Article Fibonacci -14!11!09

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Equity Prices- Application of Fibonacci Numbers

(A study of India, Singapore, Taiwan,South Korea and Hongkong)

Authors:-

Dr. N. S.Malik

Faculty, Haryana School of Business,

Email:- [email protected]

Rajat Singla

Student, MBA (Finance),

Haryana School of Business,

Email:- [email protected]

Ph. +91925742555
mailto:[email protected]:[email protected]


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Equity Prices- Application of Fibonacci Numbers

(A study of India, Singapore, Taiwan, South Korea and Hong Kong)

Abstract

This paper is mainly aimed to make a prediction about the equity indices of the various markets by

using Fibonacci technique. The predictions made are totally based on the Fibonacci numbers. The

main aim of this paper is to predict the prices and then to find the reasonable opportunity for the

purpose investment as well as to take the proper decision regarding the withdrawal of their investment

from the market. This prediction has its own success rate based on the predictor experience.

Introduction

The most widely used process to analyze investment decisions particularly in financial assets fall into

two very broad categories: fundamental analysis and technical analysis. Fundamental analysis involves

analyzing the characteristics of a company in order to estimate its value, however, Technical analysis

takes a completely different approach; it doesn't care one bit about the "value" of a company or a

commodity for short period. Technicians (also called chartists) are always looking for predicting the

possible movement in the prices of the concerned assets/securities primarily based on the historical

price trends. Despite all the fancy and exotic tools it employs, technical analysis really just studies

supply and demand in a market in an attempt to determine what direction, ortrend, will continue in the

future. In other words, technical analysis attempts to understand the emotions in the market by

studying the market itself, as opposed to its components. If you understand the benefits and limitations

of technical analysis, it can give you a new set of tools or skills that will enable you to be a better

trader or investor. The field of technical analysis is based on three assumptions which are:- The

market discounts everything, Price moves most of the times in random and History tends to repeat.

Fundamental Vs. Technical Analysis

Technical analysis and fundamental analysis are the two main schools of thought in the financial

markets. As we've mentioned, technical analysis looks at the price movement of a security and uses

this data to predict its future price movements. Fundamental analysis, on the other hand, looks at

economic factors, known as fundamentals. Let's get into the details of how these two approaches
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differ, the criticisms against technical analysis and how technical and fundamental analysis can be

used together to analyze securities. Yet there are some differences in both of the above which are:-

At the most basic level, a technical analyst approaches a security from the charts, while a fundamental

analyst starts with the financial statements. By looking at the balance sheet, cash flow statement and

income statement, a fundamental analyst tries to determine a company's value. In financial terms, an

analyst attempts to measure a company's intrinsic value. In this approach, investment decisions are

fairly easy to make - if the price of a stock trades below its intrinsic value, it's a good investment.

Although this is an oversimplification (fundamental analysis goes beyond just the financial statements)

for the purposes of this tutorial, this simple tenet holds true. Technical traders, on the other hand,

believe there is no reason to analyze a company's fundamentals because these are all accounted for in

the stock's price. Technicians believe that all the information they need about a stock can be found in

its charts.

Fundamental analysis takes a relatively long-term approach to analyzing the market compared to

technical analysis. While technical analysis can be used on a timeframe of weeks, days or even

minutes, fundamental analysis often looks at data over a number of years. The different timeframes

that these two approaches use is a result of the nature of the investing style to which they each adhere.

It can take a long time for a company's value to be reflected in the market, so when a fundamental

analyst estimates intrinsic value, a gain is not realized until the stock's market price rises to its

"correct" value. This type of investing is called value investing and assumes that the short-term market

is wrong, but that the price of a particular stock will correct itself over the long run. This "long run"

can represent a timeframe of as long as several years, in some cases. Furthermore, the numbers that a

fundamentalist analyzes are only released over long periods of time. Financial statements are filed

quarterly and changes in earnings per share don't emerge on a daily basis like price and volume

information. Also remember that fundamentals are the actual characteristics of a business. New

management can't implement sweeping changes overnight and it takes time to create new products,

marketing campaigns, supply chains, etc. Part of the reason that fundamental analysts use a long-term

timeframe, therefore, is because the data they use to analyze a stock is generated much more slowly

than the price and volume data used by technical analysts.

Not only is technical analysis more short term in nature that fundamental analysis, but the goals of a

purchase (or sale) of a stock are usually different for each approach. In general, technical analysis is
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used for a trade, whereas fundamental analysis is used to make an investment. Investors buy assets

they believe can increase in value, while traders buy assets they believe they can sell to somebody else

at a greater price. The line between a trade and an investment can be blurry, but it does characterize a

difference between the two schools.

Although technical analysis and fundamental analysis are seen by many as polar opposites - the oil and

water of investing - many market participants have experienced great success by combining the two.

For example, some fundamental analysts use technical analysis techniques to figure out the best time

to enter into an undervalued security. Oftentimes, this situation occurs when the security is severely

oversold. By timing entry into a security, the gains on the investment can be greatly improved.

Alternatively, some technical traders might look at fundamentals to add strength to a technical signal.

For example, if a sell signal is given through technical patterns and indicators, a technical trader might

look to reaffirm his or her decision by looking at some key fundamental data. Oftentimes, having both

the fundamentals and technicals on your side can provide the best-case scenario for a trade. While

mixing some of the components of technical and fundamental analysis is not well received by the most

devoted groups in each school, there are certainly benefits to at least understanding both schools of

thought.

One of the most important concepts in technical analysis is that of trend. The meaning in finance isn't

all that different from the general definition of the term - a trend is really nothing more than the

general direction in which a security or market is headed. Take a look at the chart below:

Figure 1It isn't hard to see that the trend in Figure 1 is up. However, it's not always this easy to see a trend:
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Figure 2

There are lots of ups and downs in this chart, but there isn't a clear indication of which direction this

security is headed.

A More Formal Definition

Unfortunately, trends are not always easy to see. In other words, defining a trend goes well beyond the

obvious. In any given chart, you will probably notice that prices do not tend to move in a straight line

in any direction, but rather in a series of highs and lows. In technical analysis, it is the movement of

the highs and lows that constitutes a trend. For example, anuptrend is classified as a series of higher

highs and higher lows, while a downtrend is one of lower lows

and lower highs.

Figure 3

Figure 3 is an example of an uptrend. Point 2 in the chart is the first high, which is determined after the

price falls from this point. Point 3 is the low that is established as the price falls from the high. For this
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to remain an uptrend, each successive low must not fall below the previous lowest point or the trend is

deemed a reversal. There are three types of trend:

Uptrends

Downtrends

Sideways/Horizontal Trends

As the names imply, when each successive peakandtrough is higher, it's referred to as an upward

trend. If the peaks and troughs are getting lower, it's a downtrend. When there is little movement up

or down in the peaks and troughs, it's a sideways or horizontal trend. If you want to get really

technical, you might even say that a sideways trend is actually not a trend on its own, but a lack of a

well-defined trend in either direction. In any case, the market can really only trend in these three

ways: up, down or nowhere.

Along with these three trend directions, there are three trend classifications. A trend of any direction

can be classified as a long-term trend, intermediate trend or a short-term trend. In terms of the stock

market, a major trend is generally categorized as one lasting longer than a year. An intermediate trend

is considered to last between one and three months and a near-term trend is anything less than a

month. A long-term trend is composed of several intermediate trends, which often move against the

direction of the major trend. If the major trend is upward and there is a downward correction in price

movement followed by a continuation of the uptrend, the correction is considered to be an

intermediate trend. The short-term trends are components of both major and intermediate trends. Take

a look a Figure 4 to get a sense of how these three trend lengths might look.

Figure 4
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When analyzing trends, it is important that the chart is constructed to best reflect the type of trend

being analyzed. To help identify long-term trends, weekly charts or daily charts spanning a five-year

period are used by chartists to get a better idea of the long-term trend. Daily data charts are best used

when analyzing both intermediate and short-term trends. It is also important to remember that the

longer the trend, the more important it is; for example, a one-month trend is not as significant as a

five-year trend. A trend lineis a simple charting technique that adds a line to a chart to represent the

trend in the market or a stock. Drawing a trend line is as simple as drawing a straight line that follows

a general trend. These lines are used to clearly show the trend and are also used in the identification of

trend reversals. As you can see in Figure 5, an upward trend line is drawn at the lows of an upward

trend. This line represents the support the stock has every time it moves from a high to a low. Notice

how the price is propped up by this support. This type of trend line helps traders to anticipate the point

at which a stock's price will begin moving upwards again. Similarly, a downward trend line is drawn

at the highs of the downward trend. This line represents the resistance level that a stock faces every

time the price moves from a low to a high.

Figure 5

A channel, or channel lines, is the addition of two parallel trend lines that act as strong areas of support

and resistance. The upper trend line connects a series of highs, while the lower trend line connects a

series of lows. A channel can slope upward,downward orsideways but, regardless of the direction, the

interpretation remains the same. Traders will expect a given security to trade between the two levels of

support and resistance until it breaks beyond one of the levels, in which case traders can expect a sharp
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move in the direction of the break. Along with clearly displaying the trend, channels are mainly used

to illustrate important areas of support and resistance.

Figure 6

Figure 6 illustrates a descending channel on a stock chart; the upper trend line has been placed on the

highs and the lower trendline is on the lows. The price has bounced off of these lines several times,

and has remained range-bound for several months. As long as the price does not fall below the lower

line or move beyond the upper resistance, the range-bound downtrend is expected to continue. It is

important to be able to understand and identify trends so that you can trade with rather than against

them. Two important sayings in technical analysis are "the trend is your friend" and "don't buck the

trend," illustrating how important trend analysis is for technical traders.

Technical Analysis: Support and Resistance

Once you understand the concept of a trend, the next major concept is that of support and resistance.

You'll often hear technical analysts talk about the ongoing battle between thebullsand thebears, or

the struggle between buyers (demand) and sellers (supply). This is revealed by the prices a security

seldom moves above (resistance) or below (support).
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As you can see in Figure 7, support is the price level through which a stock or market seldom falls

(illustrated by the blue arrows). Resistance, on the other hand, is the price level that a stock or market

seldom surpasses.

In technical analysis our main concentration is to identify the trend of the movement in the stock

prices and it is done with the help of various charts and by using a lot of theories and econometric

models. In the technical analysis mainly the following types of techniques can be used:-

1. Dow theory

2. Wave theory

3. Japanese candlestick

4. Fibonacci Technique & ratios.

For the purpose of the present study, the Fibonacci technique & ratios have been used for

predicting the price movement in the indices namely S&P CNX Nifty (India), TSEC Weighted

Index (Taiwan), STI (Singapore), Hang Seng (Hong-kong), and KOSPI Composite

Index(Korea)

Review of literature:-


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Brown and Jennings (1989) showed that technical analysis has value in a model in which prices are

not fully revealing and traders have rational conjectures about the relation between prices and signals.

Frankel and Froot (1990) showed evidence for the rising importance of chartists.

Neftci (1991) showed that a few of the rules used in technical analysis generate well-defined

techniques of forecasting, but even well-defined rules were shown to be useless in prediction if the

economic time series is Gaussian. However, if the processes under consideration are non-linear, then

the rules might capture some information. Tests showed that this may indeed be the case for the

moving average rule.

Taylor and Allen (1992) report the results of a survey among chief foreign exchange dealers based in

London in November 1988 and found that at least 90 per cent of respondents placed some weight on

technical analysis, and that 2 there was a skew towards using technical, rather than fundamental,

analysis at shorter time horizons.

In a comprehensive and influential study Brock, Lakonishok and LeBaron (1992) analysed 26

technical trading rules using 90 years of daily stock prices from the Dow Jones Industrial Average up

to 1987 and found that they all outperformed the market.

Blume, Easley and OHara (1994) show that volume provides information on information quality that

cannot be deduced from the price. They also show that traders who use information contained in

market statistics do better than traders who do not.

Neely (1997) explains and reviews technical analysis in the foreign exchange market.

Neely, Weller and Dittmar (1997) use genetic programming to find technical trading rules in foreign

exchange markets. The rules generated economically significant out-of-sample excess returns for each

of six exchange rates, over the period 19811995.

Lui and Mole (1998) report the results of a questionnaire survey conducted in February 1995 on the

use by foreign exchange dealers in Hong Kong of fundamental and technical analyses. They found that

over 85% of respondents rely on both methods and, again, technical analysis was more popular at

shorter time horizons.

Neely (1998) reconciles the fact that using technical trading rules to trade against US intervention in

foreign exchange markets can be profitable, yet, longterm, the intervention tends to be profitable.

LeBaron (1999) shows that, when using technical analysis in the foreign exchange market, after

removing periods in which the Federal Reserve is active,exchange rate predictability is dramatically

reduced.


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Lo, Mamaysky andWang (2000) examines the effectiveness of technical analysis on US stocks from

1962 to 1996 and finds that over the 31-year sample period, several technical indicators do provide

incremental information and may have some practical value.

Fernandez-Rodrguez, Gonzalez-Martel and Sosvilla-Rivero (2000) apply an artificial neural

network to the Madrid Stock Market and find that, in the absence of trading costs, the technical trading

rule is always superior to a buyand- hold strategy for both bear market and stable market episodes,

but not in a bull market. One criticism I have is that beating the market in the absence of costs seems

of little significance unless one is interested in finding a signal which will later be incorporated into a

full system. Secondly, it is perhaps nave to work on the premise that bull and bear markets exist.

Lee and Swaminathan (2000) demonstrate the importance of past trading volume.

Neely and Weller (2001) use genetic programming to show that technical trading rules can be

profitable during US foreign exchange intervention.

Cesari and Cremonini (2003) make an extensive simulation comparison of popular dynamic strategies

of asset allocation and find that technical analysis only performs well in Pacific markets.

Cheol-Ho Park and Scott H. Irwin wrote The profitability of technical analysis: A review Park and

Irwin (2004), an excellent review paper on technical analysis.

Kavajecz and Odders-White (2004) show that support and resistance levels coincide with peaks in

depth on the limit order book 1 and moving average forecasts reveal information about the relative

position of depth on the book. They also show that these relationships stem from technical rules

locating depth already in place on the limit order book.

Objectives of the study:-

This study aims to address the following objectives:-

To understanding the price movements in indices belonging to India, Singapore, Korea,

Taiwan & Hong Kong.

To predict the price movements in the respective indices under study.

To evaluate the validity of the price predictions using Fibonacci technique.

To find if there is any similarity in the application of Fibonacci numbers for predicting equity

indices in emerging and/or developed markets in Asia.


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Research Methodology:-

This study will include five indices of India, Singapore, Taiwan, Hong Kong and Korea. Among these

indices, three are emerging markets (India, Taiwan & Korea) where as two are the developed markets

(Hong Kong and Singapore).

For the purpose of the present study daily data on the respective indices have been taken for the period

of three years stating 1st January 2006. The data have been sourced from www.finance.yahoo.com. As

to see the validity of the technique and the success rate chi-square test will be used.

The data will be analyzed by dividing the whole into two parts.

Fibonacci Technique:-

Fibonacci series is most popular widely used method out of various stock selection methods followed

by assets valuers and stock market experts around the world. A large number of Stock market

technical experts around the world strongly believe that Fibonacci analysis gives highly successful

results in predicting the movement of prices.

Fibonacci series was discovered by Leonardo Fibonacci Da Pisa who was born around 1170 A.D.,

(more than 800 years back!). He became prominent mathematician of that time and is credited with

publishing an all time great book on mathematics called Liber Abacci (Book of calculation). In that

world famous book, among other things he comes up with a series of numbers, what we now call the

Fibonacci series. Fibonacci series was discovered long before there were stock markets and amazingly

it works very well in the Stock market as it does with many other natural phenomena. A lot of

phenomena in nature, science, technology, astronomy and astrology is explained by this property of

Fibonacci series.

With the help of these techniques and formulas, you can easily catch up major up moves in your list of

stocks just before it happens and take advantage of those strong up moves to earn guarantee profits in

every trade when ever you identify these moves using Fibonacci techniques and Fibonacci arithmetic

formulas.

In mathematics, the Fibonacci numbers are a sequence of numbers named after Leonardo of Pisa,

known as Fibonacci. Fibonacci's 1202 bookLiber Abaci introduced the sequence to Western European
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mathematics, although the sequence had been previously described in Indian mathematics. The first

number of the sequence is 0, the second number is 1, and each subsequent number is equal to the sum

of the previous two numbers of the sequence itself, yielding the sequence 0, 1, 1, 2, 3, 5, 8, etc. In

mathematical terms, it is defined by the following recurrence relation:

That is, after two starting values, each number is the sum of the two preceding numbers. The first

Fibonacci numbers (sequenceA000045inOEIS), also denoted asFn, forn = 0, 1, 2, ,20 are:-

Above is the Fibonacci numbers in the true sense. But for the purpose of the technical analysis we

have to convert these true numbers into the some percentage or in further parts to calculate some

strong numbers in order to apply them in the analysis. For that purpose we can make the relation of

such numbers with the previous one or even to the earlier numbers. In order to find the strong numbers

calculations have been made as follows:- Some of the strong numbers which this study will used for

the purpose of the predicting the equity indices are as under:-

Originalnumbers

Based ofconsecutives

Based onthe third

one

Based on4th one

Based on5th one

Based on6th one

1 1 0.5 0.333333 0.2 0.125

1 0.5 0.333333 0.2 0.125 0.076923

2 0.666667 0.4 0.25 0.153846 0.095238

F0 F1F2F3F4F5F6F7 F8 F9 F10 F11 F12 F13 F14 F15 F16 F17 F18 F19 F20

0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
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3 0.6 0.375 0.230769 0.142857 0.088235

5 0.625 0.384615 0.238095 0.147059 0.090909

8 0.615385 0.380952 0.235294 0.145455 0.089888

13 0.619048 0.382353 0.236364 0.146067 0.090278

21 0.617647 0.381818 0.235955 0.145833 0.090129

34 0.618182 0.382022 0.236111 0.145923 0.09018655 0.617978 0.381944 0.236052 0.145889 0.090164

89 0.618056 0.381974 0.236074 0.145902 0.090172

144 0.618026 0.381963 0.236066 0.145897 0.090169

233 0.618037 0.381967 0.236069 0.145899 0.09017

377 0.618033 0.381966 0.236068 0.145898 0.09017

610 0.618034 0.381966 0.236068 0.145898 0.09017

987 0.618034 0.381966 0.236068 0.145898 0.09017

1597 0.618034 0.381966 0.236068 0.145898 #DIV/0!

2584 0.618034 0.381966 0.236068 #DIV/0! #VALUE!

4181 0.618034 0.381966 #DIV/0! #VALUE! #DIV/0!

6765 0.618034 #DIV/0! #VALUE! #DIV/0! #DIV/0!

10946 #DIV/0! #VALUE! #DIV/0! #DIV/0! #DIV/0!

Strongnumbers 0.618 0.382 0.236 0.146 0.09

By making the calculation the following numbers have been determined:-

1. .618 or 61.8%

2. .382 or 38.2%3. .236 or 23.6%

4. .146 or 14.6%

5. .090 or 9 %

6. .764 or 76.4%


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Analysis and interpretation:-

Nifty (India)

F-Test Two-Sample for Variances

Variable 1 Variable 2

Mean 4204.982432 4208.648649

Variance 903593.2141 896620.2898

Observations 37 37

df 36 36

F 1.007776898

P(F


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t Critical one-tail 2.379262106

P(T


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t Critical one-tail 2.392377461

P(T


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P(T


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P(T


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t Critical two-tail 2.66328694

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