INTRODUCTION:

Investments are considered to be the differentiate factor amongst the rich and the poor. While choosing investments equity plays a predominate role because of its higher return than any other investments. Good proposition of equity holdings of any individual can yield a better return compared to any other asset holdings. This makes the vitality to study the equity investment in detail and the methodology to pick and choose the stock. Adequate research has to be done before investing in equity shares. The volatility of stock prices and market movements were predicted in their study by GoutamTanty, P K Patjoshi (2016) through ARCH and GARCH models with clear picture of demonstration of the volatility clustering of stocks for investment decision purpose.

Panel Data Regression method was adopted by Bikramaditya Ghosh (2017) with Fixed Effect Model to prove the link and to develop a possible predictive model, which eventually will highlight FPI flows. Mulukalapally Susruth (2017) in their study described the volatility forecasting for the period of 200 days on the data of S and P BSE 500 index through GARCH family models and also arrived at the recommendation of the presence of volatility clustering, evidence of asymmetric and leverage effect on volatility and non-existence of risk premium. Udayan Das, et al (2017) analysed the reinvestment behaviour through snakebite effect which makes the investor reinvests the profit made out of the existing investments and vouches the method of a gambler approach to take higher risk than the initial investment. Further there was a study done by Ranjan Aneja, Anita Makkar (2017) and provided the evidence of the stock price movement pre and post financial crisis for the banking sector in India and highlighted the outcome that there is good amount persistence of volatility and substantial negative association between stock prices and its volatility. Harish Kumar Sahu (2017) made an attempt of studying various research articles for the period 2010–2017 to understand the basis of the movements of stocks and the investors’ behaviour. M. Babu, C. Hariharan (2017) in his study made an attempt to identify the linkage amongst G7 nations’ stock market indices through both Short and Long run linkages which paved the way for the investors to go for both diversification for reducing their investment risk in future. In a study conducted by Ashok Kumar Panigrahi (2011) outlined the relationship between firm size and capital structure decisions of various sectors in Indian listed companies. Alireza Azarberahman, Jalal Azarberahman (2011) adopted the panel data approach to prove the evidence of corporate capital structure of non-financial firms based in Iran based firms and concluded that the asset tangibility has positive correlation towards leverage and a negative influence was identified amongst profitability and leverage. A study was carried out by K. Raj Kumar. (2011) to understand the trends and trend reversal pattern and to notify the patterns of buying and selling points based on banking sector market price movements Though, there are various methods adopted the most street smart method is to use the fundamental and technical analysis to pick a stock. While integrating the technical analysis there are various tools and techniques popularly used. But one of the most proven tools used by researchers is the Fibonacci series. This study emphasizes the usage of retracement and arc of the Fibonacci series to predict the time for investment in the selected stock.

FIBONACCI TOOL:

According to investopedia “Fibonacci retracement is a very popular tool used by many technical traders to help identify strategic places for transactions to be placed, target prices or stop losses. There is a special ratio that can be used to describe the proportions of everything from nature's smallest building blocks, such as atoms, to the most advanced patterns in the universe, such as unimaginably large celestial bodies. Nature relies on this innate proportion to maintain balance, but the financial markets also seem to conform to this 'golden ratio.' Here we take a look at some technical analysis tools that have been developed to take advantage of it”.

a. The Fibonacci Studies and Finance:

When used in technical analysis, the golden ratio is typically translated into three percentages: – 38.2%, 50% and 61.8%. However, more multiples can be used when needed, such as 161.8%, 261.8%, 423% and so on. There are four primary methods for applying the Fibonacci sequence to finance: retracements, arcs, fans and time zones.

GOLDEN RATIO:

The golden ratio is the limit of the ratios of successive terms of the Fibonacci sequence as originally shown by Kepler. Therefore, if a Fibonacci number is divided by its immediate predecessor in the sequence, the quotient approximates φ; e.g., 987/610 ≈ 1.6180327868852. The golden ratio (symbol (φ) is the Greek letter "phi") is a special number approximately equal to 1.618. It appears many times in geometry, art, architecture and other areas. The key Fibonacci ratio of 61.8% - also referred to as "the golden ratio" or "the golden mean". It is found by dividing one number in the series by the number that follows it. For example: 8/13 = 0.6153, and 55/89=0.6179. The 38.2% ratio is found by dividing one number in the series by the number that is found two places to the right. For example: 55/144 = 0.3819. The 23.6% ratio is found by dividing one number in the series by the number that is three places to the right. For example: 8/34= 0.2352.

NIFTY PSE INDEX:

As part of its agenda to reform the Public Sector Enterprises (PSE), the Government has selectively been disinvesting its holdings in public sector enterprises since 1991. With a view to provide regulators, investors and market intermediaries with an appropriate benchmark that captures the performance of this segment of the market, as well as to make available an appropriate basis for pricing forthcoming issues of PSEs, IISL has developed the NIFTY PSE Index, comprising of 20 PSE stocks.

REVIEW OF LITERATURE:

Bhattacharya, Sukanto and Kumar, Kuldeep (2013): Among the vast assemblage of technical analysis tools, the ones based on Fibonacci recurrences in asset prices are relatively more scientific. In this paper, we review some of the popular technical analysis methodologies based on Fibonacci sequences and also advance a theoretical rationale as to why security prices may be seen to follow such sequences. We also analyze market data for an indicative empirical validation of the efficacy or otherwise of such sequences in predicting critical security price retracements that may be useful in constructing automated trading systems.

Reza Allahyari Soeini , Atefeh Niroomand and Amir Kheyrmand Parizi (2013):

These days, because doing business has become so easy through electronic commerce and electronic business, many kinds of business are being done via the internet. One of the more important implementations of electronic commerce has been in the stock market, especially because concrete and on-time forecasts in stock market are crucial. Stock marketing analysts have different ways of making business forecasts but most of these solutions are not absolute and are not able to achieve correct results. In this paper, a suitable solution for forecasting the stock market is suggested using golden ratios and Fibonacci numbers. This series and its ratios have been shown to have a beneficial effect on the stock market by ensuring on-time correct forecasts which can lead to considerable income increases.

Rajesh Kumar (2014):

Predicting the return of a financial product is a very risky task. It involves subjectivity and experts knowledge. In the development of an expert system, domain knowledge is one of the important component. For a software to be artificial intelligent, some heuristics are required, which can help in decision making. It is admitted by the technical experts of financial sectors that in predicting the support or resistance backtracking is required when prediction of support or resistance fails. In this paper, an attempt has been made to restrict the back tracking of support and resistance to a maximum of two attempts. Proposed model can be further used in machine learning to remove the subjectivity.

A. Benavoli. L. Chisci. A. Farina (2014):

“A connection between the Kalman filter and the Fibonacci sequence is developed. More precisely it is shown that, for a scalar random walk system in which the two noise sources (process and measurement noise) have equal variance, the Kalman filter's estimate turns out to be a convex linear combination of the a priori estimate and of the measurements with coefficients suitably related to the Fibonacci numbers. It is also shown how, in this case, the steady-state Kalman gain as well as the predicted and filtered covariances are related to the golden ratio φ=(5+1)/2. Furthermore, it is shown that, for a generic scalar system, there exist values of its key parameters (i.e. system dynamics and ratio of process-to-measurement noise variances) for which the previous connection is preserved. Finally, by exploiting the duality principle between control and estimation, similar connections with the linear quadratic control problem are outlined”.

Lawrence Blume, David Easley and Maureen o’hara (2014):

We investigate the informational role of volume and its applicability for technical analysis. We develop a new equilibrium model in which aggregate supply is fixed and traders receive signals with differing quality. We show that volume provides information on information quality that cannot be deduced from the price statistic. We show how volume, information precision, and price movements relate, and demonstrate how sequences of volume and prices can be informative. We also show that traders who use information contained in market statistics do better than traders who do not. Technical analysis thus arises as a natural component of the agents' learning process.

Michael L. Fredman and Robert Endre Tarjan (2015) In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated F-heaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. F-heaps support arbitrary deletion from an n-item heap in O(log n) amortized time and all other standard heap operations in O(1) amortized time. Using F-heaps we are able to obtain improved running times for several network optimization algorithms. In particular, we obtain the following worst-case bounds, where n is the number of vertices and m the number of edges in the problem graph. Of these results, the improved bound for minimum spanning trees is the most striking, although all the results give asymptotic improvements for graphs of appropriate densities.

Mohd Khoshnevisan (2015):

The homological fuzzy analysis for stock trading has been somewhat universally accepted by financial engineers. In this paper, I have made an attempt to modify the Fibonacci recurrences and apply Fuzzy Logic to create topological clusters to classify the stock patterns. In that, I have reviewed some of the previous literature, which is derived from Fibonacci numbers in asset pricing. This fuzzy logic algorithm tends to offer a greater reliability and accuracy for predication stock patterns.

Rene Kempen (2016):

In this article, a scientific approach to retracements is introduced and the myth of Fibonacci retracements refuted. The statistical analysis of the retracement data resulting from the application of the MinMax-process by Maier-Paape to a variety of stock markets reveals a logarithmic normal distribution of the retracement values in general. It is deduced that there are no overall statistically significant retracement levels. While in a local environment the 100% retracement do show significance, the Fibonacci retracements are not seen empirically.

Violeta Gaucan (2016):

In the material below I have tried to explain how can be used Fibonacci Retracement as an important tool to predict forex market. In this article I have included some graphic formats such as Fibonacci arcs, fan, channel, expansion, which are created also with Fibonacci retracement and also rules to perfect chart plotting. I have analyzed some examples of Fibonacci retracements pattern in a downtrend and in an uptrend. In this article I have used and combine material from different sources trying to create a start point for those one of you that are interested.

Kalok Chan, Allaudeen Hameed and Wilson Tong (2017):

This paper examines the profitability of momentum strategies implemented on international stock market indices. Our results indicate statiscally significant evidence of momentum profits. The momentum profits arise mainly from time-series predictability in stock market indices—very little profit comes from predictability in the currency markets. We also find higher profits for momentum portfolios implemented on markets with higher volume in the previous period, indicating that return continuation is stronger following an increase in trading volume. This result confirms the informational role of volume and its applicability in technical analysis.

NEED FOR THE STUDY:

Every investor wants to know the potential areas of support and resistance level of stock to buy, sell and to hold in the market. This can be done by using appropriate technical analysis out of which this study highlights the risk through the levels of prediction by using Fibonacci tools and also it can easily identify the target and support level in the market. Through this, the investors can be able to take clear decisions in the trading and also can suggest the investors to buy and sell or to hold in the market.

OBJECTIVE OF THE STUDY

· To Study the stocks behaviour of companies from Nifty PSE Sector through Fibonacci sequence

· To identify the technical tools are used to predict the future behaviour of the stocks.

· To know how investors can take investment decision based on Market trends.

SCOPE OF THE STUDY:

From this analysis the tool can able to understand the behaviour of equity market, then it indicates the support and resistance signal to the investors in taking good decisions about investing in equity share and also helps in understanding the technical analysis to take a decision of investing in Nifty PSE Sector stocks. It provides accuracy in target price of the stock level than any other tool and also solves the problem of finding the levels of support and resistance. It anticipate the movement of the stock to minimize the risk and maximize the return and also shows the buying and selling area by analysing in a proper way.

RESEARCH METHODOLOGY:

RESEARCH DESIGN;

the research is based on secondary data analysis. The study is an analytical research, as it aims at examining the secondary data for analysing the past data and that have been done in the technical analysis of stocks and it can also be used in scientific researches as they are unbiased and systematic. The Research design is Quantitative research because the data related to measurement, frequency of occurrences and prediction of future movement. In quantitative research provide quite accurate and reliable measures. Here, the sampling technique used is stratified sampling in probability sample. The sample of the stocks for the purpose of collecting secondary data to analyse its movement in the stock market that has been selected on the basis of Market capitalisation, Dividend, Bonus and Earning per share value. The stocks are chosen from the Nifty Public Sector Enterprise.

Sample Size:

The sample size is extracted from five Nifty PSE companies out of twenty companies listed in NSE and are selected on the following criteria :

a. The Company Market Capitalisation should be Rs.25,000 Crores and above.

b. The Company which issued a regular Dividend for past five years.

c. The Company Earning Per Share (EPS) should be Rs.9 and above.

d. The Company which earned continuously profit for past 5years.

The selected five Nifty PSE companies are:Coal India Limited

i. Gas Authority India Limited

ii. Indian Oil Corporation

iii. National Thermal Power Corporation Limited

iv. Power Grid Corporation of India Limited.

Period of Study;

The stocks are examined for the period of one year on weekly basis i.e. from April 2016 to March 2017.

Statistical Tools used

i. Fibonacci retracement

ii. Fibonacci arc

FIBONACCI RETRACEMNET:

Fibonacci retracement is a very popular tool among technical traders and is based on the key numbers identified by mathematician Leonardo Fibonacci in the thirteenth century. However, Fibonacci sequence of numbers is not as important as the mathematical relationships, expressed as ratios, between the numbers in the series. Fibonacci retracement is developed by taking two extreme points namely a major peak and trough on a stock chart and dividing the vertical distance by the key Fibonacci ratios of 23.6%, 38.2%, 50%, 61.8% and 100%. Once these levels are identified, horizontal lines are drawn and used to identify possible support and resistance levels.

Consolidation stage:

In consolidation stage the stocks will be in stagnation stage for a particular time at a particular level. It may be done when there is no trading process done in the companies, at this stage the investors does not prefer these shares to buy or sell. Mostly, the traders will not trade in this stage.

FIBONACCI ARC:

Fibonacci Arcs are half circles that extend out from a trend line. The first and third arcs are based on the Fibonacci ratios 0.382 (38.2%) and 0.618 (61.8%), respectively. These numbers are often rounded to 38% and 62%. The middle arc is set at 0.50 or 50%. After an advance, Fibonacci Arcs are measured using a Base Line that extends from trough to peak. Arcs are drawn along this line with radii that measure .382, .50 and .618 of the Base Line. These arcs mark potential support or reversal zones to watch as prices pullback after the advance. After a decline, Fibonacci Arcs are used to anticipate resistance or reversal zones for the counter-trend bounce. This article will explain the Fibonacci ratios and provide examples using Fibonacci Arcs to project support and resistance.

RESULTS AND DISCUSSIONS:

COAL INDIA:

Figure showing Fibonacci retracement Consolidation Stage

INTERPRETATION:

The Fibonacci Consolidation stage is taken on weekly basis to identify the sustaining stage. The Support level was at 0% and the Entry level was at 100%. Here, the stock got sustained without any volatility from the period of June to July in between 0% to 100%. (i.e. the price level between 304.49 to 3

Figure showing Fibonacci Upward arc

INTERPRETATION:

The tool extended from low to high from december to february respectively to identify the potential support and resistance. The Fibonacci Arcs show dynamic retracements that evolve over time. When the Support level is at 38.2% i.e. 303.45, then the resistance will be at 50% and 61.8%. Here, the target is to get 50% of resistance level, but it crossed more than 61.8% and thus the target was achieved.

Figure showing Fibonacci Downward arc

INTERPRETATION

The tool extended from August high (350) to December low (282.88) to identify the potential support and resistance. The Fibonacci Arcs show dynamic retracements that evolve over time and it can be drawn after a decline that it works slowly their way low and denotes the falling resistance zones. When the support level is at 38.2% then 50% and 61.8% act as a resistance. Here the target is to achieve 50% of resistance level but it crossed more than that and shows the reversal trend. So the tool is successful.

GAIL STOCK:

Figure showing Consolidation Stage

INTERPRETATION

The consolidation approach is drawn on the weekly basis by choosing consolidation high and low to identify the sustaining stage of the stock. The entry level was at 100% and the support level was at 0%. The stock sustained from the period of May to September between the levels of 0 to 100% (i.e. the price level from 275.12 to 302.37).

Figure showing Fibonacci arc uptrend

INTERPRETATION:

The Fibonacci arc is drawn from September low (269.39) to March high (400.62) to identify the areas of resistance and support level. The stock crossed the first resistance at 319.00 of 38.2% level in a side way. Then it crossed the 50% resistance at 327.00 and also crossed the 61.8% level at 340.51 price level and still it trends to upward.

Figure showing Fibonacci downward arc

INTERPRETATION:

The Fibonacci arc is drawn from January high to March low to identify the support and resistance areas. The Gail stock reached the 50% of the resistance level and turns it to reversal then it crossed the 61.8% of resistance at 240.64 price level. Then the reversal takes place towards up trend.

IOC STOCK:

Figure showing Consolidation stage

INTERPRETATION:

The Fibonacci consolidation stage is drawn on weekly basis to identify the sustaining stage of the stock. The stock entry level was at 100% and support level at 0%. The stock gets stagnated from the period of August to September between 0% to 100% level and their price level will be from 270.86 to 289.00.

Figure showing Fibonacci arc uptrend

INTERPRETATION:

The Fibonacci upward arc is drawn from November low to February high to identify the potential support and resistance level. The stock crossed the support level of 38.2% in side way and the resistance levels were 50% and 61.8%. By next week the resistance level also crossed by the stock and the trend still continues the uptrend by achieving the target.

Figure showing Fibonacci arc downtrend

INTERPRETATION

The Fibonacci downward arc is drawn from January high to February low to identify the potential support and resistance level. The stock reached the three levels of resistance (i.e. 38.2%, 50% and 61.8%) by consecutive weeks. After the reach of resistance level the reversal takes place and trend changes.

NTPC STOCK

Figure showing Consolidation approach

INTERPRETATION

The Consolidation stage is drawn on weekly basis to identify the sustaining stage of the stock. The entry level was at 100% i.e. price level of 141.28 by maintaining the support level at 0% and its price level was 128.17. The stock stagnated from the period of May to August (i.e. 12weeks) in between 0% to 100%. The price level of that period was between 128.17 to 141.28 levels.

Figure showing Fibonacci arc upward

INTERPRETATION:

The Fibonacci upward arc is drawn from October low to February high to identify the potential support and resistance level. The support level was at 143.50 of price level and its entry level at 149.00. Here, the target were fixed at 161.8%, 261.8% and 423.6% of resistance level and the stock reached all the resistance in a side way by achieving the target level.

Figure showing Fibonacci downward arc

INTERPRETATION:

The Fibonacci downward arc is drawn from the period of August high to October low to identify the potential support and resistance. After drawing the arc, the resistance levels are identified to find the potential support and the resistance are 38.2%, 50% and 61.8%. Here, the stock crossed all the three resistances level consecutively and took a reversal at 143.04 of price level.

POWER GRID:

Figure showing Consolidation stage

INTERPRETATION
The consolidation stage is drawn from the period of September to November by choosing the consolidation high and low to identify the sustaining stage of stock. During that period the volatility of stock was between 0 to 100% (i.e. the price level from 104.32 to 93.9). At that stage the stock movement will be stagnated to the particular level of price.

Figure showing Fibonacci arc uptrend

INTERPRETATION

The Fibonacci upward arc is drawn from the period of May low to September high on weekly basis to identify the potential support and resistance level. The support level was at 38.2% and other two arcs are considered as resistance level. In that period the trend towards up, so it crossed the first resistance level of 50% in the month of July and also crossed the second resistance of 61.8% in the month of August. After crossing the resistance level it still continues towards uptrend.

Figure showing Fibonacci arc downtrend

INTERPRETATION:

The Fibonacci downward arc is drawn from the period of February high to March low to identify the support and resistance. Within a few weeks the stock reached the 38.2% of resistance level and continued to cross the level of 61.8% of resistance. Thus the stock crossed all the resistance within a few weeks by achieving the target.

SUMMARY:

COAL INDIA:

· In Fibonacci buying approach the stock moves upward from the support level of 282.50 to 337. Though the volatility was high and also reached the resistance level of 423.6% so the investors can earn huge profit.

· In consolidation stage the stock stagnated from 0 to 100% level i.e the price between 304.49 to 315.9. So the investors cannot earn profit during this stage.

· The Fibonacci arc shows the support level from 38.2% to 61.8% ie. From the price between 303.45 to 316.59. In this stage the investors can get more profit because the stock moves towards upward, instead of side way.

GAIL INDIA:

· In Fibonacci consolidation stage the movement of the stock was measured by taking consolidation high and low. This will able to analyse the sustaining stage of the stock.

· In Fibonacci buying arc method, the arc low was at 269.39 and high at 400.62. The stock crosses the resistance area of 50% and 61.8% and still shows upward to raise up the earning value.

· During the year 2016 to 2017 the GAIL stock movement was high and also earns profit through that.

IOC STOCK

· In IOC buying approach the stock was showed little volatility but the price moved from 290.89 to 370 and above.

· To identify the potential resistance level the investor has to analyse the closing and opening price of the stock and have to fix the target level. Here the stock started from 227.43 level and moved towards down at the level of 181. This creates an investors to earn huge profit.

· The consolidation was sustained during the period between august and September of the price level between 270.86 to 289.00.

· Here the Fibonacci downward arc was drawn to identify the potential support and resistance level from the high to low i.e. 225 to 169.32 of price level.

NTPC STOCK:

· In buying approach the stock was drawn on the weekly basis to identify the potential support and resistance level and the support level was at 0% i.e. the price level of 143 and target level was at 423.6%. Here the stock earns nearly 25% of profit.

· In consolidation stage the stock sustained during the period of May to August between 0% to 100% i.e. from the price level between 128.17 to 141.28.

· The Fibonacci arc shows the dynamic levels thus helps to identify the potential support and resistance level of the stock

· The stock moved from the price level of 143.50 to 173.13 and creates a more profit during the particular month.

POWER GRID:

· The entry level was at 100% i.e. 145.78 and support level was at 0%. The stock reached the 161.8% of first resistance and gets the return from the sale of stock.

· The Fibonacci selling approach was at 139.50 of price level and during the period it reached to 122.60 level thus creates a profit to the investors.

· The consolidation stage was to identify the sustaining stage of the stock. During that period the volatility of stock was between the price level of 104.32 to 93.9.

· The Fibonacci upward arc was drawn to identify the support and resistance area, here the stock was moving towards up and reached the resistance level.

SUGGESTIONS:

· The consolidation stage of the Fibonacci series helps the investor to arrive at the decision. When the stocks are in stagnation stage and the price goes towards the target level and breaches the target price it signals the profit booking mode whereas in the same way if the price moves downwards towards the support level and breaches the support price that signals the investors to invest more.

· Fibonacci Arcs are measured using a Base Line that extends from trough to peak. Arcs are drawn along this line with radius of the base line. These arcs mark potential support or reversal zones to watch as prices pullback after the advance. After a decline, Fibonacci Arcs are used to anticipate resistance or reversal zones for the counter-trend bounce and provide examples to support and resistance.

· Half baked knowledge of stock market is very dangerous. Every individual who are willing to invest in stock market should undergo the basic training and imbibe the technicality of the nature of the stock movements. This makes them to attain benefit from the stock market rather than going with the opinion of others.

CONCLUSION:

The Fibonacci Tools can be used effectively to identify the potential support and resistance level based on the volatility of the stocks in the market. It is used in all markets such as online stock trading, forex trading and also in the futures markets. The tool can also be analysed for any period wise i.e. minutes, hourly, daily, weekly, monthly and yearly. The Fibonacci tool is more advantageous than other tools in terms of future prediction of market prices, fixing the price target, analysing the trend in bullish and bearish trend. Thus the tool plays an important role technical analysis and stock market analysis.

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Received on 02.04.2018 Modified on 16.04.2018

Asian Journal of Management. 2018; 9(2):896-908.

DOI: 10.5958/2321-5763.2018.00142.7