“In the Dutch Republic already by 1623,

“In the Dutch Republic already by 1623, the sum of 12000
guilders- considerably more than the value of a smart townhouse in Amsterdam –
was offered to tempt one tulip connoisseur with only ten bulbs of very
beautiful and extremely rare, Semper Augustus- the most coveted tulip variety”
–  claims BBC. The Dutch republic of the
17th century is known with so-called “tulip mania”, the situation when the
speculators traded tulip’s bulbs for extraordinary sums of money, until
unexpected market collapse happened.  It
was the first example of an economic bubble.

Bubbles are associated with a situation when asset prices
increase dramatically which is followed by a collapse.  When Bubbles happen, asset prices increase so
much that they exceed their fundamental value. The reason is that the asset
owners think they will have a possibility to have a gain from reselling them more
expensive in the future compared to the current price. Asset prices can affect
the real allocation of an economy and that is why it is a matter of a great
importance for economists to understand why the asset prices can be different
from their fundamental value. The valuation of assets is an important question
of a long-lasting debate in economics. 
It is interesting to understand if there is really any rational
foundation to assess the prices of assets such as stocks or money itself.  In finance theory, general assumption is that
the price of an asset equals the present discounted value of its dividends
which is the same as its market fundamental. But in some cases investors value
assets more than their fundamental value and it refers to the well-known
economic distortion- price bubbles.

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Bubbles have always been an intrigue for economists and that
is why there exist many different models with different assumptions and
conclusions, there exist many empirical tests and experimental studies. Models
identify the conditions which are necessary for existence of bubbles. First
type of models is based on the assumption of rational expectations and
identical information. This kind of models insists that bubbles follow an
explosive path. The second class of models assumes that investors are
asymmetrically informed, bubbles can reveal but their existence is not commonly
known. Third type of models refers to the interaction between non-rational
(behavioral) and rational investors. According to these models bubbles can
reveal because there exist limits to arbitrage and thus rational investors
cannot eradicate the price impact which is due to behavioral investors. The
last type of models state the reason of emerging the bubbles is the
heterogeneous beliefs of investors which have psychological biases and they refuse
the fundamental value of an asset.

As the price bubbles are the matter of a huge debate, there
are different opinions and arguments how to rule out the rational bubbles which
happen in certain conditions. For example, in case of rational expectations and
identical information, Tirole (1982) concentrates on general equilibrium and
insists that bubbles cannot persist if everyone knows that the initial
allocation is Pareto efficient. Bubble makes the seller better off but because
the initial allocation was Pareto efficiency, bubble makes the buyer worse off;
hence no one wishes to buy an asset.

In case, when there is no identical information and thus we
have asymmetric information between investors, the prices can have informative
signal roles because they partially help traders’ to aggregate information
(Brunnermeier, 2001). When investors don’t have the identical information, the
presence of bubble is not commonly known. For example, even if everybody knows
that the price of an asset is overvalued, they do not have information about
the knowledge of others. Information asymmetry it is not the situation when
everyone is aware of the fact that the initial allocation is Pareto efficient. If
everyone knew that, no trade would have occurred. The reason is that the buyer
would have known that the seller is better off in expense of him as he is worse

Investors have to gain something in order the trade to occur.
Allen and Gorton (1993) describe one of these kinds of situations when fund
managers have a possibility to gain from trading, by buying the assets which
are overpriced and benefit in expense of their clients as they think fund
managers have an access to the information about trading.

Bubbles can be revealed because of the
limited arbitrage possibilities when rational and well-informed investors
communicate with behavioral investors who are irrational and whose trade decisions
are affected by psychological biases. Although proponents of the “efficient
market hypothesis” argue that bubbles cannot happen in this situation, because
rational investors can go against the behavioral traders and undo their impact
on the price, the literature challenges this view with limits on arbitrage. It
suggests that bubbles can happen because of three kinds of risks which may be
the reasons why the fully-informed and sophisticated market participants cannot
fully eradicate the mispricing which is due to the behavior of the irrational
traders.  The first kind of risk is the
fundamental risk which makes investors hesitate about selling bubble assets in
advance as the positive changes in fundamentals may in fact cancel the original
overpricing. The second type of risk is the noise trader risk. It is risky for
rational traders to lean against the bubble even when there is no fundamental
risk, as behavioral traders might increase the price further and widen the
mispricing. Rational traders with short horizons only partially correct the
mispricing because they care only about the near future and long-run fundamental
value.  For example, the fund managers often
care about short-run price movements. Short-term mispricing and large outflows
can be reasons which force managers to loosen their positions.  Because this scenario is anticipated, fund
managers try to be less destructive against the mispricing. Third type of risk
is synchronization risk (Abreau and Brunnermeier, 2003) which means that a
single rational trader cannot influence the market alone, so the coordination
is required between rational traders of the market. This creates a
synchronization problem.  Each trader has
a problem to decide when to attack the bubble. If he attacks too early, he
losses profits from the subsequent run-up by behavioral traders. If he attacks
late, he will experience the subsequent crash. Each trader tries to guess when
other traders attack the bubble. Traders realize that the economy faces the
bubble but they are not aware of it at the same time that is why the
forecasting is not easy. Traders do not have information whether other traders
have knowledge about the existence of the economic bubble. As we see in models
about arbitrage limits, traders do not try to attack the bubble very
destructively, but they still short the assets which are overpriced due to
bubble. Unlike of this, Abreau and Brunnermeier (2003) write that sophisticated
traders are more likely to ride the bubble than attack it. There exists
empirical evidence which support the “bubble-riding hypothesis”. For example,
in 1998-2000 hedge funds were tilted toward high price technology stocks.
(Brunnermeier and Nagel, 2004) But hedge funds did not go for price-correcting
although they are considered to be rational investors. Also Richard Dale (2004)
writes about the case when Hoared Bank was profitably riding the South Sea
bubble in 1719-1720. But it should be marked that many other investors which
were trying to ride the South Sea Bubble were not very successful. Disappointed
Isaac Newton claimed: “I can calculate the motions of the heavenly bodies, but
not the madness of people”. 
(Kindleberger, 2005, p. 41).


Investors’ heterogeneous
beliefs can be the reason of the bubbles. Investors’ beliefs are heterogeneous
if their opinions are different because of some psychological biases. As Miller
(1977) argues combining short-sale constraints with heterogeneous beliefs leads
to overprice since the impact of optimistic investors have a positive influence
on asset price. It is worth mentioning that the asset price can even be higher
than the most optimistic investor can expect. As Harrison and Kreps (1978)
argue this happens because optimistic investors which currently own the assets
have a possibility to resell them relatively expensive when their optimism level is
decreased. The point is that at this time other investors’ optimism level will
be higher and they wish to buy an asset as optimism is oscillating in time among
investors. As Scheinkman and Xiong (2003) discuss the investors who are less
optimistic prefer to short assets but they are prevented to do so because of the
short-sale constraints. Bubbles which appear due to heterogeneous beliefs are
described with large trading volume and frequent price fluctuations.


As we see,
the phenomena of price bubbles is the question of long-lasting debate as it is
very important for reaching the efficient economic allocation. This paper will
summarize the debate about the rational bubbles. It will concentrate on the
question whether can price bubbles exist under the rational behavior of
investors or this phenomenon requires some amount of “irrationality”. There
will be discussed different models and opinions about “rational bubbles” with
different assumptions and conclusions about how can the bubbles be prevented.
This paper will summarize the findings of some empirical findings and after
analyzing the literature and taking into account different issues or ideas, it
will talk about the author’s own opinion whether the rational bubbles are
plausible or not.