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JOURNAL OF RESEARCH IN NATIONAL DEVELOPMENT VOLUME 5 NO 2, DECEMBER, 2007

STATISTICAL ANALYSIS OF THE SHARE PRICE MOVEMENT OF STOCKS
Iwuagwu Chukwuma E.
 Department of Statistics, Abia State Polytechnic,  Aba
.

Abstract
This study was aimed at providing the investor with timing evidence in decisions with regards to the purchase of and sale of equities that will lead towards higher annual returns from his stock investment as well as to understand the causes and pattern of shares price movements as it affects investment decisions in the Nigeria Stock Exchange by carrying out an analysis of average monthly prices of the quoted stock of First Bank and Union Bank for 2006.The method of least square and correlation analysis was carried out on the average monthly prices for the period under study. Among the major findings were; the average monthly share prices decreased with respect to time. There existed a significance difference in the average monthly share prices quoted by these banks. It was recommended among other things that investors should sell shares between May to August and buy other months.
Key words: Share; Stock; Investment; Market


Introduction
0ften times after necessary expenses, one may be left with some additional money as surplus or excess, and may wish to create a reserve for any future emergency use. The person may ask, should this excess or surplus money be used to improve living standard or to be invested to earn more income or build capital for the future. If investing is the choice, one of the most known avenue over the years now has been common stock (or shares), that is investing in the capital market.
Defining the capital market, wikipedia, the free encyclopedia defined the capital market (Securities Market) as the market for securities where companies and the government can raise long-term funds.
The capital market includes the stock market and the bond markets. Financial regulars such as the Nigeria Securities And Exchange Commission, oversee the capital markets in their respective countries to ensure that investors are protected against fraud.
Stocks can be considered a tool for building wealth, as they are a part of almost every investment portfolio. They represent the ownership of a company and are brought in the form of shares. Shares refer to the stock of a particular company. Your stake in a company depends on how many shares you posses, because these are considered a part of the company’s capital. The popularity of investing in the stock market is increasing constantly. Today investment in stocks and shares is not limited to the well to dos; even the average middle class is getting into it fully.

Statement of the Problem
The Nigeria capital market, is believed has not fully developed to the level it should giving the fact that it came into being about forty six year ago. Government and organization are still unable to raise enough funds from the market when required and returns on investment on the part of the investors are not quite encouraging. This is so because of lack of data and some basic information that will make investors and fund seekers fully tap the potential of the market. For instance most investors do not know when to buy or sell their stock.

 

Objectives of the Study
The research is intended to achieve the following objectives:

        1. To determine whether the average monthly share price of First Bank Of Nigeria Plc And Union Bank Nigeria Plc exhibit any trend and if so, to find out the nature of the trend.
        2. To determine if there is any significance correlation between the average monthly share price of the two banks.
        3. Proffer solutions on techniques that guarantee the success of the market.

Statement of Hypothesis
HO ;There is no significance difference in average monthly share price movement between First Bank and Union Bank.
Hi ; There is significance difference in average monthly share price movement between First Bank and Union Bank.

Significance of the Study

  1. This study will help investors, stockbrokers, stock market analyst and fund managers to better understand the characteristics of quoted stocks in the Nigeria Stock Exchange.
  2. This study will contribute to the body of knowledge from which policy makers will draw information while formulating or preparing regulations for the stock market.

Scope of the Study
This study is limited to average monthly Stock prices of First Bank and Union Bank Plc covering a period of one year 2006. My interest was on the share price of the two banks considering their contributions in banking sector in particular and Nigeria at large.

The Literature
Several studies have been undertaken on related topics on share prices movement of stock.
According to Osaze (1985), dividend trends, earnings, trading, volume, money supply are some of the causes of prices movement in the stock exchange. There are three main schools of thought on the subject of prices behavior- the fundamental analysts; the technical analyst and the random- walk hypothesis. The fundamental analysis believe that there are discrepancies between intrinsic value or justified price, and market prices of share that can be exploited by an investor to beat the market.
“ The fundamental analysis of stock valuation is a forward- looking process in determining the value of a stock’’ (REILLY 1979).
“Unlike the fundamental analysts, the technical analysts concentrate on the study of stock exchange information principally in the form of prices and volume data’’ (REILLY 1979). The word “technical’’ here implies a study of the market itself and not of those external economic factors that are reflected in the market.
The efficient market theory is one that is based on the concept that “capital markets should operate to a high degree of perfection’’ (Winfield and Curry, 1981). The root of this concept, that is in the random walk hypothesis which postulates that share price changes are of a random nature rather than a correlated nature.
The random walk analysts see the stock market as a perfect one and the market stock prices as reflecting all the information available to the market participant. Hence, they conclude that the price changes are completely unrelated and therefore unsystematic. For random walk theory, the market has no money.
According to Bello (1995) in his work “ investment in stocks and share price movement”. He tested for seasonality only using the monthly net advances of stock prices of quoted stocks over a given year period. The result  indicated that the annual market stock prices experienced alternating periods of increased and reduced trend.
Anyantonwu (1999) in his article “share prices reaction in the stock market’’ was of the opinion that psychological factors may result in exaggerated stock price movements. According to the article, psychological research has demonstrated that people are predisposed to seeing patterns and often will perceive a pattern in what is in fact, just noise.

This in turn means that a succession of good news items about a company may lead investors to overreact positively.

Sources of Data
Data for the study were collected mainly from secondary sources. These data were the average monthly price of quoted stock of First Bank Nigeria Plc and Union Bank Nigeria Plc for 2006. These were obtained by dividing each month total by the number of business days in the month.

The data collected were analyzed using the method of least square (Times Series) correlation analysis.
Method of Least Square
The equation of linear trend is defined yt = bo + b1t. Where b1 = sfs.
Correlation Analysis
Correlation coefficient otherwise known as the product moment of correlation coefficient is denoted by r and given by
sfsg       -1< r < +1  and sfsgfsg

Data Presentation
Data were collected on daily basis and average for each month obtained by dividing each total by the number of business days in the month.
The summary of the average monthly share prices for the year 2006 is shown in the table below.


Table 4. 1 Data Summary for Average Monthly Share
Price 2006 for First Bank and Union Bank.

Month

Share Price (FB)

Share Price UB)

January

32 .6

25 .48

February

35 .7

25 .48

March

37 .2

25 .48

April

39 .2

25 .48

May

48 .3

25 .48

June

51 .7

27 .80

July

59.6

29 .62

August

51 .6

29 .01

September

38 .3

26 .57

October

36 .3

24 .41

November

32 .7

23 .34

December

32 .8

23 .42

Source: Cash Craft Asset Management Ltd Member of N S E

Data Analysis
The data collected were analyzed using the method of least square (Times Series) and Correlation analysis.


Method of Least Square

         Table 4.2 Trend of Share Price Movement for First Bank 2006.

Month

T

Price (Y)

t2

Yt

January

- 6

32 .6

36

- 195. 6

February

- 5

35 .7

25

- 178 .5

March

- 4

37 .2

16

- 148 .8

April

-3

39 .2

9

- 117 .6

May

- 2

48 .3

4

- 96 .6

June

-1

51 .7

1

-  51 .7

July

+1

59 .6

1

59 .6

August

2

51 .6

4

103 .2

September

3

38 .3

9

114 .9

October

4

36.3

16

145 .2

November

5

32 .7

25

163 .5

December

6

32 .8

36

196 .8

TOTAL

0

496

182

- 5 .6

The equation of least square line is given by   Yt = bo  + b1t
  Where  b1   =   EYt    =  - 5.6                  and  b0 =   EY  =  496
                         Et2         182     =  - 0 .03                    n          12     =   41 .33
Therefore         Yt   = 41.33 – 0.03 t.

Table 4.3 Trend of Share Price Movement for Union Bank 2006

MONTH

T

         Y

t2

        Yt

January

-6

25 .48

36

- 152 .88

February

-5

25 .48

25

- 127 .4

March

-4

25. 48

16

- 101 .92

April

-3

25. 48

9

- 76. 44

May

-2

25. 48

4

- 50. 96

June

-1

27. 80

1

- 27. 80

July

1

29. 62

1

- 29. 62

August

2

29. 01

4

- 58. 02

September

3

26. 57

9

78. 71

October

4

24. 41

16

97. 64

November

5

23. 34

25

116. 7

December

6

23. 42

36

140. 52

TOTAL

0

307. 57

182

- 15. 19

The equation of least square line is given by  Yt  = bo  +  b1 t
Where b1 = Ety  =  - 15. 19                 and             bo = Ey   = 307. 57
                 Et2           182     = -0.08                               n            12      = 25.63
Therefore  Yt    = 25 .63  - 0. 08 t


Table 4.4 Correlation Analysis of the Relationship Existing between Average Monthly Share Price Movement for First Bank and Union Bank for 2006.



Month

Price (FB) X

Price (UB) Y

XY

X2

Y2

JAN

32 .6

25 .48

830 .65

1062 .76

649 .23

FEB

35 .7

25 .48

909 .64

1274 .49

649 .23

MAR

37 .2

25 .48

947 .86

1383 .84

649 .23

APR

39 .2

25 .48

998 .82

1536 .64

649 .23

MAY

48 .3

25 .48

1230 .68

2332 .89

649 .23

JUNE

51 .7

27 .80

1437 .26

2672 .89

772 .84

JULY

59 .6

29 .62

1765 .35

3552 .16

877 .34

AUG

51 .6

     29 .01

1496 .92

2662 .56

841 .58

SEPT

38 .3

26 .57

1017 .63

1466 .89

705 .96

OCT

36 .3

24 .41

886 .08

1317 .69

595 .85

NOV

32 .7

23 .34

763 .22

1069 .29

544 .76

DEC

32 .8

23 .42

768 .18

1075 .84

548 .50

TOTAL

496

307 .57

13052 .29

21407 .94

8132 .98

r  = nExy       - ExEy
       {{nEx2 –(Ex)2}{nEy2 – (Ey)2}}1/2
r  = 12 (13052 .29)    -     (496) (307 .57)                        = 4072.76   = 0.71          {{12 (21407 .94)- (496)2}{12 (8132.98)-(307.57)}}1/2    5709.57
   TEST STATISTIC
     tc  = r  n –2     = 0.71   12 –2       = 0 . 71 (4 .43)   =   3 .15.
              1- r2                 1-(0.71)2


Difference between average share price movement for First Bank and Union Bank.

Ho : There is no significance difference in average share price movement                        
        between the two Banks.
H1: There is significance difference in average share price movement
        between the two banks.

Critical region: From the t-distribution table, the tabulated value at 5% level of significance is 2.23 = t1 -&/2; n-2.

Decision: Since tc = 3 .15 > 2 .23 = t0.975;10, we reject the null hypothesis (Ho) and conclude that there is significance difference in share price movement between First Bank of Nigeria Plc and Union Bank of Nigeria Plc.

 

Discussion of the Result
From table 4.2, the trend equation for First Bank Nigeria Plc is Yt = 41.33 – 0.03 t. The slope b1 = - 0.03 indicates that the share price movement decreased by 0.03 for any unit change in time (month). This decrease is a minor change.
From table 4.3, the trend equation for Union Bank of Nigeria Plc is Yt = 25.63 – 0.08t. The slope b1 = - 0.08 indicates that the share price movement decreased by 0.08 for any unit change in time (month). This decrease is a minor change. From table 4.4, on correlation analysis of the relationship existing between average share price movement for the two Banks indicated a strong positive relationship (i.e. r = 0.71).
This means that prices increase and decrease at the same time as signified by the trend equation for each of the bank.
 From the hypothesis tested, it indicated that there is significant difference in share price movement for the banks. This is true, as shown on table 4.1.

         The share prices for First Bank is higher than of Union Bank.

Findings.
The overall data analyzed in this study reveal the following;

  1. From the method of least square conducted, the trend line b1 = - 0.03 and – 0.08 for First Bank and Union Bank respectively indicates that the average share price movement for both Banks decreased with respect to time.
  2. The correlation coefficient of 0.71 showed that there existed a positive relationship between average share price movement for First Bank and Union Bank.
  3. From the t- test conducted, the hypothesis tested indicated that there is significant difference in the average share price movement for the Banks.

Recommendation
Having carried out an exhaustive analysis of this work and considering the results of the analysis undertaken, the following are thus recommended.
Since the average monthly stock prices tend to be higher between May to August, it is recommended that investor should take advantage of this seasonal effect by way of selling their shares during the periods already stated in order to make profit. On the other hands, investors wishing to buy shares should do so during the other periods of the year.

  1.  Due to the existence of positive correlation in the price of shares in the Banks, I also recommend that investors should always find out the average share price for immediate past period (month or day) as this would assist them to know what the current period stock price would be.
  2.   Since the study indicated a significant difference in the prices between the banks, the investors should consider the Banks that will give them better dividends or profit.

 

References
Ajayi o. (1984): Financial and Legal Implications of the Nigerian Capital Market Ibadan: Evans Brother (Nig Publishers) Limited.

Akintola B.O. (1995) “A guide to Investors” The Nigeria Stock Market.

Bodie Z. Kane A.and Maris A.J (1988): Essential of Investment. New York. Irwin Mc Graw Hill. 
                                      
Croxton F.E and Cowden D. J (1962): Applied General Statistics London:  Pitman and Sons.

Gill D. (1982): Developing The Securities Market Bullion News Of Central Bank Of Nigeria Vol.7 No 4.

Iwuagwu C.E. (2004): Statistics For Practical Application (Decision Making) Owerri:Nation wyde Publishers

Mish kin F.S. (1998): The Economics Of Money Banking and Financial Market London:. Addition Wesley  Inc.

Mpamugo C.S. (2006): “ Investment Decision In The Nigeria Stock Market A Time Series Analysis Approach’’ Journal of Business And Management Technology Vol .pp 63 – 68 Abia State Polytechnic Aba.