Fundamental Price

The determinants of stock prices are often a matter of debate. Economists and financial market participants hold different views as far as the pricing of an asset is concerned. Economists believe that the price of an asset should equal to the fundamental value, given the assumption of rational behavior and of rational expectations.

Market fundamental is the value of an asset depending on the current and future information about the returns from the asset. Any divergence of the actual price from the fundamental price will give rise to a ‘bubble component’ (Lucas 1978). However Brooks and Katsaris (2002) claimed that in certain periods the fundamental value of an asset seems to be irrelevant in the pricing policy.

On the other hand, financial market participants believe that fundamentals are only part of the price of an asset and extraneous events may well influence the price (Blanchard and Watson 1982). Further economists have overstated their views as there may be rational deviations of price from the fundamental value that is rational bubbles. Also there has been no consensus which view is correct (Allen and Gorton 1993).

There are two approaches which can explain the behavior of prices in the equity market during the 1920s, the 1980s and the 1990s. These periods witness market prices growing significantly followed by abrupt market collapses (Brooks & Katsaris 2005). Firstly, there was a non-linear relationship between actual prices and fundamental values. The second approach was that self-fulfilling expectations and speculative bubbles causes the actual price to diverge far away from the fundamental values.

As such studies on the relationship between actual price and fundamental value were important and the indirect test was used to identify the presence of bubbles in the financial data (Shiller 1981). However, the indirect test is not a good approach as it suffers from the problem of interpretation since bubble effects in the stock prices could not be distinguished from the effects of unobservable market fundamentals (Brooks & Katsaris 2005). Also the indirect test is a joint test for the presence of bubbles. It only provide ‘hints’ of there existence (Brooks & Katsaris 2002).

For this reason, the direct test which directly tests for the presence of bubbles was developed and adopted (Flood and Garber 1980). Under this particular test, the researcher select the type of bubble that might be present in the data set and examine whether this form of speculative bubble have any explanatory power for stock market returns. Financial Crisis

The crises of Oct 1929 and the Oct 1987 raised several questions regarding market rationality and the relevance of fundamental values. Several researches claim that this movement was of irrational herd behavior. However, the rational bubble theory rejects such a conclusion as investors were being compensated for such a behavior (Brooks and Katsaris 2001).

On the black Thursday 24^th Oct 1929, Dow Jones Industrial registered a loss of an average of 39.6% within a week. Wanniski (1978) claims that the correction of stock prices were expected since the presence of bubbles resulted in an overvalued market. The main problem with the bubble is that it will burst at a given time and create a financial panic in the market.

Bubbles

Blanchard and Watson (1982) defined bubbles as the movements in the price, apparently unjustified by information available at the time, taking the form of a rapid increase followed by a burst or at least a sharp decline. A famous example will be the South Sea Bubble whereby the stock value of the South Sea Company rose by over 700% during the first half of 1720. And at the end of 1720, the price fell back to about fifty percent of its value at the start of the year.

Speculative Bubbles

Brooks & Katsaris (2003) defined speculative bubble as a persistent, systematic and increasing deviation of prices from their fundamental value defined as the risk-adjusted present value of all expected future cash flows.

Boucher (2003) defined speculative bubbles as the difference between the market value of a security and its fundamental value. He classified bubbles into three main categories: rational bubbles, irrational bubbles, fads and noise traders and finally inefficiencies that are due to imperfect and heterogeneous information.

Speculative Bubbles are generated when investors amend their information set regarding the future cash flows of an asset. The expected future price will be a good determinant of demand and supply. A positive expected bubbles return will lead to an increase in demand resulting in a deviation from their fundamental values (Brooks & Katsaris 2001).

Hamilton (1986) showed that self-fulfilling speculative bubbles may well be formed part of the fundamental value. West 1984 argued that self-fulfilling speculative bubbles may account for the excess volatility of stock prices. Tirole (1982) and Obstfeld and Regoff (1983) showed that a self-fulfilling appreciation of asset prices is difficult to reconcile with optimizing behavior in general equilibrium.

The characteristics of the speculative bubble is that of a positive feedback sent to the market from the increasing prices to an increase in investors’ enthusiasm, hence increasing the quantity demanded and finally the price increases. However it should not be ignored that an asset cannot go on increasing in price i.e. at a point in time, the price will be stagnant, and then there may be a negative turn in the sequence of prices and demand (Shiller 2001).

Rational bubble

Rational bubble theory can be defined as an investor acting rationally in inflating prices (Brooks and Katsaris 2001). The theory of rational bubbles shows that even with rational expectations, asset price deviates from the fundamental value. The self-fulfilling expectations about the positive future price increase help the bubbles to grow even faster. Furthermore it can be noted that rational bubbles have explosive conditional expectations implies that a negative rational bubbles component cannot exist, because given free disposal, stockholders cannot rationally expect a stock price to decrease without bound and hence to become negative at a finite future date (Sophia E.Stavrati 2006).

An important factor of the rational bubble is that investors are aware that share prices are inflated however; they believe that there is a high probability that the bubble will grow which will lead to a higher return than expected, as they are compensated for the probability of a market crash. This may be illustrated as the rational behavior of investors whereby they follow the market. As James (2003) put it in his own words, “one may be a fool for buying an asset which is overpriced, one will profit if there are greater fools who will pay even more for the asset”.

Historically stock prices have the tendency to rise substantially over an extended period and then fall very quickly. Such movements can be hard to reconcile with the notions of investor rationality and market efficiency. But literature developed in the recent years showed that consistent change of stock prices from the fundamental does not necessarily reflect irrational behavior on the part of the investors. This is so because there is an expectation to hold the asset till the indefinite future and to make a capital gain. Also, stock buyers will only be willing to pay for a higher price than that set by the fundamental if they believe that someone else will subsequently pay a higher price and thus they will be compensated for holding an inflated asset (Koutas 2003).

The existence of bubbles has numerous implications both for the asset and risk management practices and for the authorities in charge of the monetary policy and financial market supervision. In order to avoid a financial crash, bubbles test can be used to identify the risk associated and impose measures in order anticipate the financial crash for e.g. freeze the market to avoid speculation about the share price of an asset. (Sebastien Morin, 2003)

Bubbles Collapse

Stochastic bubbles are bubbles that may either survive or collapse in each period (Schaller & Van Norden 1997). The existence of stochastic bubbles means that there are two regimes generating the market, one where the bubble collapses and one where it survives. This factor is taken into account by rational investors when deciding whether or not to hold an asset. For example in the surviving regime, returns should be comparatively high so as to compensate the investor for taking additional risk in terms of the bubble component.

Schaller & Van Norden (1997) showed that bubbles are more likely to collapse when they comprise a large portion of the stock price. Also, in periods where positive bubbles collapses, returns should be negative and the probability of collapse should increase while the bubbles grow larger. An exception to the above will be the case of rational bubbles.

Situation giving rise to bubbles

It is argued below that one of the manifestations of asymmetric information in this context is that asset prices can deviate from their fundamental values and be subject to bubbles. The activities of bad portfolio managers may cause bubbles (Allen and Gorton 1993).

They defined the bad portfolio managers as those who do not have the same information set as good portfolio managers. They showed how the bad portfolio managers try to speculate the market and make a capital gain despite knowing that if the bubbles burst, investors will be losing their money that has been invested.

Overinvestment and malinvestment may create bubbles in the market. Overinvestment means investing in too many capital assets to meet the required demand. On the contrary, malinvestment means investing in the wrong capital assets to produce goods and services. A most recent example will be Asian Financial Crises 1997.

The Chinese Government injected a lot of assets in the red chips companies in the expectation to increase the share price. The stock price did increase but it did not last for long as a bubble was being created (Jim Saxton 2003). The bubble component caused a financial panic and many other markets suffered from this situation.

A bubble can arise when the actual price is directly related to its own expected rate of change, as normally occurs in asset markets. In this situation, the arbitrary, self-fulfilling expectation of price changes may drive price changes independently of market fundaments and thus being in a state of bubbles (Flood and Garber 1980).

EMH

The concept of bubble is against the Efficient Market Hypothesis (initiated by E. Fama). The deviation of the asset price from the fundamental value caused bt the bubble is often driven by psychological factors. It can be noted that Efficient Market Hypothesis ignores market psychology in the formation of a stock price.

Also, the random walk theory is used to test for the efficiency of the market. It implies that stock prices are expected to change randomly and investors cannot forecast the fluctuations. In simple terms, stock prices are not determined by the law of demand and supply. As such the random walk theory contradicts with fundamental analysis. It seems to describe the stock price behavior without considering the fundamental value (Sophia E.Stavrati 2006).

The market is further considered to be not efficient if there exist speculative bubbles in the market. A speculative bubble can be distinguished as a persistent rise in the price of an asset. The initial rise creates forecasts of further rises and attracting new buyers, in general speculators interested in the rise of the price of the asset rather than in its use or its potential incomes (Shiller 2002). Also the fundamental value of a stock is hard to renconcile and furthermore if the bubble last for a long time, the fundamental relation may not be observed except in very long sample periods.

The existence of speculative bubbles, when stock prices deviates from the level suggested by market fundamental, does not necessarily violate the rational expectations and efficient market hypothesis. Investors cognizant of market overvaluation are compensated for the risk of the bubble collapsing with the excess positive returns (Waters & Payne 2005).

However in order to be able to achieve the above, two conditions should be met. Firstly, there must be restrictions in short selling (Li and Yung 2004) and secondly in the presence of informational asymmetries and market efficiency, the stock prices should be underpriced limiting the ability to capture the market (Ghosh et al 2000).

Further bubble is not a random deviation of price from value, for the law of large numbers suggests that purely random deviations will wash out over time without any necessity of collapse.

Nevertheless, if investors have finite time horisons then the resale price of their assets becomes a major determinant of their investment decisions and a bubble can emerge. This is not however sufficient. It has been shown that even with a finite time horizon, a bubble can not exist if expectations are rational, and that is if investors’ forecasts are optimal. Hence, bubbles require both finite time horizons and non optimal forecasting. Stated differently, bubbles require inefficient markets.

Ruling out bubbles

Koutas (2003) stated that a firm may rule out bubbles if it imposes a limit on the highest price of the asset. As such once the asset reached the maximum price it can no longer be governed by the market forces which are the most deterministic variable for the price of an asset.

Bubbles cannot exist in a model with a finite number of infinite-lived rational agents since they will be rule out as and when they existed (Tirole 1982). For example if an asset price has a bubble component, market participants will short sell the asset, invest some of the proceeds in order to pay for dividend stream and have positive wealth left over. As such the arbitrage would rule out bubbles.

Finally he has shown that in the context of an overlapping generations model, a bubble cannot arise when the interest rate exceeds the growth rate of the economy. This is because the bubble would eventually become infinitely large in relation to the wealth of the economy, thus violating some agent’s budget constraint.

There is a need to counter bubbles as and when they arise. As bubbles are the causes for financial crashes example include the south sea bubble, Mississippi bubble, the great crash of 1929 and this may disrupt the functioning of the financial market. Banks can counter bubbles through the tools available to them. For instance, by imposing early credit restrictions or by influencing forecasts in way of publishing any overvalued stock. However in order to be able to carry out this task, they need to, first of all, detect the speculative bubbles and detecting these bubbles are not always an easy task.

Two main reasons are:

• Speculative bubbles definition is somewhat ambiguous and controversial. For example it covers in fact two kinds of bubbles: rational bubbles and irrational bubbles.

• Speculative bubbles test have some drawbacks. The major drawback is based on the interpretation as the test can sometimes confuse with other phenomenon.

Moreover, bubbles affect the riskiness of the market and it may also contribute to the fluctuations of the macroeconomic variables as it had been the case during the occurrence of the October 1929 Wall Street Crash and the Great Depression. It is interesting to note that bubbles create excess demand in the market while supply remains constant (Rappoport and White 1993). Therefore, in other words, there will be a shortage and this will lead to an increase in the share price.

Flood and Hodrick (1986) stated that test should be carried out in the specification of model. Most often the model is not rightly specified which rule out the bubbles despite their very existence. He further demonstrated how the failure of variance bound tests should not be taken as evidence of rational speculative bubbles. Finally he argued that designing a bubble test is hard since the path of a bubble in the data would like some forms of incorrect modeling of agents’ expectations.

Mistakes for model specification of intrinsic value of a bubble can be avoided in an experiment in which intrinsic values are controlled as via the experiment it is easier to control the variables but in real life situations it is not always the case.

Boucher (2003) used the classical Engle-Granger cointegration test to test for the presence of bubbles in the US market. He concludes that rational bubbles exist in the market. However the long term relationship should not be ignored as stock prices adhere to fundamentals in the long run and that mechanism is asymmetric. The Convention co-integration test does not take into account the long term relationship.

Hassan and Jung-Suk Yu (2006) tested for the presence of rational speculative bubbles for the rapidly growing frontier emerging stock markets (Bangladesh, Cote d’Ivoire, Ecuador, Ghana, Jamaica, Kenya, Mauritius and Trin. & Tobago). The identification of rational bubbles can be important in policy making decisions and international portfolio diversification.

They, first of all, used the long established bubble tests (co-integration test, Unit Root test and Variance Ratio test) and found that they did not reject the null hypothesis of bubbles. Finally they use the fractionally-integrated autoregressive-moving average model, denoted ARFIMA, They concluded that using the ARFIMA model they did not find any evidence for the presence of bubbles.

Suraya et al. (2006) used the Duration Dependence Test to test for the existence of bubbles in the Malaysian Stock Market. This duration dependence test builds on the rational dependence. According to the duration dependence method, the probability that a run of positive abnormal ends should decrease with the length of the run (sequence of returns of the same sign) if bubbles exist in the market. The study showed that bubbles were present in the market. However, the pre-crisis period (1994-1996) was bigger than that of the post crisis period (1999 – 2003)

Renatas Kizys and Christian Pierdziorch (2007) studied the international linkages of the stock markets of the Central Eastern Europe (CEE) countries. The analysis was based on whether the long-term international linkages of the stock markets of the CEE countries reflect international linkages of fundamentals or international linkages of speculative bubbles.

The results provide evidence about co-integration between speculative bubbles and it was further concluded that the Hungary and Poland were co integrated during the period from 2000 to 2005. On the other hand, for the CEE countries, there have co-integration in the early years of the 20^th century but for the period 2004 and 2005, they were not co integrated. This co-integration sound important as the existence of co-integration indicate the presence of bubbles.