studies by Saunders (1993) support this notion by suggesting that capital markets, on average, have higher returns on days of good weather than on days with heavy clouds or rain.

A recent study by Lo and Repen (2002), as cited in Elton and Gruber (2007), attempts to measure the affect in real time of emotions through documenting physiological changes experienced by investors. Lo and Repen attached wires to a number of investors at a hedge fund company to enable the researchers to monitor their responses to risk and volatility. The results of their findings indicate that news events and volatility extract emotional responses with experienced traders remaining calmer in these circumstances. Lo and Repen's study ultimately concluded that emotion plays a role in the decision making of trader, which contradicts the theory of rational investors.

4.2 Behavioural Finance Models

There have been a number of models developed in an attempt to capture the behaviour of investors. Perhaps the most influential of these is prospect theory (Kahnemand & Tversky, 1979). This theory will be explored below and will provide the foundations for the research study.

4.2.1 Prospect theory

The traditional finance theory assumes that investors make decisions under uncertainty by maximising the expected utility of wealth or consumption. The expected utility theory, which was formalised by Von Neuman & Margenstein in 1947, shows that if preferences satisfy a number of plausible axioms - completeness, transivity, continuity, and independence - then they can be represented by the expectation of a utility function (Baberis & Thaler, 2002). However, the underlying assumptions of this theory have been shown by many studies to be an inaccurate explanation of how people actually behave when choosing between risky alternatives. Prospect theory seeks to explain decisions which are inconsistent with rational probability assessment and standard utility theory.

The proponents of the expected utility theory assume that investors are fully rational when facing a gamble. The theory assumes that every individual has an information set which might differ among investors, but it also assumes that every individual analyses this data in a rational manner. According to expected utility theory, all information is equally weighted. This is, however, one of the main contradictions with both prospect theory and behavioural finance. Under expected utility theory, risk preferences are captured by the shape of the utility function. Decision makers are risk averse if U(x) is concave, and risk seeking if U(x) is convex, with the most classical financial theory based on the tenet that decision makers are risk-averse. One standard interpretation for risk aversion is that the usefulness of an additional dollar decreases as a person gets wealthier, a principle known as diminishing marginal utility. A utility function which exhibits diminishing marginal utility is concave and hence the decision maker is risk averse.

In relation to the investor's attitude to risk, the expected utility hypothesis adopts a stance which seems to be contradicted by empirical research. Even though it allows for different attitudes towards risk, it does perceive this attitude to be constant. Therefore, if an investor faces a loss or a gain prospect, they will always have the same attitude to risk. Moreover, this theory relies on the assumption that investors think about final wealth states and not about gains or losses, which once again contradicts the behavioural finance paradigm.

Prospect theory seeks to explain decisions which are inconsistent with rational probability assessment and standard utility theory. Prospect theory is an important theory for decision making under uncertainty. It departs from the traditional expected utility framework as it provides a psychological explanation to the behavioural tendencies of portfolio selection. Prospect theory was developed in 1979 by two psychologists, Daniel Khaneman and Amos Tversky, who advised that prospect theory is a descriptive model of decision making under uncertainty which can be used to explain behavioural tendencies. It implies that individuals value gains and losses differently and as a result will base their decisions on perceived gains rather than losses. Therefore, prospect theory evaluates people's attitudes to risky gambles and presumes that agents are risk averse in the domain of gains but risk-seeking when all changes in wealth are perceived as losses. According to Kahneman & Tversky (1979), people violate the expected utility theory in three main ways - the certainty effect, the reflection effect and the isolation effect.

The first problem Kahneman and Tversky found relates to the fact that people tend to put too much weight on certainties. That is, if the investor is faced with a gamble which has an outcome that is certain, they will favour this if the other option is merely probable. This clearly contradicts the expected utility hypothesis which states that a rational investor will make his choice of action only depending on the outcomes utility. The best know counter-example to expected utility theory which exploits the certainty effect was introduced by the French economist Maurice Allias in 1953. Kahneman & Tversky (1979) use a set of experimental questions which are adapted from this original theory to further highlight this effect. They show that people prefer a certain outcome over a probable one, even if the average payoff for the uncertain outcome is far higher. This research agrees with the work previously completed by Allias, and shows a clear contradiction to the expected utility hypothesis in which the rational individual is assumed to choose the option yielding the highest payoff.

The second critique redefines the investor's attitude towards risk. In relation to the expected utility hypothesis, the investor's attitude towards risk is assumed to be constant and is usually risk averse. However, Kahneman & Tversky (1979) state that this is not in line with reality and find that an individual's attitude towards risk is not a constant. They found that when a person is faced with a gamble which yields a positive outcome in relation to their initial level of wealth, then they are risk averse. However, K&T find that this attitude changes to risk seeking or loving when the gamble contains negative outcomes in relation to the initial level of wealth. For example, when a gamble was offered where you could either loose 3000 for certain or lose 4000 with a probability of eighty percent, an overwhelming majority selected the uncertain gamble, even though the utility would be lower for a rational individual. If a person was given two identical choices, one expressed in terms of possible gains and the other in terms of possible losses, people would choose the latter even if they achieve the same result. According to prospect theory, losses have a more emotional impact than an equivalent amount of gains. For example, based on the traditional way of thinking, the amount of utility gained from receiving £50 should be equal to a situation in which you gained £100 and then lost £50. In both circumstances the end result is a net gain of £50. However, despite the fact that you still end up with the same result, the majority of people would favour a single gain of £50.

The following experiment by Kahneman and Tversky (1979) illustrates prospect theory. A number of subjects answered questions which involved making judgements between two monetary decisions involving prospective gains and losses.

The following questions were asked in the experiment -

You have $1,000 and you must pick one of the following choices :

A- You have a 50% choice of gaining $1,000 and a 50% chance of gaining 0.

B- You have 100% chance of gaining $500

You have $2,000 and you must pick one of the following choice

A - You have a 50% choice of losing $1,000 and 50% chance of losing 0.

B - You have 100% chance of losing $500.

The results of the study found that the majority of people chose B for the first question and A for the second question. This implies that people are prepared to reconcile for a reasonable level of gains, even if there is a possibility of winning more, but are ready to participate in risk-seeking behaviour where there is the possibility they can limit their losses. Therefore, people place greater emphasis on their losses than an equivalent amount of gains. This is once again clearly in contrast with the expected utility theory as individuals focus on the gains or losses made instead of on final wealth.

The final critique that Kahneman & Tversky (1979) explore is the isolation effect. It tries to explain people's behaviour when facing a complex situation and concludes that in order to be able to evaluate information, investors tend to evaluate it in isolation of other information. The results show that people do not make decisions based on the final outcome, instead investors isolate the later game and the probabilities involved and their decision will wholly depend on the probabilities of the part of the game they are involved in at that time.

Prospect theory has an asymmetric attitude towards risk, depending on how the potential gains or losses relate to a certain reference point. This reference point could be current wealth, a neighbour's wealth, or the price at which an asset is purchased (Elton & Gruber, 2007). Kahneman and Tversky's utility function is concave above the given reference point and convex below the point. This structure creates risk aversion with respect to gains and risk seeking with respect to losses and can lead to different decisions depending on whether the outcomes are posed as gains or losses.

Prospect theory can also be applied to explain the occurrence of the disposition effect. The disposition effect is defined as the tendency for investors to hold on to losing stocks for too long and sell winning stocks too soon. The rational view of an individual would be to hold on to the winning stocks in order to further their gains and increase profit margins and to sell losing stocks in order to minimise potential losses.

There has been a number of empirical studies which agree with the above theory. Odean (1998) analysed the accounts at a large brokerage firm and found that there was a greater tendency to sell stocks with paper capital gains than losses. A further study found a similar effect among all types of investors in Finland where the investors failed to recognise losses. As cited by Elton and Gruber (2007), a study far afield from investing by Chen, Santos & Lakshminarayanan (2005), has identified loss-aversion behaviour in Capuchin monkeys, suggesting that loss aversion is instinctive.

Prospect theory can thus be seen to be applied to a diverse range of situations which appear inconsistent with standard economic rationality.

5.0 Conclusion

In conclusion, the last five decades have seen the introduction and development of many leading theories in financial literature. One of the main theories to dominate this period was the subject of efficient markets. The Efficient Market hypothesis was initially well-favoured but it relied on many unrealistic assumptions. More recently, scholars and investment professionals have started to investigate an alternative theory to try and explain the mispricing which occurred using the traditional models. Behavioural finance attempts to inform people of the emotional factors and psychological processes which influence the individuals who invest in financial markets. Behavioural finance argues that not all investors are rational and are able to value correctly their decisions or the importance of new information. Behavioural Finance does not attempt to replace the traditional views and models of finance. Instead, it looks to fill some gaps and to offer realistic explanations as to why mispricing can occur in the stock markets.

This chapter has attempted to outline the key factors of behavioural finance and highlighted prospect theory as one of the main models used to demonstrate this theory. Based on this literature review, the subsequent chapter will address the methodologies used to achieve the research objectives.

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