1. INTRODUCTION:
The empirical studies on predictability of
asset returns over long and short time horizons for both individual stocks and
stock market indices produced mixed results both in India and abroad. Many of
these studies have documented that the stock price movements in markets are the
function of a host of factors ranging from rational fundamentals to irrational
psychosomatics. Here, identifying the forces that drive stock prices during a
particular market condition is the major concern for both practical investors
and academicians. Even though they study the behavior of stock prices by
following different methods or approaches- fundamental or technical, ultimately
their intention is to provide useful and reliable information to conclude with
profitable investment decisions. This paper also falls in the same arena of
research looking for a potentially important aspect related to the predictability
of long run stock returns in India by holding a more deductive approach.
The remainder of this paper is constructed
as follows: the next section presents the existing theories and some literature
on stock returns behavior; Section 3 describes the data and methodology;
Section 4 reports empirical findings, followed by concluding remarks in Section
6.
2. THEORIES AND EMPIRICAL LITERATURE ON STOCK RETURNS
BEHAVIOR:
In predicting the stock
market movement, two theories have greater relevance Random walk theory and
Efficient Market Hypothesis. Infact, both of these
theories are discouraging the possibility of prediction of stock prices.
Originally
examined by Maurice Kendall (1953), the random walk theory states that stock
price fluctuations are independent of each other and have the same probability
distribution, but that over a period, prices maintain an upward trend. In
short, random walk says that stocks take a random and unpredictable path. The concept of Efficiency Market Hypothesis
(EMH) trace their roots to the arguments raised by Samuelson (1965), that is,
anticipated price of an asset fluctuate randomly. In EMH, the price of a
security is a reflection of complete market information. Whenever a change in
financial outlook occurs, the market will instantly adjust the security price
to reflect the new information. This means that given the information, no
prediction of future change in the price can make. Only things that the market
has not taken into account are things that have not happened yet. Fama (1970) gives empirical evidence on this hypothesis.
The absence of information efficiency
signals the possibility of abnormal returns to the selected investors of the
market. One group known as Technical analysts argue that this is possible
simply by looking for patterns in stock prices during the past, then assess the
present position and make a decision accordingly. Another group, called,
Fundamentalists claim that the strength of overall economy, industry and of
companies issuing stocks shall be the decisive factors to stock returns. When
studies like Brown et al. (1998) and Jegadeesh and
Titman (2001) validates the arguments of technical analysts, Lo and MacKinlay (1988) Chiang et.al (1995) Bae and Duvall (1996) Cauchie and
Isakov (2003), Mohanty
(2002) and Courteau et al. (2005) provides empirical
evidence on the utility of fundamental approach in making excess stock returns.
Research findings on stock price behavior in emerging
markets are most often more controversial than that in developed markets. Some
of the researchers,(Branes, (1986); Chang and
Ting(2000); Karemera et.al, (1999); Ramasastri (1999)
and Samanta (2004))find evidence of weak form
efficiency and cannot reject the random-walk hypothesis in emerging markets.But researchers like Campbell (1994); Poshakwale(1996 ); Khaba (1998),
Gupta and Basu (2007) and Srinivasan
(2010) find the evidence of non-randomness of stock pricebehavior
and reject the weak-form efficiency in the developing and emerging markets.
3. DATA AND METHODOLOGY:
The study is based on share prices of 52
companies belonging to different industries in India over the period from 1st
April 2000 to 31st March 2010. Stocks completed ten years of listing
in NSE and included in Nifty or Nifty Junior Index constitute the sample for
this purpose. The required data have collected from published sources of NSE.
To know whether long run stock returns in
India pursue random walk, two tests binomial test and runs test haveused in the study. Auto Correlation Function and LjungBox Q-statistic have used for
knowing whether changes in stock prices are overtime correlated or not. Further
explanation of the methodology is detailed with the results and discussions.
4. RESULTS AND DISCUSSIONS:
The analysis part of the present paper is
organized in to two sections. In section 1, we test random walk behavior of stock
prices and a test of independence of price changes overtime conduct in section
2.
4.1 Testing random walk
behavior of long run stock returns in India:
In order to explore whether there exists any chance for
equity investors to earn abnormal returns from their investments in Indian
stock market, random walk behavior of stock returns needed to be tested at
first. This has done through two distinct processes.
4.1.1: Random expectation of stock returns
Binomial distribution model:
Initially a simple test of random walk is
observed by examining the annual growth in stock prices. This test is a model
of the test conducted by Brealy (1983) for studying
the successive changes in corporate earnings. Under this test the stocks are
grouped according to the number of years in which their growth rate of price (
returns) in a particular year was above the average rate of growth in prices of
all 52 stocks in that year.
Table
1: Number of companies experiencing a given number of years of above average
annual growth in their stock prices:
|
Years
|
Actual no. of Companies
|
Expected no. of Companies
|
|
0
|
2
|
0
|
|
1
|
6
|
1
|
|
2
|
18
|
2
|
|
3
|
17
|
6
|
|
4
|
9
|
11
|
|
5
|
0
|
12
|
|
6
|
0
|
11
|
|
7
|
0
|
6
|
|
8
|
0
|
2
|
|
9
|
0
|
1
|
|
10
|
0
|
0
|
|
Chi square value - 103.20
|
P value 0.000
|
In most cases the growth in prices found
above average only in two to three years (Table.1). None of the stocks gained
growth at that level in five or more years. Only two stocks have growth, which
was below the average in all ten years.
The third column of the table lists the number of companies
one would expect to observe in each group if stock returns distributed randomly
among companies. Then for a sample of 52 companies, one would expect to find
one stock with only one year of above average growth and two stocks with only
two years of above average growth. At the other end of the spectrum, two stocks
with eight years of above average growth and one stock with nine years of above
average growth all simply due to random chance. The expected frequencies of
the sample distribution have estimated by fitting a binomial distribution
model. Then actual results were compared with expected results and the
difference between the two is tested with the classical hypothesis methodology
for determining its statistical significance. The test results found
significant difference between the actual and expected which deny the validity
of market efficiency hypothesis and random movement of stock pricesin Indian context.
4.1.2: Run test:
Using run test the study considered whether years of
above or below average growth tended to bunch up for individual stocks. The number of runs for all the stocks in the
sample is determined and reported in the second and third column of Table 2.
Table:
2 Runs of successive years with growth greater or less than average:
|
Length of run (years)
|
Actual No.
of runs of good years
|
Actual No. of runs of bad years
|
Expected No. of runs of good years
|
|
1
|
94
|
47
|
37
|
|
2
|
5
|
21
|
24
|
|
3
|
5
|
24
|
10
|
|
4
|
1
|
22
|
3
|
|
5
|
0
|
17
|
1
|
|
6
|
0
|
2
|
0
|
|
7
|
0
|
0
|
0
|
|
8
|
0
|
0
|
0
|
|
9
|
0
|
1
|
0
|
|
10
|
0
|
1
|
0
|
|
Chi square value - 107.60
|
P value 0.000
|
The mean length of the run for 52 stocks
studied found too small. 94 runs of good (+ runs) years and 47 runs of bad
years (- runs), 5 runs of good years and 21 runs of bad years, 5 runs of good
years and 24 runs of bad years and 1 run of good years and 22 runs of bad years
having run length of 1, 2, 3 and 4 years respectively were observed by the
study. Zero runs of good years and 17 runs of bad years were seen for run
having length of 5 years. Poisson distribution model was applied (as the mean
length of the runs is too small and distribution is discrete) for expecting the
number of runs of good years having a finite run length which are reported in
column 4 of the Table 2. Then the actual runs are compared with the results one
would expect if stock price changes are distributed in a random fashion. Again,
classical statistical tests applied here do not prove that stock prices in
India change in a random fashion in the long run.
Irrelevance of random walk hypothesis in
Indian context justifies the possibility of making abnormal returns by the
investors of the stock market. Here again one more question arises: How it is
possible to them- whether by studying the past price changes as technician
suggests or through a top down method of analysis of a stock. If the theory of
past price changes shall affect the further price movement in the stock
market fails it automatically, accept the argument of fundamentalist price
movement of a stock in the market is subject to the influence of earning
prospects of the issuer firm.
4.2: Auto Correlation Function Test of
independence of price changes overtime:
If we can forecast the price of a stock by
looking at its prices in previous periods, then changes in stock prices over
time will be correlated. Table 3 dealt with autocorrelation of growth in stock
prices of selected companies.
Auto Correlation Function (ACF) measures the amount of
linear dependence between observations in a time series that are separated by
lag k. Autocorrelation of growth in stock prices refers to the relationship
between the current growth in price of stock of a particular company and its
own growth in previous years. If, the price changes of the stocks are
independently distributed, its Auto correlation will be zero for all time lags.
The autocorrelation function of price
change or return(y) is
An autocorrelation of lag 1 refers to the
stock price changes in adjacent years. An autocorrelation coefficient of lag 2
refers to the correlation coefficient of the stock price change in a particular
year with the price change 2 years before. An important issue here is the
choice of lag length. A rule of thumb is to compute Auto Correlation Function
(ACF) up to one-third to one-quarter the length of the time series (Gujarati,
p.812). Therefore, the study has chosen
lag length 4.
Table .3: Autocorrelation coefficients of Annual stock
price changes (Nifty stocks)
Note:
Bold figures
indicate statistically significant Autocorrelations.
Then for testing the significance of
autocorrelation coefficient of stock price changes over the period the LjungBox Q-statistic (1978) is also used in this
study.
It is a type of statistical test
of whether any of a group of autocorrelations
of a time series is different from zero.
Instead of testing randomness at each distinct
lag, it tests the "overall"
randomness based on a number of lags, and is therefore a portmanteau
test. The high sample autocorrelations lead to large
values of Q. If the calculated value of Q exceeds the appropriate Chi square
values in a table, we can reject the null hypothesis of no significant
autocorrelations. The test statistic is expressed in the form:
Where, N is the sample size, 
(j)
is the autocorrelation at lag j, and n is the number of lags
being tested.
From the analysis we can see that the values of Q test
accept the joint null hypothesis of zero autocorrelations for the full period
in all the companies except that of BPCL and National. When ACFs are found
significant at all lags in both companies, Q test rejects the joint null
hypothesis of zero autocorrelations at one per cent level in National and at
five per cent level in BPCL.
5. CONCLUDING REMARKS:
Thus this exploratory sample study found lack of
autocorrelation in growth of stock prices in the long run which appears that
forecasts of future return from stock investments based on simply extrapolating
the historical stock prices are unlikely to be much of value. Here arguments of
technician would be rejected. While the historical price data is not providing
a convenient point of departure, then the average forecasts will have to be
based on the analysis of a large variety of economic variables- among these
there would be economic environment the firm is expected to operate in, the
profile of the industry it belongs to and its expected competitive position,
operating efficiency, dividend policy after all quality of management. Since
most of these information components are available only quarter or annual basis
(except economic variables which is monthly available), the investors has to
frame their investment plans on a long term perspective for deriving benefits
under this approach. In sum, we propose that fundamental approach to valuation
of shares can produce better returns to long term equity investors in India.
6. REFERENCES:
1.
Bae CS. and Duvall JG. An Empirical Analysis of
Market and Industry factors in StockReturns of U.S.
Aerospace Industry. Journal of Financial and Strategic Decisions. 9 (2); 1996:
85-94.
2. Branes P.
Thin trading and stock market efficiency: A case of the Kuala Lumpur Stock
Exchange. Journal of Business Finance and Accounting. 13(4); 1986: 609- 617.
3.
Brealy RA. An Introduction to
Risk and Return from Common Stocks. M.I.T, Cambridge, Mass. 1983.
4.
Brown SJ, Kumar A and Goetzman WN. Dow Theory:
William Peter Hamiltons Track Record Re-Considered. The Journal of Finance.
LIII (4); 1998: 1311-1332.
5.
Campell RH. Predictable Risk and Returns in Emerging Markets. NBER
Working Paper No. 4621 National Bureau of Economic Research, Inc. 1994.
6. Cauchie SV
and Isakov D.The
Determinants of Stock Returns in a Small Open Economy. 2003. Available at SSRN:
http://ssrn.com/abstract=391996.
7. Chang KP and Ting KS. A variance Ratio Test
of the Random Walk Hypothesis for Taiwans Stock Market. Applied Financial
Economics. 10; 2000: 525-532.
8. Chiang R; Liu P and Okunev J. Modeling mean reversion of asset prices towards
their fundamental values. Journal of Banking and Finance. 19(8);
1995:1327-1340.
9. Courteau L; Kao J; Keefe T and Richardson G. Relative accuracy and
Predictive ability of direct valuation methods, price to aggregate earnings
method and a hybrid approach. 46; 2006: 553-575.
10. Gujarati DN. Basic Econometrics.
McGraw-Hill International, New York. 2005.
11.
Fama E. Efficient Capital
Markets II. Journal of Finance. 26(5);
1991:1575-1617.
12. Gupta R and Basu
PK. Weak Form Efficiency in Indian Stock Markets. IBER Journal. 6(3); 2007:
57-64.
13. Jegadeesh N and Titman S. Profitability of momentum strategies: an
evaluation of alternative
explanations. Journal of Finance. 56; 2001: 699-720.
14. Karemera,
D, Ojah K and Cole JA. Random Walks and Market
Efficiency Tests: Evidence from Emerging Equity Markets. Review of Quantitative
Finance and Accounting.13; 1999: 171-188
15.
Kendall
M. The Analysis of Economic Time Series. Journal of the Royal Statistical
Society. 96; 1953: 13-32.
16.
Lo A
and MacKinlay A. Stock Market Prices Do not Follow
Random Walks: Evidence from a Simple Specification Test. The Review of
Financial Studies.1; 1988: 897-916.
17.
Ljung G and Box GEP. Box. On a Measure of Lack of Fit in Time Series
Models. Biometrika. 66; 1978: 67-72.
18. Samuelson PA. Proof that Properly Anticipated Prices
Fluctuate Randomly. Industrial Management Review. 6(2); 1965: 41-48.
19. Mohanty P. Evidence of Size Effect on Stock Returns in India. Vikalpa. 27(3); 2002: 27-37.
20. Khababa N.
Behavior of stock prices in the Saudi Arabian Financial Market: Empirical
research findings.Journal of Financial Management and
Analysis. 11(1); 1998: 48-55.
21. Poshakwale S. Evidence on Weak Form Efficiency and Day of
the Week Effect in the Indian Stock Market. Finance India. 10(3); 1996:
605-616.
22. Ramasastri S. Market Efficiency in
the Nineties: testing Unit Roots. Prajnan..28;
1999: 155-161.
23. Samanta P. Evolving weak form informational efficiency of Indian stock
market. Journal of Quantitative economics. New Series-2; 2004. Srinivasan P. Testing Weak form Efficiency of Indian Stock
markets. APJRBM. 1 (2); 2010