Efficient Market Hypothesis
B.Sc. 4th Year
Prakash Chanda Gupta
Econophysics
Content
• Concepts, Paradisms and Variables
• Arbithrage Efficient Market Hypothesis
• Algorethmic Complexing Theory
• Amount of Information in financial time series
• Idealize system in Physics and finance.
Concepts, Paradigms and Variables: Market
Financial markets are systems in which a large number of traders interact
with one another and react to external information in order to determine
the best price for a given item. The term market means the aggregate of
possible buyers and sellers of a ce rtain good or services and the transection
between them. A financial market is market in which financial assets are
traded. These are systems in which a large numbe rs of traders interact one
another and react to external information in order to det ermine the best
price for a given item.
Concepts, Paradigms and Variables: Market
In financial market people trade financial commodities and other
fungible items (items which can be exchange or buy or sell at the
same price) of value at low transection costs at price that reflect
supply and demand.
The goods that are sold in markets are stocks and commodities
along with services there are many types of markets which are
capital market,commodities market, money market,insurance
markets etc.
Nature of Market
Actually the financial market is highly non-linear,
deterministic and hi gh dimensional As it is impossible to find
all its dimension and underlying sub dimensions we assume
that the financial market follows the stochastic process.
When one inpects a time series of the time evolution of the
price volume and no. of transection of a financial product,
one recognizes that the evoluti on is unpredictable.
Arbitrage
A key concept for the understanding of markets is the concept of arbitrage which is the
process in which someone purchases and sale the financial assets or same or equivalent
security in order to profit from price discrepancies (differences). In another way it is the
process of taking advan tage of different price of same of different places.
For example:
Suppose the price of orange is Rs. 95 per Kg in Gulmi. Rs. 125 in Kathmandu at same
time. Then anybody can buy oran ges in Gulmi and sale it in Kathmandu to make profit
instant ly. This type of profit is considered as risk free.
If someone exploits the arbitrage condition, then he reduces the r ate of gain from that
process at the same time. Someone buying oranges in Gulmi increases its price there and
exporting excess of it in Kathmandu reduces its price there. After a sufficiently long
time the price becomes almost equ al so the arbitr age possibility neutralizes.
Summary
1.New arbitrage opportunities continually
appear and ar e discovered in markets but
2.As soon as the arb itrage opportunity
begins to be exploited the system moves
in a direction th at gradually eliminates
the arbitrage opportunity.
Efficient Market Hypothesis:
Markets are the complex systems that incorporate information about a given asset in the time
series of its price. The market itself determines the most rational price of the asset.
A market is said to be efficient if all the available information is instantly processed when it
reaches the market and it is immediately reflected in a new value of price of the assets
traded. According to EMH property anticipated price fluctuate randomly. There are three types
of efficient market hypothesis they are.
1. Weak form of EMH
2. Semi-strong form of EMH
3. Strong form of EMH
Efficient Market Hypothesis:
1. Weak form of EMH
It implies that the market is efficient, reflecting market is efficient, reflecting all the market information. This hypothesis assum es
that the rates of return on the market should be independent. Past rates of return have no effect on the future rates.
2. Semi-strong form of EMH
It implies that the mar ket is efficient, reflecting all the publically available information. This hypothesis assumes that stocks adjust
quickly to absorb new information. The semi strong form of EMH also incorporates the weak form.
3. Strong form of EMH
It implies that the market is efficient, it reflects the information both public and private. It incorporates both weak and semi strong
form of EMH. According to this form no investa can earn above average value even through new in formation is supplied.
Martingle
Martingle is the stochastic (non-deterministic) process obeying
the conditional probability given by the equation
𝐸
𝑋
!"#
|𝑋
$
, 𝑋
#
… … . , 𝑋
!
= 𝑋𝑡
…..(1)
Where, 𝑋
!"#
=
Expected value of price of a given asset at a time t+1
𝑋
$
, 𝑋
#
… … . , 𝑋
!
= previous values of prices.
Note: The efficient market hy pothesis was formula ted explicity in 1965 by Samue lson, who showed mathematically tha t property anticipated prices
fluctu ate rand o mly using the hypothesis of ratio n a l behaviour and market efficiently and able to de m onstrate the above rela tio n given by equation (1)
Martingle
A Martingle is the model of game where knowledge of past events never
help to predict the mean of the future events. In particular a martingle is
a sequence of random variable for which at a particular time in the
realized sequence, the expectation of the ne xt value in the sequence is
equal to the present observed values for a non-martingle process. It is
possible to produce the uncertainty by using prior information.
Complexity of Information
The complexity of a given piece of information is the length of the shortest possible
description of the string (any other information) in same fixed universal description
language. The length of shortest descripends – depends upon the choice of
description language. The minimal sensible length of the information is called the
kolmogrov complexity.
The Kolmogorov complexity of any information string cannot be more than a few
bytes larger than the length of the string itself. Strings whose Kolmogorov
complexity is smaller relative to strings size are not considered complex.
Algorithmic Complexity Theory
The algorithmic complexity theory, developed by Kolmogorov and Chaitin in the middle of
1960s, states that “ the complexity of a given object coded in an n-digit binary sequence is
given by bit length k
(n)
of the shortest computer program that can print the given symbolic
sequence”.
Algorithmic complexity theory helps us understand the behaviour of a financial time series.
Within algorithmic complexity theory a series of symbol is considered unpredictable if the
information embodied in it cannot be compressed or reduced to a more compact form.
This statemen t is made more formal by saying that the most efficient symbols has the some
length as the symbol seque nce itself.
Algorithmic Complexity Theory
Actually, Algorithmic complexity theory helps us to determine/understand the behaviour of a financial time series of the following
sense:
1. Algorithmic complexity theory m akes a clearer connection between efficient m arket hypothesis and the unpredictable character of
stock returns. Such a connection is now s upported by the property that the time series that has dense amount of non-redundant
economic information exhibits st atistical features that are almost indistinguishable from those observed in a time series that is
random.
2. Measurements of the deviations from the randomness provide a tool to verify the validity and limitations of efficient market
hypothesis.
3. From the point of view of ACT, it is impossible to discriminate between trading on ‘noise’ and trading on ‘information’
(fundamental information concerning the traded asset, internal and external to the market). It detects the no. of differences between a
time series carrying a large amount of non-redundant economic information and a pure random process.
Amount of information in financial Time series
In ideal market the time series of price of financial assets doesnot reflect any valuable and important information because its
size is very very large and the data appears to be random. Financial time series looks unpredictable and their future values
according to efficient market hypothesis, are essentially impossible to predict. But in reality the opposite is true. The time
series of the price in financial market carries a large amount of non-redundant information. Because the quantity of this
information is large. So that it is difficult to extrac t a subset of economic information associated with the some specific aspet.
The difficulty in making predictions is thus related to abundance of inf ormation, net a lack of it.
The market in which certain information can affect the price in fixed way is not efficient. This allows us to detect the presence
of information in the given financial data. Using a response of market price in fixed direc tions to a certain information, we
can devise arbitrage opportunity which lasts until the market recovers efficiency in mixing all the sources of information
during the price information.
Idealized system in Physics and economics
In physics problems are solved starting with a very simplified assumptions. Sometime the assumptions could be very
idealized that nature would never offer such ideal processes and systems. Neve rtheless the idealization of situations helps us
to solve very challenging and analytically unsolvable problems. After solving problems with ideal approximations we can
make some realtime generalizations to make the ideal situation a real one. One cannot imagine physics in this stage without
idealizations such as frictionless motion, point motion, massless string, reve rsible processes and so on. Physicists use these
abstractions in order to develop theories and to design experiments with the realization that idealized systems only
approximate real systems and the behaviour of real system will always deviate from that of idealized system.
Similar approach can be taken in the study of financial system. We can a ssume realistic ‘ideal’ conditions such as perfectly
efficient market and within this ideal framework develops theories and perform empirical tests. Real markets are only
approximately efficient. Thus the validity of the assumptions made under the pa radigm of efficient market hypothesis. We can
characterize the statistical properties of the random process observed in financial market.
