Ones who applied chaos theory to the financial markets maintained opinions opposite to the Efficient Market hypothesis and CAPM in their studies so far. Their studies gave rise to significant doubts about Efficient Market hypothesis and CAPM, and proved that these theories fail to explain unusual price movements on the markets. Chaos theory brought along consistent explanations about how investors like Peter Lynch and Warren Buffet can beat the market. Also, it has generated important signals and strategies regarding anticipation of panic and downfall periods and about how to catch mega trends which generate high profits using technical and fundamental analysis.

Reminder;

Efficient Market Hypothesis It is impossible to generate a high level of return from the market in the long term and steadily

Capital Asset Pricing Model (CAPM) It is a must to take high risk for high returns

THE WAY TO HIGH RETURNS

Tonis VAGA has filled an important gap in the market estimations and risk-return relationship with his Coherent Market Hypothesis and Non–Linear Model developed within the scope of Chaos theory.

Vagas market model takes off with the presumption that markets tend to move from incoherent conditions to coherent conditions. Market movements will become more coherent and estimable when certain conditions concur. Naturally this will make it possible for high returns with low risk. So, Vaga called this hypothesis the Coherent Market Hypothesis.

4 Different conditions exist regarding markets according to the Coherent Market Hypothesis

EFFICIENT MARKET

1) Random walk market.

2) 0 market return in the long term.

3) Fundamental analysis valuation methods may be applicable for stocks.

4) Stock prices are often close to their actual value.

STATE TRANSITION

1) Uneven transition condition (inefficient market)

2) It is hard to make estimations and distribution charts and parameters must be considered to be able to determine the direction of the movement in order to make estimations.

3) Investors act individually and there is no herd mentality.

COHERENT MARKET

1) Market dynamics are coherent.

2) Market is predictable for a certain period of time.

3) It is possible to make high returns without taking high risks.

4) It applies to both directions. It can be referred as coherent BULLISH market and coherent BEARISH market. 5) Herd mentality is dominant. Mega trends and downfalls are predictable which allow for high returns.

CHAOTIC MARKET

1) It is an inconsistent market.

2) High risks for minor returns are the case.

3) A herd mentality with the prospect of a weak Bearish mentality is dominant.

The Table above shows 4 conditions which might be the trend at the moment according to the Coherent Market Hypothesis.

Now, the question of which one of these conditions is the dominant trend is the most important point an investor must decide on. Afterwards, a strategy in line with this decision must be developed. For example, a golfer knows he/she must use another club, change his/her stand and develop a strategy accordingly when it is windy.

It can be identified using certain parameters which one of these 4 conditions dominant on the markets.

Vaga used two parameters, namely k and h, for return distributions of different market periods.

k: is the measure of the market psychology. k value when it is high means that investors dont know what to do and act individually. In other words, everybody do the right thing on their own opinion and there is no collective movement. Not to mention the influx of money into the market will also increase the k value.

h: is the deviation in key indicators. k value when it is high means that a positive expectation is building up in the markets (triggers the bullish trend). Negative expectations on the other hand decreases the h value. If both positive and negative factors cause fluctuations in the market, then the h value is in a neutral range.

Martin Zweig, being born in 40s, is a person who lived through the effects of the great depression. However, he made higher returns than the average market return in the long term. Zweig also managed to make high returns with low risk too. His success complies with the model developed by Tonis Vaga.

Zweig attributed success to the following two key conditions:

• First, never fight against the key indicators. For example, when balance is disturbed in an economy and the consensus is that things will go worse, dont argue with that (go with the herd). Close your position even if you are in loss.
• Second, never fight against the dynamics of markets. A new trend (either up or down) creates a strong market momentum and you should not carry on your old strategy which is not in line with this trend.

On a second look, you will see that these two criteria of Zweig correspond to k and h parameters. And it is in accordance with the coherent market hypothesis.