Analysis of Stock Market Efficiency

The Economic Journal of Nepal, Vol. 35, No. 3, July-September 2012 (Issue N0. 139) © CEDECON-TU

Analysis of Stock Market Efficiency

Basanta Kumar Mishra1

Abstract

This paper examines the weak form of market efficiency of the Nepalese

stock market employing autocorrelation test, runs test, variance ratio test,

and unit root test on monthly closing prices and market index for the period

mid-2003 to mid-2012. The study result reveals that the monthly return

series of Nepalese companies listed in Nepal stock exchange, and market

return series do not follow any predictable pattern. It suggests that any

speculation based on information on past stock price is fruitless. It implies

that all information conveyed in stock price in the past are impounded into

the current price of the stock. Thus, the opportunity of making abnormal

returns based on information on past stock price in the Nepalese stock

market is ruled out.

Introduction

The concept of capital market efficiency can be understood from various perspectives

namely: allocation efficiency2, operational efficiency3 and informational efficiency4. In financial

literature, market efficiency exclusively refers to informational efficiency. An efficient market

simply does not waste information. Market efficiency in this context refers to market’s ability to

price securities correctly and change securities price to reflect new information on securities

price correctly and instantaneously. Thus, an efficient market is one where current price of any

capital asset gives best estimate of its true value (the present value of the future prospects). If the

market is efficient, the current price is an unbiased estimate of its true economic value based on

the historical, public and private information. Fama formalized this concept as Efficient Market

Hypothesis (EMH) in the early 1960s. Depending on the information set to which prices adjust,

Fama (1970) divided EMH into following sub-hypothesis: a) Weak form efficient market (Prices

adjust/reflect all historical information of past stock prices or returns) b) Semi-strong form

efficient market (Prices adjust/reflect all publicly available information correctly and

instantaneously) and c) Strong form efficient market (Prices adjust/reflect all available

information including ‘insider’ information).

1 Mishra is a teacher of Nepal Rastriya College, Kathmandu. Email: [email protected] 2 There are enough securities to efficiently allocate risk. 3 Transactions costs are low, thereby enhancing trading of securities. 4 Market prices fairly and quickly reflect all available information.

mailto:[email protected]

Mishra: Analysis of Stock Market Efficiency 187

The primary role of the capital market is allocation of ownership of the capital stock of an

economy. If the stock market is efficient the limited saving is allocated to the productive

investment sector optimally resulting stream of benefits to the individual investors and to the

economy of the country as a whole.

The efficiency or inefficiency of the stock market largely depends upon availability and

accessibility of information. Information must widely available and accessible at minimum cost

and at, more or less, the same time around the market. Similarly, transaction costs, development

of regulatory institutions, awareness of investors, effective enforcement of rules and regulations,

market discipline, corporate governance etc. determine the efficiency level of stock market. A

market should to be large and liquid. Investors must also have enough funds to take advantage of

inefficiency until, according to the EMH, it disappears again. In order for a market to become

efficient, investors must perceive that a market is inefficient and possible to beat. Investment

strategies intended to take advantage of inefficiencies are actually the fuel that keeps a market

efficient.

In an efficient market, by definition, today’s price change reflects today’s news and

tomorrow’s price change will reflect tomorrow’s news. News is, by definition, unpredictable,

and, thus, resulting price changes must be unpredictable and random. If the flow of information

is unimpeded and information is immediately reflected in stock prices, in finance, such stochastic

properties of stock return series is termed by specific analogy ‘Random Walk Model (RWM)’ or

‘random walk theory’. The simplest RWM expressing such behavior of stock price can be

expressed as follow:

Pt = pt -1 + rt …...….……….…...…......... (1)

Where, Pt is the price of the stock at time t; Pt-1 is the price of the stock in the immediately

preceding period; rt is a reflection of news (return/loss) at time t.

In an efficient stock market, stock return series should move randomly with respect to new

information. Return series whose successive values are serially independent or follow random

walk, accepts the weak form EMH among three forms of EMH and the investors cannot derive

profitable investment strategy based on historical information. To the contrary, return series

whose successive returns are serially correlated, investors expect to earn an abnormal return

(above the market return) on a risk adjusted basis through either technical analysis or

fundamental analysis or both. The sense is that it is possible to ‘beat the market’. Such

dependence rejects the weak form efficient market hypothesis.

In the underdeveloped capital market, the market participants are considered not to be well

informed and irrational compared to well organize markets. Price cannot be assumed to fully

reflect all available information. It cannot be assumed that investors will correctly interpret the

information that is released. Beside this, the corporation has greater potential to influence its own

stock’s market price and there is a greater possibility that its price will move about in a manner

not justified by the information available (Samuels & Yacout, 1981).

Nepalese stock market is considered as a nascent market. At present, there is tremendous

decline in the market capitalization of the real sector while looking to the Nepal Stock Exchange

(NEPSE). Without dominating role of real sector, the capital market cannot cope with the

188 The Economic Journal of Nepal (Issue No. 139)

problem of economic growth in the long run. Adequate efforts are required to generate market

efficiency through the fair competition among market practitioners, confidence of market

participants, adequate and true liquidity, transparent regulation, timely release of market

information etc. This study is an attempt to test whether the Nepalese stock market is weak form

efficient or not.

Literature Review

Bachelier (1900) had anticipated the concept of market efficiency in ‘theory of speculation’.

It is the earliest known study on behavior of price change. Bachelier had analyzed the

commodity prices and asserted that successive price changes between two periods are

independent with zero mean and its variance is proportional to the interval between the two time

periods. Bachelier had stated, “Past, present and even discounted future events are reflected in

market price, but often show no apparent relation to price changes”. He deduced that ‘the

mathematical expectation of the speculator is zero’ before Samuelson (1965) explained efficient

in terms of martingale. But Bachelier’s contribution was overlooked until his name appeared in

economics as an acknowledged forerunner, in a thesis on options-like pricing by Samuelson in

1956 (Mandelbrot & Hudson, 2004; Dimson et al., 2000) and subsequently published in English

by Cootner (1964).

Fama (1965) examined the distribution and serial dependence of stock market returns using

serial correlation and runs test and concluded that they follow a random walk. He stated his

conclusion as “it seems safe to say that this paper has presented strong and voluminous evidence

in favor of the Random Walk Hypothesis (RWH).” Harry Roberts (1967) coined the term

‘Efficient Markets Hypothesis’ and made the distinction between weak and strong form tests

(Sewell, 2011). Fama et al. (1969) undertook the first ever event study though Ball & Brown

(1968) were the first to publish an ‘event study’ and their conclusion was that the stock market is

efficient. Fama (1970) published first of his three review papers on ‘efficient capital markets: A

review of theory and empirical work’. He defined an efficient market as: “A market in which

prices always ‘fully reflect’ available information is called ‘efficient’”. Realizing this notion as a

paradigm of efficient capital market, numerous studies have been performed to investigate the

level of efficiency of different developed and developing capital markets in the world.

Watts (1978) found statistically significant abnormal returns. He provided the first explicit

test to determine whether those abnormal returns emanate from market inefficiency or from

deficiencies in the asset-pricing model. His conclusion was that the abnormal returns are due to

market inefficiencies. Fama & French (1988) analyzed the US stock portfolio data. Their

conclusion was that the 25 to 40 percent of the variation in long holding period returns can be

predicted because of the mean reversion. Lo and MacKinlay (1988) used equal and value

weighted return regarding to NYSE listed stock for the period 1962 to 1985. They found positive

autocorrelation; inconsistent result with Fama and French (1988) for weekly holding-period

returns both for the entire sample and for all sub-periods using variance ratio test. Poterba and

Summers (1988) and De Bondt and Thaler (1989) found mean reversion in stock market returns

at longer horizons. However, Poterba and Summers (1988) found that the short periods’ stock

returns show positive autocorrelation. Fama (1991) empirically studied and detected a number of

anomalies such as the January effect, effect of holiday, effect of weekend and small size effect.


Campbell and Shiller (1988) reported that initial P/E ratios explain as much as 40 percent of the

variance of future returns. They conclude that equity returns were predictable in the past to a

considerable extent.

There are number of studies on different individual markets as well as on regional markets of

Asian countries. Pan et al. (1991) analyzed daily and weekly market returns of five Asian stock

markets (Hong Kong, Japan, Singapore, South Korea, and Taiwan) using variance ratio test.

Their results indicate that all the market returns based on the five market indices were positively

autocorrelated except for Japan. Similar results were found by Dickinson and Muragu (1994) for

Nairobi stock market; Cheung et al. (1993) for Korea and Taiwan; Poshakwale (1996) for Indian

stock market; Lee et al. (2001) for China; Hassan et al. (2007) for Karachi Stock Exchange.

Huang (1995) examined the RWH for the nine Asian equity markets using the variance ratio

statistics. He rejected the RWM hypothesis for the equity markets of Hong Kong, Singapore,

Thailand, Korea and Malaysia. Hamid et al. (2010) tested the weak form market efficiency of the

monthly stock market returns of Pakistan, India, Sri Lanka, China, Korea, Hong Kong,

Indonesia, Malaysia, Philippine, Singapore, Thailand, Taiwan, Japan and Australia for the period

January 2004 to December 2009. Autocorrelation, Ljung-Box Q-statistic test, runs test, unit root

test and the variance ratio were used. They concluded that monthly returns are not normally

distributed. They suggested that the investors can take the stream of benefits through arbitrage

process from profitable opportunities across these markets.

Groenewold and Kang (1993) found Australian market semi-strong form efficient.

Conclusion of Magnusson and Wydick (2000) is in favor of RWH for African stock market.

Cheung and Coutts (2001) used a variance ratio test and found that the Hong Kong stock market

return follow a random walk. Similar results for Korean stock market were found by Ryoo and

Smith (2002) using variance ratio test. Worthington and Higgs (2004) investigated indices of 20

European stock markets for the period August 1995 to May 2003 by applying serial correlation

test, runs test, variance ratio test and Augmented Dickey Fuller (ADF) test. They concluded that

all indices are not normally distributed and only the indices of Germany, Ireland, Portugal,

Sweden and the United Kingdom follow random walk purely and France, Finland, Netherlands,

Norway and Spain are following the RWH. Similarly, Worthington and Higgs (2009) examined

efficiency in the Australian stock market for the period of 12,519 daily and 1,575 monthly

observations and reported that the monthly Australian stock returns follow a random-walk, but

daily returns do not because of short-terms autocorrelation in returns.

Borges (2008) conducted study on the equity markets of France, Germany, UK, Greece,

Portugal and Spain, for the period January 1993 to December 2007 using serial correlation test,

ADF test, runs test and multiple variance ratio. They found that monthly prices and returns

follow RWM in all six equity markets. However, they detected the serial positive correlation for

Greece and Portugal before year 2003. Urrutia (1995) investigated the RWM for four Latin

American emerging stock markets: Argentina, Brazil, Chile and Mexico. The variance ratio test

of the monthly return data detected the RWH but runs test indicated that there exists weak form

of efficiency regarding to these markets. He pointed out the two reasons behind this scenario.

The first is the domestic investors are not enough competent to design trading strategies that may

allow them to earn excess returns and the second is both the economy and the capital markets of

developing countries have been growing at an unusually rapid pace, and it is likely that positive


autocorrelations are indicators of economic growth rather than evidence against the efficient

market hypothesis. Linking between the market inefficiency and economy, he concluded that the

four Latin American emerging equity markets are weak form efficient.

Pradhan and Upadhyay (2004) made a conclusion that the Nepalese stock market may not be

termed as ‘weekly efficient’ in pricing of shares. They conducted a opinions survey and

concluded that the current market price of shares are useful to make buy or sell decision, to

predict average returns, and to predict future prices. K.C. and Joshi (2005) examined the various

forms of anomalies empirically in the Nepalese stock market for daily data of Nepal stock

exchange return from February 1, 1995 to December 31, 2004. Using regression model with

dummies, they found persistent evidence of day-of-the week anomaly but disappearing holiday

effect, turn-of-the-month effect and time of-the-month effect. They also documented no evidence

of month-of-the-year anomaly and half-month effect. The results indicate that the Nepalese stock

market is not efficient in weak form with regard to the day-of-the week anomaly but weakly

efficient with respect to the other anomalies.

Dangol (2008) examined the impact of new unanticipated political events in the Nepalese

stock market using the event analysis methodology. He concluded that good-news/bad news

generate positive/negative abnormal returns in the post-event period. Bhatta (2010) tested the

RWH on daily, weekly and monthly market returns and returns of 30 individual listed companies

in NEPSE for the period of 1996 to 2005 using autocorrelation test and runs test. The results

show that stock prices in Nepal are not moving independently confirming the Nepalese stock

market is not weak form efficient.

Methodology of the Study

Statistical and Econometrical Tools

Autocorrelation Test

The autocorrelation is correlation between members of same series. Thus, it is used to detect

the relationship between the value of a time series in time t and its value of the k period earlier in

the same time series. A significant positive autocorrelation implies that the value of a time series

in time t depends on its value of the k period earlier in the same time series and vice-versa. Thus,

a time series needs a zero autocorrelation coefficient at different lags to be random. The sample

autocorrelation coefficient k is defined as:

k = 1.1.3..............................................)(

),(

t

ktt

rVar

rrCov

A time series is purely random, that is, it exhibits white noise, when the autocorrelation

coefficients are normally distributed with zero mean and variance equal to one over the sample

in the large samples. Symbolically, k ≈ N(0, 1/n) (Bartlett, 1946). Instead of testing the

statistical significance of any individual autocorrelation coefficient, this study has tested the joint


hypothesis that all the k up to certain lags is simultaneously equal to zero using the Ljung Box

(LB) statistic (Ljung & Box, 1978) which is defined as:

LB = n(n+2) 2.1.3.............................2

1

2

m

k kn

k

Where, n = sample size and k = lag length.

The LB-statistics follow the chi-square (χ2) distribution with m degrees of freedom. The null

hypothesis of independence is rejected if LB-statistic is greater than χ2 with m degrees of

freedom at the corresponding significance level (α).

Runs Test

A run is defined as an uninterrupted sequence of one symbol or attribute, such as + or -. The

number of elements in a run is defined as a length of run (Gujarati et al., 2012). If return/loss

series (Rt) = -3, +2, +1, -2, +1 then Rt contains four runs. The probability that the tth value is

larger or smaller than the µ value (i.e. mean or median or any custom value) follows a binomial

distribution, which forms the basis of the runs test. The premise behind the runs test is that too

few or too many runs, as compared with the number of runs, expected in a random series,

indicates non-randomness. If there are too many runs in Rt, it would mean that the stock returns

change sign frequently, thus, indicating a negative autocorrelation and vice-versa. If the observed

runs are not significantly different from the expected number of runs then it is concluded that

successive prices changes are independent.

The runs test is a non-parametric test of randomness in a series. This approach test and

detects statistical dependency which may not be detected by the autocorrelation analysis. It is

possible that securities prices might change randomly most of the time but occasionally follow

trends that autocorrelation cannot detect and runs test are used to determine if there are such runs

in price changes. Under the null hypothesis, the successive outcomes (here monthly returns) are

independent and identically distributed; the number of runs is asymptotically normally

distributed with

mean: E(R) = 12 21

N

NN and variance:

)1()(

)2(22

21212

NN

NNNNNR

Where, N = total number of observations = N1 + N2, N1 = number of positive returns, N2 =

number of negative returns and R = number of runs.

These parameters do not assume that the positive and negative elements have equal

probabilities of occurring, but only assume that the elements are independent and identically

distributed. For a large sample the test statistic is defined as:


Z = 1.2.3......................................)(

2

R

RER

The Z-value greater than or equal to ± 1.96 rejects the null hypothesis at 5 percent level of

significance. Alternatively, if the value of asymptotic significance is found greater than 0.05 the

RWH should be accepted at 5% level of significance.

Variance Ratio Tests

Variance ratio tests are widely used and particularly useful for examining the behavior of

stock price indices in which returns are frequently not normally distributed. These tests are based

on the variance of returns and have good size and power properties against interesting alternative

hypotheses and in these respects are superior to many other tests (Campbell et at., 1997). The VR

methodology consists of testing the RWH against stationary alternatives, by exploiting the fact

that the variance of random walk increments is linear in all sampling intervals, i.e. the sample

variance of the k-period return (or k-period differences), Pt-Pt−k, of the time series Pt, is k times

the sample variance of the one-period return (or the first difference), Pt - Pt−1. This can be

expressed symbolically as follow:

Var(Pt -Pt - k) = kVar(Pt - Pt - 1) or

Var(rk) = kVar(r1) ………………………………….(3.3.1)

In which, k is any positive integer. The variance ratio is given by:

VRk = )Var(r

)Var(r

1

kk1

= )(

2

)(21

1r

rk k

……………….…………(3.3.2)

Where, rk is k-period’s continuously compounded return.

The variance ratios computed at each individual lag interval k (k = 2, 3, . . .) should be equal

to unity for a random walk process. Variance-ratio values below one and decrease with increase

in k indicates negative serial correlation in the returns i.e. mean reversion. Variance-ratio values

above one and increase with increase in k indicates positive serial correlation in the returns i.e.

mean aversion.

Lo and MacKinlay (1988) generate the asymptotic distribution of the estimated variance

ratios and recommended two test statistics, Z(k) and Z*(k), both of which have asymptotic standard

normal distributions under the null hypothesis. Z(k) is derived under the assumption that the

disturbances of time series are homoscedastic but under the heteroscedastic assumption Z*(k) is

derived. Z*(k) statistic is not only sensitive to correlated changes in stock prices, but also robust to

many general forms of heteroscedasticity and nonnormality and so is particularly useful with

stock returns because often they are not normally distributed (Smith et al., 2003). The test

statistic Z(k) is given by:


Z(k) = VR(rt; k)−1

∅(k)1/2 ……………………………..……..….(3.3.3)

Where, the asymptotic variance,∅(k), is given by:

∅(k) =2(2k−1)(k−1)

3kN …………………..….……….…….. (3.3.4)

The test statistic Z*(k) is given by given by:

Z*(k) =

VR(rt; k)−1

∅∗(k)1/2 ………………...……………….…..……. (3.3.5)

Where,

∅∗(k) = )()(2

21

1

jk

jkk

j

and,

2

1

2

1

22 )()()()(N

t

t

N

jt

jtt xxxj

Both statistics follow the standard normal distribution asymptotically under the null

hypothesis that VR(k) = 1.

It is usual to examine the VR statistics for several k values (ki, i = 1, 2, 3, ……., m). The null

random walk is rejected if it is rejected for some k value. Chow & Denning, (1993) have

suggested a procedure for the multiple comparison of the set of variance ratio estimates with

unity as an alternative of such sequential procedure. This test consider the joint null hypothesis

H0: VR (ki) = 1 for all i = 1, . . . , m, against the alternative H1: VR(ki) ≠1 for some ki. The test

statistic is given by,

a. Under homoscedastic assumption: Max {| Z(k1) |,….., |Z(km)|} and,

b. Under heteroscedastic assumption: Max {| Z*(k1) |,….., | Z*(km)|}.

The null hypothesis is tested on the basis of following results:

a. Under homoscedastic assumption: Prob.{max (| Z(k)| ≤ SMM (α, m , N)} ≥ 1- α and

b. Under heteroscedastic assumption: Prob. {max (|Z*(k)| ≤ SMM (α, m , N)} ≥ 1- α.

Where, SMM (α; m; N) is the upper α point of the Studentized Maximum Modulus (SMM)

distribution with m parameters and N (sample size) degrees of freedom. When N is infinite,

asymptotically,

SMM (α, m, N) = 2

Z …………………………….(3.3.8)

In which, 2

Z= standard normal distribution and α+ = 1-(1-α)1/m.


If the maximum absolute value of chosen statistic, Z(k) or Z*(k), is greater than the SMM

critical value at a predetermined significance level then the RWH is rejected. Chow and Denning

(1993) control the size of the MVR test by comparing the calculated values of the standardized

test statistics, either Z(k) or Z*(k) with the SMM critical values.

Unit Root Test

Let us write the equation (1) as:

Pt = ρPt-1+ rt ………………… (3.4.1)

Where, ρ lies between -1 to 1 i.e. -1 ≤ ρ ≥ 1.

If ρ is 1 i.e. unit root, then (3.4.1) becomes a RWM. Such stochastic process is said to be unit

root or nonstationary. Nonstationarity is the necessary condition for RWM. Unit root test is a

popular test of nonstationarity (or stationarity). We cannot estimate equation (3.4.1) by OLS and

test the hypothesis that ρ = 1 by the usual t test because that test is severally biased in the case of

unit root (Gujarati et al., 2012) Therefore, manipulating equation (3.4.1) can be written as:

ΔPt = rt-1 + rt ……………………………………..(3.4.2)

Where, ΔPt =Pt - Pt-1 and = (ρ -1).

Hence, null hypothesis is = 0. Acceptance of the null hypothesis indicates the time series

is nonstationary or unit root. The errors (residuals) in the equation (3.4.2) may be serially

correlated. Therefore, to obtain unbiased estimate of ADF test (Dickey & Fuller, 1979 &

1981) has been used. In the case of random walk without drift and trend the ADF test consists of

estimating the following regression:

ΔPt = )3.4.3(..................................................i-t

1

1 t

m

i

it rPP

Schwarz information criterion has been used to determine the optimal lag length (m).

Nature and Sources of Data

Monthly closing NEPSE index, monthly closing price per share and dividend per share has

been used in this study. Monthly return series during mid 2003 to mid 2012 have been used in

this study. These data are collected from NEPSE, Securities Board of Nepal and individual

sample companies listed in NEPSE.

Market return on period t (rmt) is calculated as:

Rmt = ln(PIt) - ln(PIt-1) …………………………………(7)

Where, ln = natural logarithms, PIt = Price Index at time t and PIt-1 = Price Index at time t-1


Similarly, return of an individual company on period t (rt) is calculated as:

ln(Pt +Dt) - ln(Pt-1) ………………………………….. (8)

Where, Pt = Price per share at time t, Pt-1 = Price per share at time t-1 and Dt = Dividend per

share of an individual company at time t.

Logarithms price difference is continuously compounded and free from magnitude bias.

Without logarithm price difference, a fifty rupees increase on a share initially priced at hundred

is similar to a fifty rupees increase on a share initially priced at thousand, is an example of

magnitude bias.

Selection of Companies

Some periods may show a zero return as a result of the thin trading. Estimated returns may

differ from true returns. Therefore, highly frequently traded companies are selected from

respective sub-groups to save the data from thin trading bias. At least one company has been

selected to represent all the sub-groups, as categorized by NEPSE as shown in table 1.

Table 1: Selection of Companies Sub-groups CB DB FC IC Hotel MP Trading Hydro Other Total

Total listed companies 26 68 69 21 4 18 4 4 2 216

No. of selected companies 9 5 4 4 1 1 1 2 1 28

Source: NEPSE, Mid 2012

Where, CB = Commercial Banks, DB = Development Banks, FC = Finance Companies, IC =

Insurance Companies and MP = Manufacturing and Processing companies. In addition the return

series of these 28 individual companies, NEPSE return series also has been analyzed in this

study.

Presentation and Analysis

Outcomes of autocorrelation test (Ljung-Box (LB) statistics), runs test, variance ratio test

(multiple comparison of the set of variance ratio suggested by Chow & Denning (1993)) and unit

root test (ADF test statistics) have been presented in table 2.

Autocorrelation coefficients were calculated up to 30 lags. LB values and respective

probabilities in the Table 2 represent LB statistics of lag 30. Same values for 1, 5, 10, 15, 20, 25

and 30 lags are presented in appendix-I. Z values and respective probabilities of runs test are

presented in this table. Details of runs test are presented in appendix-II. |Z(k)| and |Z*(k)| values

were calculated for k = 2, 3, …, 16, i.e. parameter value (m) = 15. Among those largest |Z(k)| and

|Z*(k)| values and respective k values and probabilities are presented in this table. Details of

variance ratio test of NEPSE (only) are presented in appendix-III. ADF (t) values and respective

probabilities of unit root test at level are presented in this table. Details of ADF test at level and

at first difference are presented in appendix-IV.


Table 2: Statistical Tests

Autocorrelation

Test

Runs Test

Multiple Variance Ratio Test

Unit Root Test Joint Test Under

homoscedastic assumption

{Z(k)}

Joint Test Under

heteroscedastic assumption

{Z*(k)}

Companies LB

Values Prob.

Z

Values Prob.

|Z(k)|

Max at k

Max |Z(k)|

Values

Prob. |Z*(k)|

Max at k

Max |Z*(k)|

Values

Prob. ADF

Values Prob.

ACEDBL 28.097 .565 2.051** 0.040 k = 7 1.094 0.992 k = 7 1.052 0.995 -1.473 0.131

BBC 23.978 .773 -0.281 0.779 k = 15 0.553 1.000 k = 3 0.705 1.000 -0.556 0.473

BOK 47.025** .025 -1.954 0.051 k = 16 2.207 0.340 k = 16 2.342 0.252 0.595 0.844

BUDBL 22.748 .825 0.906 0.365 k = 6 0.734 1.000 k = 6 0.903 0.999 -0.917 0.315

CEDBL 20.528 .902 0.177 0.860 k = 5 1.112 0.990 k = 4 1.659 0.784 -0.988 0.285

CHCL 31.967 .369 0.173 0.862 k = 14 0.747 1.000 k = 14 0.812 1.000 1.056 0.923

EBL 25.126 .719 -0.906 0.365 k = 2 2.485 0.178 k = 2 1.000 0.997 1.014 0.918

HBL 70.281* .000 0.480 0.631 k = 10 1.206 0.979 k = 10 1.208 0.979 -0.181 0.619

ICFC 15.201 .989 1.782 0.075 k = 2 3.241** 0.018 k = 2 2.723 0.093 -0.903 0.322

ILFC 42.695 .062 1.005 0.315 k = 15 1.634 0.802 k = 6 1.512 0.877 -0.071 0.656

KBL 30.900 .420 -1.262 0.207 k = 2 1.461 0.903 k = 2 1.362 0.942 0.051 0.697

LICN 26.719 .638 -1.544 0.123 k = 16 1.598 0.826 k = 16 1.562 0.849 1.873 0.985

NABIL 49.909** .013 0.196 0.845 k = 16 2.067 0.447 k = 16 2.105 0.416 0.616 0.848

NBB 27.761 .583 0.190 0.849 k = 2 2.390 0.225 k = 2 1.701 0.753 -0.300 0.576

NDEP 46.756** .026 2.301** 0.021 k = 2 2.493 0.174 k = 2 2.112 0.412 -3.507* 0.001

NEPSE 41.218 .083 -2.529** 0.011 k = 16 2.954** 0.046 k = 16 2.893 0.056 1.021 0.919

NHPC 13.407 .996 -2.200** 0.028 k = 4 0.957 0.998 k = 5 0.767 1.000 -0.901 0.323

NIB 38.977 .126 -1.283 0.199 k = 4 1.396 0.930 k = 4 1.572 0.843 -0.062 0.660

NLIC 47.182** .024 -1.846 0.065 k = 16 1.664 0.780 k = 16 1.639 0.798 1.747 0.980

NTC 11.212 .999 -0.076 0.939 k = 2 2.559 0.147 k = 2 5.309* 0.000 -1.264 0.188

OHL 32.251 .356 -0.785 0.432 k = 16 2.652 0.114 k = 16 2.494 0.174 0.770 0.878

PLIC 21.040 .887 -0.151 0.880 k = 3 1.457 0.905 k = 3 1.092 0.992 0.301 0.767

PRFL 45.482** .035 0.881 0.379 k = 3 3.018** 0.037 k = 3 3.625* 0.004 -3.234* 0.002

RIBSL 41.442 .080 1.362 0.173 k = 4 1.821 0.656 k = 4 2.139 0.390 -1.664 0.090

SBI 34.400 .265 0.468 0.640 k = 3 1.193 0.981 k = 3 1.235 0.974 0.646 0.855

SCB 59.598* .001 -2.546** 0.011 k = 16 1.414 0.923 k = 16 1.414 0.923 0.062 0.701

SIL 14.327 .993 0.383 0.702 k = 2 1.689 0.762 k = 2 1.337 0.950 -0.203 0.609

SUPRME 24.503 .749 -0.217 0.828 k = 3 2.082 0.435 k = 3 1.571 0.843 -0.361 0.550

UNL 26.717 .638 -0.861 0.389 k = 2 0.930 0.999 k = 2 1.098 0.992 3.583 1.000

* Significant at 1% level, ** Significant at 5% level

Autocorrelation Test

Autocorrelation test (LB statistic) results support the weak form efficiency for 21 (75%)

individual companies and reject for rest 7 (25%) individual companies at 5 percent level of

significance. Autocorrelation test (LB statistic) results have supported the weak form efficiency

for NEPSE return series at 5 percent level of significance.

Runs Test Runs test results support the weak form efficiency for 24 (85.71%) individual companies and

reject for rest 4 (14.29%) individual companies at 5 percent level of significance. Runs test

results have rejected the weak form efficiency for NEPSE return series at 5 percent level of

significance. The result of runs test of NEPSE are similar to the findings of Poshakwale (1996)

who found that the actual number of runs significantly lower than expected number of runs for

daily returns in India, Philipins, malaysia, and Thailand.

Variance Ratio Test (Z(k) Statistics) The hypothesis that the logarithm of the stock price follows a homoscedastic random walk is

accepted for return series of 26 (92.86%) individual companies and rejected for rest 3 (10.71%)

individual companies at 5% level of significance. Like the runs test, variance ratio test statistic

(Z(k)) has rejected the weak form efficiency for NEPSE return series at 5% level of significance.

In principle, the rejection of the hypothesis that the logarithm of the stock price follows a


homoscedastic random walk could result from either heteroscedasticity or autocorrelation in the

stock price index.

Variance Ratio Test (Z*(k) Statistics)

Variance ratio test statistics (Z*(k)) results accept the weak form efficiency for 26 (92.86%)

individual companies and reject for rest 2 (7.14%) individual companies. Unlike the test statistic

(Z(k)), (Z*(k)) has accepted the weak form efficiency for NEPSE return series at 5 percent level of

significance. Hence, rejection of the hypothesis that the logarithm of the NEPSE return follows a

homoscedastic random walk results from heteroscedasticity rather than autocorrelation in the

NEPSE return.

Unit Root Test ADF test results support the null hypothesis of unit root in return series for 26 (92.86%)

individual companies and reject for rest 2 (7.14%) individual companies. ADF test result has

accepted the null hypothesis of unit root in NEPSE return series at 5 percent level of

significance. By applying unit root test the results reveal that the data series become stationary at

order I (1).

Conclusions

Findings of different tests, though some inconsistency between them, indicate that Nepalese

stock market is efficient in weak form. The study result reveals that the monthly return series of

Nepalese companies listed in Nepal stock exchange and market return series do not follow any

predictable pattern. It implies that all information conveyed in stock price in the past are

impounded into the current price of the stock. Thus, the opportunity of making excess returns

based on information on past stock price in the Nepalese stock market is ruled out. This finding

is inconsistent with previous studies by Pradhan and Upadhyay (2004), Bhatta (2010) etc. It is

also doubtful about consistency of the result, when the observations are split up into sub-

samples. Little bit predictability on stock price is cancelled by costly transaction process. Hence,

analysis of past stock price of the companies listed in NEPSE is fruitless.

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Appendix I: Autocorrelation test

Companies Lags 1 5 10 15 20 25 30

ACEDBL

Autocorrelation Coefficients -0.068 -0.002 0.043 0.042 -0.247 -0.043 .007

LB Statistics Values 0.342 6.063 10.442 13.247 26.161 27.092 28.097

Prob. 0.559 0.3 0.403 0.583 0.161 0.351 .565

BBC

Autocorrelation Coefficients 0.003 -0.131 0.131 -0.082 0.057 -0.092 .010


Prob. 0.981 0.282 0.603 0.565 0.742 0.683 .773

BOK

Autocorrelation Coefficients 0.076 -0.163 0.123 0.035 0.094 -0.108 .008


Prob. 0.398 0.174 0.032 0.046 0.088 0.034 .025

BUDBL

Autocorrelation Coefficients -0.06 -0.005 -0.026 0.13 -0.168 -0.002 .140


Prob. 0.634 0.975 0.995 0.896 0.666 0.785 .825

CEDBL

Autocorrelation Coefficients -0.126 0.136 0.049 -0.156 -0.25 -0.054 -.039


Prob. 0.349 0.412 0.777 0.701 0.588 0.819 .902

CHCL

Autocorrelation Coefficients -0.027 -0.182 0.08 0.091 0.024 -0.105 .058


Prob. 0.798 0.405 0.186 0.087 0.156 0.279 .369

EBL

Autocorrelation Coefficients -0.233 -0.012 0.028 0.068 -0.054 0.029 -.010


Prob. 0.01 0.163 0.44 0.198 0.372 0.557 .719

HBL

Autocorrelation Coefficients -0.096 -0.003 0.31 0.132 -0.01 -0.035 -.118


Prob. 0.291 0.178 0.005 .000 .000 .000 .000

ICFC

Autocorrelation Coefficients -0.242 -0.098 -0.061 -0.041 -0.062 -0.048 .026


Prob. 0.043 0.304 0.503 0.794 0.936 0.985 .989

ILFC

Autocorrelation Coefficients -0.074 0.19 0.067 -0.028 0.054 -0.014 .000


Prob. 0.483 0.177 0.027 0.052 0.052 0.043 .062

KBL

Autocorrelation Coefficients -0.144 0.057 0.159 0.084 -0.071 -0.048 -.005


Prob. 0.131 0.165 0.315 0.194 0.152 0.251 .420

LICN

Autocorrelation Coefficients 0.052 0.024 0.002 0.086 0.049 -0.022 -.067


Prob. 0.572 0.932 0.858 0.818 0.843 0.851 .638

NABIL

Autocorrelation Coefficients -0.005 0.074 0.031 -0.128 -0.018 0.039 .121


Prob. 0.959 0.896 0.594 0.005 0.019 0.009 .013

NBB

Autocorrelation Coefficients -0.182 -0.074 0.163 0.006 0.036 0.124 .059


Prob. 0.047 0.322 0.26 0.419 0.483 0.423 .583

NDEP

Autocorrelation Coefficients -0.354 0.285 0.013 -0.01 -0.172 -0.171 .078


Prob. 0.01 0.038 0.218 0.444 0.247 0.017 .026

NEPSE

Autocorrelation Coefficients 0.094 -0.071 0.237 -0.033 0.055 -0.109 .062


Prob. 0.299 0.083 0.007 0.019 0.041 0.049 .083

NHPC Autocorrelation Coefficients -0.07 0.132 0.018 0.112 0.106 0.054 -.035



Prob. 0.552 0.625 0.899 0.926 0.956 0.991 .996

NIB

Autocorrelation Coefficients 0.033 -0.124 0.188 0.06 0.001 -0.046 .011


Prob. 0.717 0.079 0.004 0.022 0.045 0.109 .126

NLIC

Autocorrelation Coefficients 0.115 0.168 0.247 0.02 0.023 -0.067 -.019


Prob. 0.207 0.061 0.003 0.004 0.009 0.024 .024

NTC

Autocorrelation Coefficients -0.05 0.006 -0.01 0.034 -0.085 -0.095 -.014


Prob. 0.695 0.517 0.761 0.953 0.985 0.993 .999

OHL

Autocorrelation Coefficients -0.002 0.284 0.145 -0.073 0.025 -0.062 -.146


Prob. 0.982 0.038 0.034 0.085 0.209 0.386 .356

PLIC



Prob. 0.34 0.212 0.639 0.387 0.597 0.695 .887

PRFL

Autocorrelation Coefficients -0.214 0.187 0.299 0.038 0.265 -0.137 -.073


Prob. 0.097 0.084 0.023 0.061 0.023 0.017 .035

RIBSL

Autocorrelation Coefficients -0.19 -0.094 -0.024 0.132 -0.148 -0.125 .002


Prob. 0.167 0.074 0.208 0.45 0.29 0.128 .080

SBI

Autocorrelation Coefficients 0.057 -0.132 0.093 -0.005 0.062 -0.061 -.010


Prob. 0.532 0.511 0.511 0.325 0.404 0.405 .265

SCB

Autocorrelation Coefficients 0.046 -0.084 0.083 -0.166 0.124 -0.062 -.206


Prob. 0.608 0.55 0.387 0.001 0.002 0.001 .001

SIL



Prob. 0.119 0.501 0.844 0.906 0.966 0.995 .993

SUPRME

Autocorrelation Coefficients 0.235 0.088 0.006 0.007 -0.071 -0.031 .041


Prob. 0.09 0.446 0.827 0.979 0.997 1 .749

UNL

Autocorrelation Coefficients 0.092 -0.015 0.099 -0.234 -0.039 -0.105 -.048


Prob. 0.385 0.513 0.606 0.4 0.676 0.56 .638


Appendix II: Runs test

Companies

Test Value

(Mean)

Cases <

Mean

Cases ≥

Mean

Total

Cases

Number of

Runs Z

Asymp. Sig. (2-

tailed)

ACEDBL -0.024 37 34 71 45 2.051 0.04

BBC -0.004 31 38 69 34 -0.281 0.779

BOK 0.009 65 55 120 50 -1.954 0.051

BUDBL -0.019 31 30 61 35 0.906 0.365

CEDBL -0.021 22 30 52 27 0.177 0.86

CHCL 0.016 46 39 85 44 0.173 0.862

EBL 0.012 62 58 120 56 -0.906 0.365

HBL -0.001 57 62 119 63 0.48 0.631

ICFC -0.019 38 29 67 41 1.782 0.075

ILFC 0.004 46 41 87 49 1.005 0.315

KBL 0.002 54 53 107 48 -1.262 0.207

LICN 0.022 65 51 116 50 -1.544 0.123

NABIL 0.008 62 58 120 62 0.196 0.845

NBB -0.002 59 57 116 60 0.19 0.849

NDEP -0.043 26 24 50 34 2.301 0.021

NEPSE 0.008 64 56 120 47 -2.529 0.011

NHPC -0.016 39 30 69 26 -2.2 0.028

NIB 0.001 60 60 120 54 -1.283 0.199

NLIC 0.024 69 48 117 48 -1.846 0.065

NTC -0.015 27 32 59 30 -0.076 0.939

OHL 0.011 64 38 102 45 -0.785 0.432

PLIC 0.007 19 17 36 18 -0.151 0.88

PRFL -0.025 33 24 57 32 0.881 0.379

RIBSL -0.036 21 29 50 30 1.362 0.173

SBI 0.01 61 58 119 63 0.468 0.64

SCB 0.002 57 63 120 47 -2.546 0.011

SIL -0.001 32 31 63 34 0.383 0.702

SUPRME -0.009 27 22 49 24 -0.217 0.828

UNL 0.023 50 36 86 39 -0.861 0.389

Appendix III: Variance ratio test of NEPSE

Test Under homoscedastic assumption {Z(k)} Test Under heteroscedastic assumption {Z*(k)}

Joint Tests Value Prob. Joint Tests Value Prob.

Max |z(k)| (at k=16)* 2.954035 0.0460 Max |z*(k)| (at k=16)* 2.892914 0.0557

Individual Tests Individual Tests

Period (k) Variance Var. Ratio Z-Statistic Prob. Period (k) Variance Var. Ratio Z*-Statistic Prob.

1 0.00632 - - - 1 0.00632 - - -

2 0.00699 1.105849 1.159517 0.2462 2 0.00699 1.10585 1.138511 0.2549

3 0.00818 1.292988 2.153011 0.0313 3 0.00818 1.29299 2.142748 0.0321

4 0.00867 1.371524 2.175423 0.0296 4 0.00867 1.37152 2.140544 0.0323

5 0.00865 1.367155 1.835773 0.0664 5 0.00865 1.36715 1.779404 0.0752

6 0.00851 1.345633 1.531601 0.1256 6 0.00851 1.34563 1.474501 0.1403

7 0.00833 1.317594 1.276468 0.2018 7 0.00833 1.31759 1.227689 0.2196

8 0.00835 1.320906 1.188405 0.2347 8 0.00835 1.32091 1.144828 0.2523

9 0.00865 1.367156 1.267181 0.2051 9 0.00865 1.36716 1.223209 0.2213

10 0.00913 1.443140 1.437735 0.1505 10 0.00913 1.44314 1.390467 0.1644

11 0.00987 1.560066 1.719738 0.0855 11 0.00987 1.56007 1.666345 0.0956

12 0.01065 1.684544 2.000174 0.0455 12 0.01065 1.68454 1.942028 0.0521

13 0.01153 1.823051 2.298657 0.0215 13 0.01153 1.82305 2.236970 0.0253

14 0.01238 1.956895 2.563958 0.0103 14 0.01238 1.95689 2.500933 0.0124

15 0.01313 2.075553 2.773644 0.0055 15 0.01313 2.07555 2.711075 0.0067

16 0.01383 2.186987 2.954035 0.0031 16 0.01383 2.18699 2.892914 0.0038

* Probability approximation using studentized maximum modulus with parameter value 15 and infinite degrees of freedom


Appendix IV: Unit root test

Companies

Unit Root Test at level Unit Root Test at first Difference

t-Statistic 1% level 5% level 10% level Prob.* t-Statistic 1% level 5% level 10% level Prob.*

ACEDBL -1.473 -2.598 -1.945 -1.614 0.131 -8.626 -2.598 -1.946 -1.614 0.000

BBC -0.556 -2.599 -1.946 -1.614 0.473 -8.129 -2.599 -1.946 -1.614 0.000

BOK 0.595 -2.584 -1.944 -1.615 0.844 -10.008 -2.585 -1.944 -1.615 0.000

BUDBL -0.917 -2.603 -1.946 -1.613 0.315 -7.987 -2.604 -1.946 -1.613 0.000

CEDBL -0.988 -2.610 -1.947 -1.613 0.285 -7.866 -2.611 -1.947 -1.613 0.000

CHCL 1.056 -2.592 -1.945 -1.614 0.923 -9.040 -2.593 -1.945 -1.614 0.000

EBL 1.014 -2.585 -1.944 -1.615 0.918 -13.625 -2.585 -1.944 -1.615 0.000

HBL -0.181 -2.585 -1.944 -1.615 0.619 -11.900 -2.585 -1.944 -1.615 0.000

ICFC -0.903 -2.600 -1.946 -1.614 0.322 -12.491 -2.600 -1.946 -1.614 0.000

ILFC -0.071 -2.592 -1.945 -1.614 0.656 -9.936 -2.592 -1.945 -1.614 0.000

KBL 0.051 -2.587 -1.944 -1.615 0.697 -11.737 -2.587 -1.944 -1.615 0.000

LICN 1.873 -2.585 -1.944 -1.615 0.985 -9.520 -2.585 -1.944 -1.615 0.000

NABIL 0.616 -2.584 -1.944 -1.615 0.848 -10.838 -2.585 -1.944 -1.615 0.000

NBB -0.300 -2.585 -1.944 -1.615 0.576 -13.607 -2.585 -1.944 -1.615 0.000

NDEP -3.507 -2.613 -1.948 -1.613 0.001 -8.827 -2.613 -1.948 -1.613 0.000

NEPSE 1.021 -2.584 -1.944 -1.615 0.919 -9.718 -2.585 -1.944 -1.615 0.000

NHPC -0.901 -2.599 -1.946 -1.614 0.323 -8.871 -2.599 -1.946 -1.614 0.000

NIB -0.062 -2.584 -1.944 -1.615 0.660 -10.476 -2.585 -1.944 -1.615 0.000

NLIC 1.747 -2.585 -1.944 -1.615 0.980 -8.955 -2.585 -1.944 -1.615 0.000

NTC -1.264 -2.605 -1.946 -1.613 0.188 -12.756 -2.605 -1.947 -1.613 0.000

OHL 0.770 -2.588 -1.944 -1.615 0.878 -9.978 -2.588 -1.944 -1.615 0.000

PLIC 0.301 -2.631 -1.950 -1.611 0.767 -6.726 -2.633 -1.951 -1.611 0.000

PRFL -3.234 -2.608 -1.947 -1.613 0.002 -10.938 -2.607 -1.947 -1.613 0.000

RIBSL -1.664 -2.612 -1.948 -1.613 0.090 -7.940 -2.613 -1.948 -1.613 0.000

SBI 0.646 -2.585 -1.944 -1.615 0.855 -10.161 -2.585 -1.944 -1.615 0.000

SCB 0.062 -2.584 -1.944 -1.615 0.701 -10.353 -2.585 -1.944 -1.615 0.000

SIL -0.203 -2.602 -1.946 -1.613 0.609 -9.288 -2.603 -1.946 -1.613 0.000

SUPRME -0.361 -2.613 -1.948 -1.613 0.550 -4.188 -2.615 -1.948 -1.612 0.000

UNL 3.583 -2.592 -1.945 -1.614 1.000 -7.368 -2.592 -1.945 -1.614 0.000

* MacKinnon (1996) one-sided p-values.

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Analysis of Stock Market Efficiency

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