Abstract

The dearth of empirical studies substantiating the merits of technical analysis limits the legitimacy of the field. This study seeks to address that by offering evidence that Pakistan does not conform to the assumptions of weak form efficiency and therefore offers opportunities to generate abnormal returns using historical data such as that employed by technical analysts. Results of three versions of the runs test, the Augmented Dickey Fuller test, the Phillips Perron test, and an autoregressive model of order one, point to a lack of randomness, and thus a lack of weak form efficiency, over the two periods studied.

Introduction

This study employs parametric and non-parametric tests to assess whether Pakistan’s KSE- 100 Index is weak form efficient. Eugene Fama (1965, 1970) posited via the Efficient Market Hypothesis (EMH) that stock prices are unpredictable. The weak form of Fama’s EMH implies that stock prices include all past information. When that is the case, prices move randomly which suggests that tools used by technical analysts such as past prices, charts, and pattern recognition are not helpful in assessing the future direction of prices. Therefore, any attempt at routinely finding undervalued securities using these methods is futile. If, however, prices are not random, that condition violates weak form efficiency and provides a theoretical foundation for the value of technical analysis.

Pakistan’s benchmark index serves as the test case for this analysis. Daily closing prices, as well as price returns, for the Karachi Stock Exchange’s KSE-100 index between January 1, 2008 and December 31, 2010, as well as January 1, 2019 through 2021, are tested for randomness. Since published literature does not appear to include data on the latter period and little, if any, research evaluates market efficiency specifically during bear markets, this affords the opportunity to test the hypothesis that Pakistan’s benchmark index has become weak form efficient over time and remains so during market downturns when emotions may cause investors to act irrationally.

The results of statistical tests evaluated in this article suggest that returns in Pakistan’s main stock market are not random and not weak form efficient. This implies that investors can generate above-market returns using technical analysis. Following a review of the literature on Random Walk theory, the Efficient Market Hypothesis, and the Adaptive Market Hypothesis, the methodology is presented, and results are analyzed.

Literature Review

Among other functions, stock markets channel investment and act as a gauge of the financial environment of a country. When stock prices incorporate all available information and thus accurately reflect the value of listed companies, capital flows optimally based on risk-reward tradeoffs. In such an efficient market, where securities are always priced at fair value, attempts to predict market outcomes and identify undervalued assets are useless. Efficiency in the context of the EMH is therefore a reference to the information content of a security that links asset prices to their value.

The efficiency of developed markets is well documented. Market efficiency implies that prices fully incorporate all available information, are random, and are unpredictable. Investors are only able to earn above-market returns in these jurisdictions by assuming above-market levels of risk. Even in developed markets, however, a degree of ambiguity remains regarding the type of information that is included in stock prices, as well as the speed that constitutes instantaneous incorporation of information. Dsouza and Mallikarjunappa (2015) point out that some interval of time is necessary for the market to absorb new information, even if that period is only split seconds.

The situation is different in many developing markets where even the most basic form of market efficiency has not been empirically established and no consensus exists as to the validity of EMH. Developing countries often differ from those in developed markets in terms of liquidity, regulation, trading infrastructure, and information availability, among other things. To that point, past studies by Han Kim and Singal (2000) suggest that liberalization via opening markets to foreign capital can lead to market efficiency. Naidu and Rozeff (1994), as well as Jain (2005), show that electronic trading can also improve efficiency while Antoniou, Ergul, and Holmes (1997) demonstrate efficiency increases as the regulatory environment in a market improves. At the other extreme, one factor that can reduce market efficiency is the use of circuit breakers that place a ceiling or floor on prices, thus limiting price movements.

If markets are not efficient and prices and returns are not random, then opportunities exist for investors to profit by leveraging past information and chart patterns. Methods for evaluating weak form efficiency ascertain whether prices are predictable by testing their randomness.

Random Walk Theory

The random walk model was first evaluated by Bachelier (1900) with the hypothesis that generating above market returns is not feasible. By definition, a random walk lacks a pattern. As applied to stock markets, randomness implies that asset prices are a function of the prior period’s price plus or minus a zero-mean, random, independent quantity. Stated differently, tomorrow’s stock price is anyone’s guess and the likelihood of stocks increasing or decreasing on any given day is independent of what occurred the prior day or during any previous period.

Efficient Market Hypothesis (EMH)

Random Walk Theory and EMH have similarities. Fama (1965, 1970) suggested that because the information flows in efficient markets take place randomly, changes in stock prices should also occur randomly. Both theories suggest an inability to profitably predict stock prices. One key difference between the two theories, however, is the EMH assumption that investors act rationally. This implies that investors use information advantages to arbitrage away any price discrepancies, thereby ensuring that prices remain at their fair value and markets stay efficient.

EMH was independently pioneered by Paul Samuelson (1965) and Eugene Fama (1965, 1970). Fama used US stock market data from 1956 through 1962 to test the statistical dependence between stock prices. Finding none, he was the first to use the label “efficient” to denote this condition.

Fama (1970) conceptualized three stages of market efficiency, each of which build on the prior stage. Weak form efficiency predicts that all historical information is fully incorporated into stock prices, thereby negating the value of technical analysis. Semi- strong efficiency predicts all historical and publicly available information is incorporated into prices and suggests neither technical nor fundamental analysis is useful for generating abnormal returns according to the website myaccountingcourse.com (n.d.). Strong form efficiency occurs when even inside information cannot be leveraged to generate above market returns. In short, Fama described efficient markets as those where asset prices match their fair value and where no amount of proprietary information will allow for returns above those that are commensurate with the level of risk assumed.

Adaptive Market Hypothesis (AMH)

Not all evidence in all countries supports that markets are efficient. Lo’s Adaptive Market Hypothesis (2004) bridges the gap between EMH and evidence refuting it by implying that efficiency varies over time and among markets. This condition allows for the more realistic possibility that market efficiency varies on a spectrum between complete efficiency and complete inefficiency. It also implies certain markets may be predictable at certain times if EMH does not always hold. Myriad reasons may explain a lack of efficiency but one of them may be Fama’s exacting requirement for prices to “fully” incorporate all available information which establishes a high standard for complete efficiency.

The predictions of AMH are therefore consistent with a periodic lack of weak form efficiency. AMH also helps explain phenomena such as trends, bubbles, anomalies, and cycles, all of which are well known to technical analysts. AMH theory is aligned with scholarship such as that of Grossman and Stiglitz (1980) indicating that investors who expend effort to compile information regarding profitable trading opportunities require compensation for doing so. The logical follow-on is that, particularly in developing markets where information gathering can present a challenge, investors must be incentivized to pursue costly due diligence efforts. All of these issues point to possible gaps in EMH theory.

Pakistan’s Stock Market

Hussain and Qasim (1997) share that the KSE-100 index was launched and the Pakistani stock market was opened to foreign investors in 1991. This was followed by the implementation of electronic trading in 1998 and a series of other regulatory improvements over time to address governance, transparency, and investor protections.

Despite the steps to improve efficiency scholars such as Haque and Liu (2011), Irfan, Saleem, and Irfan (2011), Riaz, Hassan, and Nadim (2012), Mudassar and co-authors (2013), and Rizwan Qamar and Sheikh (2014) conclude that the KSE-100 index lacks weak form market efficiency. However, when using monthly data, Khan and Khan (2016) find the KSE- 100 to be weak form efficient. The same is true for Mustafa and Nishat (2007) after adjusting for thin trading, while Chakraborty (2006) finds indications of weak form efficiency only during the most recent sub-periods of a longer study. The data are therefore inconclusive and merit further evaluation.

Methodology

Using closing prices for the KSE-100 obtained from Bloomberg (2022) for the periods January 1, 2008 through December 31, 2010 (“early data”) and January 1, 2019 through December 31, 2021 (“recent data”), this study evaluates the weak form efficiency of Pakistan’s stock index by testing for randomness.

Tests of Normality

Both parametric and non-parametric tests are employed to evaluate the study’s null hypothesis that returns are random. However, parametric tests are only valid when distributions are normal. In the absence of normality, inferences may be unreliable. Normality is therefore evaluated via the Shapiro-Wilk test (1965), the Shapiro-Francia test (1972), and the Kolmogorov-Smirnov test created by Kolmogorov (1933) and Smirnov (1948) and amended by Lilliefors (1967).

The Kolmogorov-Smirnov test measures the widest point between a sample distribution and a normal distribution and fails to reject the null hypothesis of normality when that distance is within tolerable levels. The Shapiro-Wilk and Shapiro-Francia tests are goodness of fit tests that resemble the Kolmogorov-Smirnov methodology in that they assess the relationship between the sample data and a normal distribution, but they do so by weighting differences of paired data.

For time series data, Wooldridge (2020) suggests that each collection of data represents one possible realization of a random draw that is determined by historical conditions. The same draw would be different in the face of different conditions. Therefore, it is acceptable to assume time series data are random which allows researchers to perform parametric tests such as the Augmented Dickey Fuller test below, created by Dickey and Fuller (1979, 1981), even when normality is not assured.

Tests for Randomness

Runs Test

Rather than testing raw prices for randomness, Fama’s seminal research (1965) uses returns. A price change of $5 on a $100 stock represents a 5% change, but that same 5% change constitutes a $50 move for a stock that is priced at $1,000. A method to neutralize the effect that rising prices have on variability is to employ logarithmic price returns as the unit of analysis. To do so, the data are transformed via the equation

where r is the price return, P equals price, t represents the current time period and t-1 represents the prior time period.

Data that are transformed per equation (1) above are used to test the null hypothesis that returns are random first by employing the non-parametric runs test as postulated by Wald and Wolfowitz (1940). Naghshpour (2016) defines a run as a string of consecutive trading days where one-day price returns are entirely positive or negative. Each consecutive string of positive days forms a single run, as does a string of negative days. This is somewhat similar to the strings of x’s and o’s used by point and figure technicians except that, instead of beginning a new column each time a change occurs, the runs test registers a reversal as an additional run. In the extreme case where the market increases (or decreases) every day over a test period, the data would contain a single run whereas alternating between positive and negative returns every day would entail a number of runs equal to the sample size.

The claim of the runs test is that returns are not random if the data contain too many or too few runs compared to the number that is expected by chance. In other words, according to Gibbons and Chakraborti (2011), returns that lack randomness are expected to have clusters of up or down days that produce fewer, longer runs than random returns. Additional runs tests, used to provide more conclusive results, compare the number of observations falling above and below the mean and the median. Weak form efficiency is assumed when a sufficiently high p-value causes the researcher to fail to reject the null hypothesis. This implies that returns follow a random walk and past returns, therefore, cannot be used for predictive purposes.

To obtain critical values when the number of observations exceeds 20 (the maximum covered by existing statistical tables), a continuity correction factor is recommended. In that instance, the mean expected number of runs (𝜇𝜇̂R) is calculated as:

where n1 is the number of observations that increase versus the prior trading day and n2 is the number of observations that decrease compared to the prior day. The expected standard deviation for the number of runs is:

while the Z statistic is computed as:

Finally, the continuity correction factor (h) is calculated with the formulas:

One drawback of the runs test is that it fails to account for the magnitude of price changes and, instead, considers only whether returns are positive or negative. Another limitation of this test is its low power. When power is defined as the potential for a Type II error, this implies that the runs tests has a somewhat poor record of properly rejecting the null hypothesis when it is incorrect.

Augmented Dickey-Fuller (ADF) Test

The parametric ADF test, created by Dickey and Fuller (1979, 1981), is a tool used in time series analysis to test for stationarity. As defined by Hill and his co-authors (2017), a process is stationary when it lacks trends or seasonality, is identically distributed across all time periods, and has an unchanging mean and variance over time. Stationarity can be tested by assessing whether the data contain a unit root, with a unit root being a necessary condition for randomness and therefore weak form efficiency. The precise methodology, which is beyond the scope of this study, uses an autoregressive model to evaluate whether a unit root is present. The null hypothesis for the ADF test is non- stationarity, meaning the data have a unit root. In practice, failing to reject the null hypothesis therefore implies a lack of randomness and a degree of predictability.

Phillips-Peron (PP) Test

The Phillips-Peron test (1988) also tests for randomness by evaluating whether the series contains a unit root. It modifies the Dickey Fuller methodology by correcting for any autocorrelation or heteroskedasticity. Like the ADF test, the null hypothesis is non- stationarity, indicating the presence of a unit root.

Autoregressive (AR) Models

With autoregressive time series models, lagged values of the dependent variable are used as explanatory variables to determine the statistical significance of the association between past and current values. An autoregressive model of order one (AR1) uses only a one-period lag as a predictor

In the above model, Y represents the logarithmic return while the coefficient ẞ1 represents the presence of a unit root when the absolute value of the coefficient is one. Again, the presence of a unit root indicates randomness and conformity with weak form efficiency.

Analysis

Descriptive statistics for both time periods studied are found in Table I. As can be seen in the table, both series are negatively skewed and leptokurtic.

Table I Descriptive Statistics of KSE-100 Daily Price Returns

This skewness and kurtosis are the reasons the data are not normal. P-values for all three normality tests in both time periods are 0.0000, offering evidence of the lack of normality.

The runs tests is a non-parametric test that does not assume normality. Its null hypothesis is randomness, meaning that a failure to reject the null hypothesis is consistent with weak form efficiency. Tables II-IV illustrate that returns are not random in either time period based on evidence from the standard runs test and from alternative runs tests using median and mean. Again, this indicates that the KSE-100 is not weak form efficient.

Table II Results of Runs Tests

Table III Results of Runs Tests Based on Median

Table IV Results of Runs Tests Based on Mean

The 2008-2010 data contain a 110-day period between August 2008 and December 2008 when the circuit breakers were implemented to limit price movements during the market uncertainties of the Great Recession. The total price return for the KSE-100 during this period was 0.46% due to negligible or zero price changes on most days. By comparison, the price return for the US market over the same time period was -31.8%. When circuit breakers were lifted in December 2008, the KSE-100 fell by 46.8% over 13 trading days, representing a particularly long run. This inability of prices to move freely clearly inhibits the efficiency of markets. Excluding the period during which circuit breakers were engaged, the longest string of runs for the early data occurred in June and July 2008 when the index fell by 19.8% over 15 trading days as is illustrated by the shaded area in in Figure I. The length alone suggests that prices may not immediately incorporate new information, although further empirical studies are needed to confirm that hypothesis.

Figure I Run Length versus Cumulative Returns During the Run

By contrast, the longest string of runs for the 2019-2021 data was a 13-trading day stretch when the market increased by 8.6%. While not conclusive evidence, this could suggest that a lack of randomness may not be a function that occurs only in bear markets.

The results of the ADF and PP tests using closing prices support the conclusions from the runs tests. Failing to reject the null hypothesis that prices have a unit root implies that prices lack randomness and are therefore inconsistent with weak form efficiency.

Table V P-Values for the ADF and PP Tests

Finally, autoregressive models using a one-period lag of the dependent variable to explain the price return for the following period are significant. The p-value of the model is 0.0000 for the 2008-2010 data and 0.0003 for the 2019-2021 data. Again, this points to a non- random relationship between past and current values which is inconsistent with weak form efficiency.

Conclusions

Randomness is a feature of weak form efficiency of the Efficient Markets Hypothesis. The normative question of whether weak form efficiency is positive or negative is not debated here. Instead, the tested hypothesis, that Pakistan’s benchmark index has become weak form efficient over time and remains so during market downturns, is evaluated by examining whether prices and returns on the KSE-100 conform to the assumption of weak form efficiency by displaying a random distribution.

The relative dearth of academic studies regarding the merits of technical analysis is often mentioned as concerning in terms of the legitimacy of the field. This study sought to address that issue by offering empirical evidence that at least one emerging market, Pakistan, does not conform to the assumptions of weak form efficiency and therefore offers evidence of opportunities to generate abnormal returns using historical data such as that employed by technical analysts. Based on three versions of the runs test, the Augmented Dickey Fuller test, the Phillips Perron test, and an autoregressive model of order one, the evidence points to a lack of randomness over the two periods studied. This implies a lack of conformity with weak form efficiency and a degree of predictability in the market. However, because the results may not be generalizable to other developing markets, further research is merited.

While the findings are inconsistent with the Efficient Market Hypothesis, they conform to the predictions of the Adaptive Market Hypothesis. Numerous factors may impede market efficiency, but the EMH requirement for investors to act rationally represents a material hurdle that may not hold for myriad reasons. As this study demonstrated, investors may be slow to incorporate information in a market that is moving strongly in one direction or the other. In addition, institutional constraints may impede investors from acting rationally in the presence of circuit breakers. While not addressed in this study, factors such as fake news and behavioral biases, among other things, could also affect rational behavior. This message is encouraging for active investors and technical traders. Because prices are not random and the KSE-100 is not weak form efficient, the use of historical price information offers a way to systematically leverage profitable trades.

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