Informational Efficiency Characteristics of the Philippine Stock Market By Rodolfo Q. Aquino * Abstract The objective of this essay is to test the informational efficiency of the Philippine stock market in the sense that stock prices already reflect all relevant information. Stock market efficiency is defined in the traditional sense of informational efficiency, i.e., weak- form, semistrong-form, and strong-form efficiency. This essay will look only at weak-form and semistrong-form efficiency. The period covered is from 1987-2000. Various statistical tools are used on daily, monthly and quarterly aggregate prices and returns. The results on weak-form efficiency are as expected from previous results in the available literature. The hypothesis that the local stock market is weak-form informationally efficient is rejected by the data on statistical grounds. However, the information carried by past prices is so negligible as to enable market participants to reap excess profits net of transaction costs. Thus, for all practical purposes, it can be stated that the market is weak- form efficient in the sense that market players cannot make abnormal profits using only past price information. When macroeconomic information is added to the information set, the statistical evidence is that the market is also not semistrong-form efficient. In addition, the degree of inefficiency may be enough to enable skilled market players to trade on publicly available information and make above average profits in excess of transactions costs. Various explanations are offered for the results. The list is not exhaustive but it includes the thinness of the local stock market and the high ownership concentration in publicly listed companies, the absence of an active investment analyst community because of limited institutional investor participation in the stock market, and shortcomings in financial disclosure requirements and practices. Any effort to address market inefficiency must address these issues. * Professor of Accounting and Finance, College of Business Administration, University of the Philippines
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Informational Efficiency Characteristics of the Philippine Stock Market
By Rodolfo Q. Aquino*
Abstract
The objective of this essay is to test the informational efficiency of the Philippine
stock market in the sense that stock prices already reflect all relevant information. Stock
market efficiency is defined in the traditional sense of informational efficiency, i.e., weak-
form, semistrong-form, and strong-form efficiency. This essay will look only at weak-form and
semistrong-form efficiency. The period covered is from 1987-2000. Various statistical tools
are used on daily, monthly and quarterly aggregate prices and returns.
The results on weak-form efficiency are as expected from previous results in the
available literature. The hypothesis that the local stock market is weak-form informationally
efficient is rejected by the data on statistical grounds. However, the information carried by
past prices is so negligible as to enable market participants to reap excess profits net of
transaction costs. Thus, for all practical purposes, it can be stated that the market is weak-
form efficient in the sense that market players cannot make abnormal profits using only past
price information.
When macroeconomic information is added to the information set, the statistical
evidence is that the market is also not semistrong-form efficient. In addition, the degree of
inefficiency may be enough to enable skilled market players to trade on publicly available
information and make above average profits in excess of transactions costs.
Various explanations are offered for the results. The list is not exhaustive but it
includes the thinness of the local stock market and the high ownership concentration in
publicly listed companies, the absence of an active investment analyst community because of
limited institutional investor participation in the stock market, and shortcomings in financial
disclosure requirements and practices. Any effort to address market inefficiency must address
these issues.
* Professor of Accounting and Finance, College of Business Administration, University of the
Philippines
1
1 Introduction
The objective of this essay is to test the informational efficiency of the Philippine stock market in the sense that stock prices already reflect all relevant information. Stock market efficiency is defined in the traditional sense of informational efficiency, i.e., weak-form, semistrong-form, and strong-form efficiency. This essay will look only at weak-form and semistrong-form efficiency.
The next section (Section 2) addresses the importance of informationally efficient markets. Section 3 defines the terms more precisely and then reviews the literature on efficiency testing. Section 4 then subjects the question of whether the stock market is weak-form efficient to a battery of tests. Section 5 tests whether the stock market is semistrong efficient with respect to available information on macroeconomic variables. Section 6 reviews the empirical results and their implications and concludes the essay.
2 Importance of Informationally Efficient Markets
From the viewpoint of economic policy-makers, the answer to the question whether the stock market is efficient is important because an efficient market can potentially have significant contributions to the country’s objectives of fostering higher savings, more efficient allocation of investible resources, better utilization of existing resources, and higher economic growth. An efficient capital market where prices of financial assets adjust quickly to new information enables more informed and efficient investment choices, reduces uncertainty, and promotes additional investments. By contrast, in an inefficient capital market where information is limited or unreliable, difficult to process, and only gradually revealed to market players, investors find it hard to make sound investment decisions. The resulting uncertainty will induce potential investors to shorten their investment horizons, demand higher returns for the risks they perceive themselves to be taking (thus raising the cost of capital), or altogether withdraw from the market, thereby reducing the supply of investible funds. The implication of this discussion is that, if the stock market is efficient, then no government intervention is required. If the stock market is inefficient, then there is a prima facie case for government intervention. However, the specific forms of intervention depend on the sources and degree of inefficiency and the consequences of intervention have to be studied carefully as there are always risks attached to any policy that can impact on the behavior of economic agents.
From the point of view of individual investors or speculators in the stock market, the answer to the question of stock market efficiency determines whether security analysis tools, whether based on so-called technical analysis or charting or based on the analysis of fundamentals, can be useful in making profitable investment decisions. If the stock market if efficient, all that a risk-averse investor can do is to buy and hold the market portfolio. No amount of technical analysis (based on the movements of past stock prices) or fundamental analysis (based on public information such as dividend and earnings announcements, releases of macroeconomic news, mergers, etc.) will enable the investor to earn trading profits over and above his transaction costs and the costs of obtaining information. At the very extreme, insiders will not be able to make use of private information to earn abnormal trading profits.
3 Efficient Market Hypothesis
3.1 Definitions
Malkiel (1992) gives the following much-quoted definition of an efficient market:
“A capital market is said to be efficient if it fully and correctly reflects all relevant information in determining security prices. Formally, the market is said to be efficient with respect to some information set, , if security prices would be unaffected by revealing that information to all participants. Moreover, efficiency with respect to an information set, . implies that it is impossible to make economic profits by trading on the basis of .”
2
Malkiel’s second sentence makes the definition of informational efficiency operational for statistical testing. In particular, this definition can be formulated in rational expectations framework. Rationality of expectations implies that (Mishkin, 1983):
(1) 0)yy(E 1tett
where ety is the one-period-ahead forecast of a variable yt generated at the end of period t-1,
t-1 is the information set available at the end of period t-1, and )(...E 1t is the expectation
operator conditional on t-1. This implies that the forecast error, e1tt yy , should be
uncorrelated with any information or linear combination of information in t-11.
Malkiel’s third definition qualifies the second definition in that it introduces transaction costs. Acceptance of the efficient market hypothesis, with respect to some information set, , based on statistical testing implies market efficiency. Rejection of the hypothesis, however, does not automatically imply market inefficiency unless it can be shown that trading on the basis of can lead to returns that exceed transaction costs. Some authors refer to this concept of efficiency as operational efficiency.
The classic taxonomy of information sets in finance, often attributed to Fama (1970)2, distinguishes among the three concepts:
Weak-form Efficiency: The information set includes only the history of prices or returns themselves. Thus, investors cannot devise an investment strategy to yield abnormal profits on the basis of analyzing past price patterns (a technique known as technical analysis).
Semistrong-form Efficiency: The information set includes all information known to all market participants (i.e., publicly available information). In this case, investors cannot earn abnormal profits by analyzing macroeconomic and financial data or any other public information about the company (a technique known as fundamental analysis).
Strong-form Efficiency: The information set includes all information known to any market participant (i.e., private information). Hence, even those with privileged or “inside” information cannot use them to make abnormal profits. There is perfect incorporation of all private information in market prices.
Note that, strong-form efficiency implies semistrong-form efficiency and semistrong- form efficiency implies weak-form efficiency. This can be seen by defining two information
sets t-1 and t-1 such that t-1 t-1 and 0)yy(E 1tett . By the law of iterated
expectations,
0)yy(E)]y(EE[y
]])y(E[Ey[E)]y(Ey[E)yy(E
1tett1ttt
1t1ttt1ttt1tett
To give (1) empirical content, the relationship between the probability distribution of future prices or returns and present prices or returns must be specified. This requires a model that describes how current equilibrium prices and returns are determined. Here, returns are
usually assumed to constitute a fair game, that is, the expected equity return etr is a constant:
1 This is weaker than independence of any information or any combination (not just linear) of
information in t, see Campbell et al (1997), Chapter 1. See also succeeding discussions. 2 Malkiel (1989) and Campbell, Lo and MacKinlay (1997) attribute first claim to an unpublished 1967
manuscript of H. Roberts.
3
(2) r~)r(Er 1ttet .
This implies that:
0)r~r(E)rr(E 1tt1tett .
3.2 Market Efficiency Tests
Cuthberston (1996) classified efficiency testing procedures into the following types:
o Tests of whether excess returns e1tt rr at time t are independent of information 1t
available at time t-1. This type is referred to as a test of informational efficiency and, as mentioned, requires an explicit representation of the equilibrium asset pricing model used by agents. Note that the essential characteristic of informational efficiency is predictability or forecastability.
o Tests of whether actual trading rules, e.g., buy low, sell high, can earn abnormal or above average profits after taking account of transaction costs and the general risk characteristics of the asset or portfolio of assets in question. These tests usually involve simulations mimicking possible investor behavior and computing simulated profits from alternative trading strategies against a benchmark like holding a market portfolio.
o Tests of whether market prices are always equal to fundamental values. Campbell and Shiller (1988) pioneered this type of tests which use past dividend data and calculate fundamental value (or the variance of fundamental value) using some form of discounted present value calculation. Then they test whether actual stock prices equal the fundamental value or, more precisely, whether the variation in actual prices is consistent with that dictated by the variability in fundamentals. For this reason, these tests are usually called volatility or variance bound tests.
Only informational efficiency testing will be used in this essay. Hence, in what follows, only the different types of informational efficiency testing will be discussed in more detail. Tests of simulated trading rules are not covered in this essay mainly because it is difficult to specify exhaustively the many trading rules possible as well as to put the tests consistently in the context of macroeconomic factors which are the subject of this inquiry. Volatility tests are also not includes partly because of the absence of long and consistent dividend history on the part of listed firms.
Tests of weak-form efficiency generally involve tests of the random walk hypothesis. Surprisingly, the random walk hypothesis has not been defined consistently in textbooks (see for example Gujarati, 1995; Pindyck and Rubinfeld, 1998; Cuthberston, 1996). Campbell, Lo and MacKinlay (1997) provide a systematic classification of the random walk hypothesis assumptions and the corresponding tests. Note that (Cuthberston, 1996) it is the behavior of the mean of the forecast error in equation (1) that is restricted. The variance of the conditional forecast error need not be constant and may indeed be partly predictable. Campbell et al (1997) define three levels of the random walk hypothesis from the strongest to the weakest. They define the strongest, random walk one or RW1, in terms of the behavior of the log stock price series {st} given by the following equation:
(3) ,ss t1tt ),0(IID~ 2t (RW1)
where is the expected price change or drift and IID (0, ) denotes that t is independently and identically distributed with mean 0 and variance 2. Random walk two or RW2 is the same as RW1 except that unconditional heteroscedasticity in t is allowed, i. e.,
(4) ,ss t1tt ),0(ID~ 2tt (RW2)
4
where ID (0, 2t ) denotes that t is independently distributed with mean 0 and not necessarily
constant variance 2t .
Random walk three or RW3 is the weakest version of the random walk hypothesis. Under RW3, the increments or first differences of the level of the random walk, i.e.,
1ttt sss , are uncorrelated at all leads and lags. Note that, for all versions
(5) 1t1ttet s)ss(Es and
(6) 0)sss(E 1tett ,
as required by the efficient market hypothesis with past prices as the information set. That is, all forms of the random walk hypothesis, as defined by Campbell et al, will have the same characteristic as the mean of the error term which in each case is zero. Under RW1 and RW2, any arbitrary transformation of future price increments (i.e., returns without dividends) is unforecastable using any arbitrary transformation of past price increments. Under RW3, any linear transformation of future price increments (i.e., returns without dividends) is unforecastable using any linear transformation of past price increments. RW3 is the one most tested in the empirical literature (Campbell et al, 1997).
As defined above, the error terms under RW1 are assumed to be IID. As Campbell et al noted, the notion of IID random variables are so central to classical inference that tests of the assumptions independence and identical distributions of error terms have a long history in statistics. Also, since IID are properties of random variables that are not specific to a particular family of distributions, the usual tests fall under the umbrella of nonparametric tests. Examples of such tests are tests of sequences and reversals and runs tests. Examples of such tests are described and applied to daily returns data in Section 4 of this essay. A more recent type of tests of RW1was developed by Lo and MacKinlay (1988) based on the notion that the variance of random walk increments must be a linear function of the time interval. For example, under RW1, the log returns for two periods must be twice the variance for one period. Lo and MacKinlay also extended this test to apply to RW3 allowing for heteroscedasticity in the error terms. Variance ratio tests are explained further and applied to monthly returns data in Section 4.
RW2 is much more difficult to test. Campbell et al stated that, without any restrictions on how the marginal distributions of the time series data can vary through time, it becomes virtually impossible to conduct statistical inference since the sampling distributions of even the most elementary distributions cannot be derived. For this reason, approaches to verifying this version of random walk have evolved mostly along non-statistical lines. In particular, tests along the lines of simulated trading rules as discussed above are the common practice. As also mentioned previously, these types of test are not employed in this study.
Test of RW3 are the most common in the literature. The most direct is to check for the presence of serial correlation using various ARIMA (autoregressive integrated moving average) representations. The null hypothesis is that the autocorrelation coefficients of the first differences (returns) at various lags are all zero. Tests include significance tests of the autocorrelation coefficients themselves, individually or as a group (e.g., using the Box-Pierce Q–statistic). These tests are applied to daily and monthly returns data in Section 4.
Still on the subject of weak-form efficiency, Campbell et al (1997) distinguished tests of the random walk hypothesis with unit root tests usually using the Dickey-Fuller or the augmented Dickey-Fuller statistics. Campbell et al emphasized that the focus of unit root tests is not on the predictability of the stock price series Pt which is the case under the random walk hypothesis. They added that while the random walk hypothesis is contained in the unit root hypothesis, it is the permanent/temporary nature of the shocks to Pt that concerns unit root
5
tests. Thus, by construction, test of unit root are not designed to test for predictability implied by the random walk hypothesis.
Tests of semistrong-form efficiency are usually conducted with respect to a specific information set. The null hypotheses in such tests generally are of the form that stock returns are unaffected by announcements of non-events (such as, under certain conditions, declarations of cash and stock dividends) and anticipated events (forecastable earnings, macroeconomic variables, political and economic events). Many of the investigations particularly with respect to one-off events take the form of event studies (see Chapter 4, Campbell et al, 1997). Given market efficiency, the rationale for an event study is that the announcement of a non-event or an anticipated event should already be incorporated in asset prices. Thus the event’s economic impact can be measured using asset prices or returns observed over a relatively short period of time. This is the advantage of event studies; by contrast the other approach based on the concept of Granger causality requires many months or years of observation. The disadvantage of event studies, particularly in the present context of this essay, is that discrete events occur irregularly (e.g., a currency devaluation) or in a firm-specific manner (e.g., merger or stock dividend declaration). For this reason and because of the focus of the essay, event studies are not used in this study.
Cointegration tests of semistrong-form efficiency are based on the following (Maddala and Kim, 1998):
“If the prices in two markets are cointegrated this implies that it would be possible to forecast one from the other. This, in turn, implies that the markets are not efficient. The MEH (market efficiency hypothesis) thus implies absence of cointegration (or the non-rejection of the no-cointegration null).”
Some researchers (e.g., Leigh, 1997 and Li, 2001) applied the same concept in testing for what they called the long-term semistrong-form efficiency of the stock market. If the return rt is cointegrated with a set or vector of variables xt relevant to the pricing of stocks, then it is possible to define the following equilibrium relationship
(7) ttt xr
where t is a stationary disturbance term. It is possible to express this in the framework of previous discussions as
(8) tet
ettt x)xx(r
where )x(Ex 1ttet is the vector of one-period ahead rational forecast of xt i.e.,
0)xx(E 1tett . This satisfies the efficient market hypothesis provided that = 0. i.e.,
no cointegrating relationship between rt and xt. Both the Engle-Granger and the Johansen procedures are used to test for cointegration. A short-term formulation of (8) is also used to test for short-term market efficiency, i.e.,
(2.9) tet
ettt x)xx(r
where is not constrained to be equal to . Efficiency implies that = 0 and that r~ is the equilibrium return-generating process. This means that only when new information hits the market will rt differ from r~ . Two approaches are commonly used. The first is the two-step procedure pioneered by Barro (1997) and the second is Mishkin’s (1983) Macro Rational Expectations (MRE) model. Barro’s procedure involved first obtaining an OLS (ordinary least
squares) estimate of etx using a set of predictor variables. Then, using this estimate, an OLS
regression on (9) is run and the null hypothesis = 0 is tested. Hancock (1989) used this procedure to test for semistrong-form efficiency of the U. S. stock market with respect to fiscal and monetary variables.
6
Mishkin’s procedure can now be described. Let xt be generated by the following equation:
( 10)
N
1it1iti0t xx .
Further, let market participants form expectations of the variables using the following regression equation:
( 11)
N
1it2it
*i
*0
et xx
and 0)(E)(E 1tt21tt1 . Under the rational expectations hypothesis, Modigliani
and
Shiller (1973) point out that the estimated i coefficients should not differ statistically from
the estimated *i coefficients.
Substituting (11) into (9 ) with r~ yields the market efficiency model:
( 12) t
N
1iit
*i
*0
N
1iit
*i
*0tt )x()x(xr~r
.
Equations (10) and (12) represent a system of equations which can be estimated econometrically. The restriction that should not differ statistically from zero and the rationality restriction that the estimated i coefficients should not differ statistically from the
estimated *i coefficients can then be tested using the likelihood ratio test. The main
difference between the two-step procedure and Mishkin’s MRE procedure is that the rationality condition = * is implicitly assumed in the two-step procedure while it is explicitly tested in the MRE procedure. Both yield consistent estimates but in finite samples, Mishkin (1983) showed that the usual F test will not apply for the two-step procedure. Mishkin’s MRE procedure is used in this essay. Mishkin also demonstrated a desirable property of this procedure which is that the exact specification of the relevant information set is not necessary for the cross-equations tests to have desirable asymptotic properties. Sloan (1996) used this procedure to test U. S. stock market efficiency with respect to anticipated annual earnings attributable to their accrual and cash flow components. Bautista (1996) also used the MRE model in testing the rationality of the Philippine 91-day treasury bill market.
Strong-form tests are not conducted in this study. There have been no formal tests in the Philippines of strong-form efficiency although anecdotal evidence such as the celebrated case of BW Resources, Inc. in year 2000 seems to point that strong form efficiency in the Philippine stock market is just too much to expect. Strong-form tests, as conducted in the U.S. (see for example, Elton and Gruber, 1994), involve two subclasses of tests. The first type of tests attempts to isolate whether excess returns arise directly from insider (nonpublic) information. This usually means examining the investment performance of individuals or groups who can be identified as in a position to have nonpublic information, e.g., the company’s directors or top shareholders. The second type looks at the performance of major market participants, e.g., the returns of large investors such as mutual funds and the ability of security analysts to forecast returns of individual stocks. Elton and Gruber (1994), after reviewing existing studies, concluded that the U. S. stock market is probably not strong-form efficient.
3.3 Empirical Literature on Efficiency Testing
The literature on the efficiency of the U. S. stock market is too ample to be reviewed here. Campbell et al (1997), Elton and Gruber (1994) and Fama (1991) contain summaries of many of the more important empirical studies. It is, however, generally accepted (Copeland and Weston, 1982) that the U.S. stock market is both weak-form and semistrong-form
7
efficient. However, as mentioned, the accepted view also is that the U. S. stock market is probably not strong-form efficient. There are some studies that do not support the semistrong version of market efficiency but the vast majority of studies support it for the U.S. market. Malkiel (1992) averred that the evidence in favor of the U.S. capital market’s “rapid adjustment to new information is sufficiently pervasive that it is now a generally, if not universally, accepted tenet of financial econometric research.”
In the Philippines, Cayanan (1994) tested for weak-form efficiency using cointegration tests on daily returns from six actively traded stocks in the stock market for the period 1990-92. He concluded, from the statistical significance of the coefficients of lagged returns, that past prices carry some information that can be used to predict current returns. He concluded that the stock market is not weak-form efficient. Saldaña and Gregorio (1990) used another approach to testing weak-form efficiency. Applying a stock trading rule based on the moving average of prices of six actively traded stocks, they found that the trading rule did not outperform a buy and hold strategy. Thus, they claimed that the stock market showed appropriate efficiency characteristics. There has been no formal test of the semistrong-form efficiency of the local stock market along the same framework adopted in this study. However, efficiency tests using publicly-known information include that of Paglomutan (1989) which concluded from the study of monthly aggregate returns from 1979 to 1986 that the local stock market was informationally inefficient during the period covered. The study made this conclusion, following Fama (1975), based on the failure to establish a hypothesized one-to-one positive relationship between stock returns and expected inflation (the Fisher effect). Some of the efficiency studies of the local market take the form of event studies. One such study by Estalilla (1995) tested whether abnormal returns can accrue by trading on calendar turning points to take advantage, for example, of the so-called January effect, the turn-of-the-month effect and the day-of-the-week effect. She found sufficient evidence to conclude that the efficient market hypothesis has been violated. The evidence is mixed but the general finding seems to be that the efficient market hypothesis is suspect as far as the local stock market is concerned.
Table 1 summarizes selected empirical literature on weak-form and semistrong-form efficiency testing mainly in countries outside the U. S. Two studies covering semistrong-form efficiency tests of the U. S. market are included because they involved tests not usually covered in reviews of efficiency testing such as those covered in the references cited above. Two other studies included the U. S. market for purposes of comparison with other markets.
Table 1
Selected Empirical Literature on Tests of Weak-form and Semistrong-form Efficiency
Reference;
Efficiency Form Country Studied (Period Covered)
Efficiency Test Results
Hancock, 1987; semistrong-form
U. S. (1960-1985) Barro-type rationality test on quarterly percentage changes in Standard and Poor’s 500 index (S&P 500) against anticipate and unanticipated changes in money supply and budget deficit.
Concludes that the efficient market hypothesis holds in general.
Cornelius, 1993; Semistrong-form
India, Korea, Malaysia, Taiwan, and Mexico (n.a.)
Granger-causality test between stock prices and money supply.
Concludes that stock markets in these countries are not informationally efficient. Changes in money supply are found to Granger-cause stock
8
prices. Sloan, 1996; semistrong-form
U. S. (1962-1991) Mishkin’s Macro Rational Expectations test on annual stock returns against annual earnings.
Results are inconsistent with efficient market’s view that stock prices reflect all publicly available information. Prices appear to correctly reflect implications of current earnings for future earnings but do anticipate rationally the persistence of earnings attributable to the accrual and cash flow components of earnings.
Yuhn, 1997; semistrong-form
U. S., Canada, U. K., Japan, and Germany (1970-1991)
Cointegration test of present value model. A present value model of stock prices is developed which predicts that stock prices (Pt) plus dividends (Dt) should be cointegrated with Pt-1.
Concludes that U. S. and Canadian stock markets are efficient but Japanese, U. K. and German stock markets are not. Johansen’s cointegration test show that Pt+Dt is cointegrated with Pt-1 for Canadian and German markets but conclusions are made based on certain other considerations.
Leigh, 1997; weak-form and semistrong-form
Singapore (1975-1991)
Unit root tests for weak-form efficiency. Johansen’s cointegration test for semistrong-form efficiency. Also used variance ratio test for stock price volatility.
Concludes that Singapore stock market is both weak-form and semistrong-form efficient.
Mookerjee and Yu, 1999; Weak-form
China (1990-1993)
Runs test and significance test of ARIMA (p, 1, q) coefficients of log prices.
Concludes that Shanghai and Shenzhen stock markets are not weak-form efficient. Runs test reject randomness hypothesis at 5% level; ARIMA models indicate that 7-8.5% of daily returns variability can be predicted from preceding day’s returns.
Mecagni and Sourial, 1999; Weak-form
Egypt (1994-1997)
Significance test of first order serial correlation coefficient of AR(1) GARCH (p, q) models of log price changes in four stock indices.
Indicates significant departures from efficiency. The proportion of daily returns variability that can be predicted from preceding day’s returns ranges from 18-26%.
Yilmaz, 1999 Eighteen developing countries and five developed countries, (1988-98)
Variance ratio (VR) test of weekly Wednesday and Friday stock returns to determine if they are serially uncorrelated at all leads and lags.
In eleven of emerging stock markets (including the Philippines) affected by equity flows, VR drops significantly and fails to reject RW hypothesis. For the rest, VR test fails to reject RW hypothesis for all period windows considered.
Mobarek and Keasy, 2000;
Bangladesh (1988-1997)
Runs test and significance test of first order serial
Concludes Dhaka stock market is not weak-form efficient. Runs test
9
Weak-form correlation coefficient of AR (p) and MA( q) models of daily log price changes in four stock indices.
reject randomness hypothesis at 0.05 level. AR(1) shows first-order coefficient of 0.249 significant at 0.01 level. Other ARIMA models show comparable results.
Chortareas, Ritsatos and Sfiridis, 2000; semistrong-form
Greece (1992-1994)
Event study using a sign test to test for changes in market returns due to events related to capital inflow liberalization.
Concludes that Greek stock market is generally efficient because of negligible changes in market returns around 2 of the 3 events. The significant change in the third event is attributed to the central bank’s defense of the local currency not by investor reactions.
Li, 2001; Semistrong-form
Taiwan (1980-2000)
Granger causality, Engle-Granger and Johansen cointegration tests, and Barro-type rationality tests on monthly data on the stock market index, M1, foreign exchange reserves, exchange rate, and consumer price index (CPI).
No cointegration between stock market index and macro variables is detected This indicates no long-term relationship between them and that information in macro variables remain unexploited over time. Also, index Granger causes the macro variables but not the other way around. These are indications of efficiency. However, Li reports mixed results on short-term efficiency. Rationality test indicates index is not efficient with respect to predictable components of exchange rate and M1 but not the other variables.
Li, 2001; Weak-form and semistrong-form
New Zealand (1993-2000)
Augmented Dickey-Duller unit root test on 4 stock indices for weak-form efficiency; pairwise cointegration and Granger causality tests of the indices for semistrong-form efficiency.
Mixed results. Concludes that 3 stock indices appear to be random processes. Two of the indices suggest semistrong-form efficiency.
Hernandez Perales and Robbins, 2001; Semistrong-form
Mexico (1990-2000)
Granger causality tests on monthly data of stock market index, index of industrial production, M1, US T-Bill rate, and Dow Jones Industrial Average (DJIA). Also tests on volatility of stock market index against index of industrial production.
Concludes that stock market is not efficient. Money supply Granger causes both stock market index and industrial production. Stock market index also Granger causes industrial production. US T-Bill rate and DJIA Granger cause stock market index. Volatility in stock market also Granger causes volatility in industrial production.
10
The general indication from this survey is that stock market efficiency seems to be related to the state of development of the general economy. Developed countries are at one end of the spectrum: the U. S., Canadian and Singaporean stock market are found to be semistrong-form efficient. At the other extreme are the stock markets in less developed countries (China, Egypt and Bangladesh) which are found not even weak-form efficient. In between are the stock markets in other countries which may be weak-form efficient but show sign of semistrong-form inefficiency, e.g., U. K., Japan, Germany, and New Zealand. It is hard to make a categorical statement on the others because the tests involved only cover semistrong-form market efficiency. Based on this survey, the place of the Philippine stock market despite being the oldest in Asia seems to be at the lower end of the spectrum. This essay attempts to either confirm or disprove that.
3 Data and Methodology
The data covered daily and monthly stock returns from 1987 to 2000. Monthly stock market return estimates are computed from the composite index (Phisix) from the Philippine Stock Exchange from 1994 and prior to that, from the Manila Stock Exchange. The individual firms comprising the index and their relative shares of the total market capitalization and total transaction value in 2000 are listed in Tables 2 and 3. The formula is (annualized) stock returns rt =ln (st/st-1)*12 where st = Phisix end of period figure. The Phisix does not include cash dividends. Thus, there is some underestimation of returns. However, Philippine corporations, particularly those listed in the exchange, typically pay little or no dividend. Ybañez (2001) puts the underestimate at an average of about 0.8% a year. This is probably not too far from the truth as the simple average of the dividend price ratios of eighteen stocks in the Phisix with continuous trading from 1994-2000 is computed to be 0.052%. Charts 1 and 2 show the closing index of the Phisix and the computed returns, respectively.
Tests of weak-form efficiency involve mainly tests of the random walk one (RW1)and random walk three (RW3) hypotheses for stock prices based on the taxonomy provided by Campbell, Lo and MacKinlay (1997). As mentioned above, RW1 is the strongest form of the random walk hypothesis where the error terms are assumed to be IID. RW1 is tested using nonparametric tests based on sequences, reversals and runs. Historically, these nonparametric tests are the most commonly used tests that certain observed phenomena are IID. Then, RW3 is tested based on the autocorrelation coefficients and variance ratios of stock returns. As seen in Table 1, these tests have become standard in empirical testing for weak-form efficiency of stock markets. The results are further evaluated based on potential profits to be made trading on information on past prices against transaction costs.
Tests of semistrong-form efficiency with respect to accessible macroeconomic variables are conducted consistent with the rational expectations framework of efficient market efficiency as expressed in equation (1). The information set used are publicly-released statistics on macroeconomic variables. Sources of macroeconomic data are NEDA, the Philippine Institute of Development Studies and the Bangko Sentral ng Pilipinas Statistical Bulletins. These data have the nice characteristic of being made available at the same time and at regular intervals to all market participants. Cointegration tests of quarterly returns are conducted with selected macroeconomic variables to test for long-term market efficiency. Then tests of short-term semistrong-form efficiency using Mishkin’s Macro Rational Expectations (MRE) procedures are conducted. As emphasized by many researchers, including Fama (1970, 1991), any test of market efficiency necessarily involves a joint hypothesis regarding the equilibrium expected rate of return and market rationality. The usual tests assume that the expected rate of return on stocks is constant through time. An alternative model is that the risk premium for holding stocks over a risk free asset is constant through time. As in the tests of weak-form efficiency, the results are evaluated based on potential profits to be made trading on publicly available macroeconomic information against transaction costs.
11
Table 2 – Firms Comprising the Phisix Composite Index
of the Philippine Stock Exchange
Code Company Industry 1 AEV Aboitiz Equity Ventures Holding Firm 2 ABS ABS-CBN Broadcasting Communication 3 AC Ayala Corporation Holding Firm 4 ALI Ayala Land, Inc. Property 5 BEL Belle Corporation Hotel, Recreation & Other Services 6 BPC Benpres Holdings Corporation Holding Firm 7 CMP C&P Homes Property 8 DGTL Digital Telecommunications Phils. Communication 9 DMC DMCI Holdings, Inc. Holding Firm
10 LND Fil-Estate Land Property 11 FDC Filinvest Development Corp. Holding Firm 12 FLI Filinvest Land, Inc. Property 13 ICT ICTS Transportation Services 14 ION Ionics Circuits, Inc. Holding Firm 15 JGS JG Summit Holdings, Inc. Holding Firm 16 JFC Jollibee Foods Corporation Food, Beverage & Tobacco 17 LTDI La Tondena Distillers Food, Beverage & Tobacco 18 LC Lepanto Consolidated Mining Mining 19 MEG Megaworld Properties & Holdings Holding Firm 20 MER Meralco Power & Energy 21 MPC Metro Pacific Corporation Holding Firm 22 MBT Metropolitan Bank & Trust Co. Bank 23 EBC Equitable PCI Bank Bank 24 PCOR Petron Corporation Power & Energy 25 PNB Philippine National Bank Bank 26 PLTL Pilipino Telephone Corp. Communication 27 TEL PLDT Communication 28 SMC San Miguel Corporation Food, Beverage & Tobacco 29 SMPH SM Prime Holdings, Inc. Property 30 CMT Southeast Asia Cement Holdings Holding Firm
12
Table 3 - Firms Comprising the Phisix Composite Index
and Their Relative Shares of the Market
Date Date % of Total % of Total Code Incorporated Listed Mkt
Capitalization Value
Turnover 1 AEV Sep-89 Nov-94 0.3 0.2 2 ABS Jun-46 Jul-92 1.5 1.2 3 AC Jan-68 Nov-76 4.3 2.5 4 ALI Jun-88 Jul-91 2.2 2.8 5 BEL Aug-73 Feb-77 0.1 5.4 6 BPC Jun-93 Nov-93 0.5 1.9 7 CMP Dec-94 Dec-94 0.0 0.1 8 DGTL Oct-87 Nov-96 0.1 0.2 9 DMC Feb-95 Dec-95 0.1 0.1 10 EBC Jun-50 Apr-97 1.7 1.9 11 LND May-94 Nov-95 0.0 0.6 12 FDC Apr-73 Dec-82 0.2 0.1 13 FLI Nov-89 Nov-95 0.2 0.6 14 ICT Dec-87 Apr-91 0.1 0.4 15 ION Sep-82 Jul-95 0.3 0.6 16 JGS Nov-90 Aug-93 0.5 0.1 17 JFC Jan-78 Jan-93 0.4 0.7 18 LTDI Aug-87 Apr-95 0.4 0.5 19 LC Sep-36 Apr-47 0.2 0.0 20 MEG Aug-89 Jun-94 0.3 0.6 21 MER 19-May Jan-82 1.9 4.8 22 MPC Oct-86 May-90 0.4 0.8 23 MBT Apr-62 Jan-81 2.3 3.7 24 PCOR Dec-57 Sep-94 0.4 0.4 25 PNB 16-Jul Jun-89 0.6 0.5 26 PLTL Jul-68 Jul-95 0.0 0.1 27 TEL 28-Nov Sep-53 5.8 14.5 28 SMC 13-Aug Nov-48 4.9 6.1 29 SMPH Jan-94 Jul-94 2.2 2.8 30 CMT May-94 Dec-94 0.1 0.1 Total 31.9 54.1
13
Chart 1 – Phisix (1987-2000)
Chart 2 – Stock Returns (1987-2000)
0
500
1000
1500
2000
2500
3000
3500
88 90 92 94 96 98 00
PHISIX
-6
-4
-2
0
2
4
6
87 88 89 90 91 92 93 94 95 96 97 98 99 00
Returns
14
4 Weak-Form Market Efficiency
4.1 Daily Returns
If the stock market is weak form efficient, then current prices already reflect all information contained in the past history of prices. The RW1 representation of this is that the log price process st follows a random walk with drift:
(13) ) IID(0, ~ ,sr~s 2tt1tt ,
where IID means “identically and independently distributed as.” Under the much weaker RW3, the increments or first differences of the level of the random walk, i.e., rt = st – st-1, are uncorrelated at all leads and lags. The first two tests are test of RW1. The third subsection deals with tests of RW3.
4.1.1 Test Based on Sequences and Reversals
Assuming symmetry, then the returns of successive periods will as likely be above r~ as below it. Define It as the random variable3
0r if 0
0r if 1I
t
tt .
A sequence represents a value of It which is equal to that of the previous period while a reversal is when It is different from that of the previous period t – 1. Given a sequence of n + 1 returns, r1, r2,…, rn+1, the number of sequences Ns and reversals Nr may be expressed functions of the It’s:
sr
n
1t1tt1tts
NnN
)]I1)(I1(II[N
.
Defining further as the probability of a sequence with its consistent estimator:
N
Nˆ s
For a nonparametric test for randomness, i.e., that t is a white noise process, define the
Cowles-Jones statistic rs N/NCJ . This statistic may be interpreted as a consistent
estimator of the ratio of the probability of a sequence to the probability of a reversal 1 - , as shown below.
1ˆ1
ˆ
N/N
N/N
N
NCJ p
r
s
r
s .
If the process is random, then =1/2 and CJ converges in probability to unity or one. As a sum of Bernoulli random variables, Ns is a binomial random variable with parameters and n. Campbell et al (1997) showed that as n grows arbitrarily large, Ns and CJ as a function of Ns converges to a normal distribution. More exactly,
.)1(n
))1((2)1(,
1N~CJ
4
233
3 The succeeding discussion is an adaptation from Campbell et al (1997). The main modification is the
assumption of IID (0, 2) instead of N(0, 2) and the symmetry around zero of the returns’ white noise process.
15
Applying this to the 1987-2000 daily returns data with n = 3,439 and median = 0.00028, the total number of sequences Ns of 2,029 or ̂ = 0.59 and CJ = 1.439 are obtained. Under the hypothesis of randomness, i.e., =1/2, CJ has a mean of one and a standard deviation of 0.0341. Under asymptotic normality, the p-value for the null hypothesis is one. In short, the likelihood of greater (or lower) than normal returns to be followed by greater (or lower) than normal returns on a daily basis is quite high. This represents ample evidence against the random walk hypothesis.
4.1.2 Runs Test
Another nonparametric test of randomness is based on the expected number of runs in a series. A run is a sequence of consecutive positive excess, i.e., greater than normal, or negative excess returns. It can be shown (Campbell et al, 1997) that the expected number of runs is given by:
.)1()1(n2]N[E 22runs
Wallis and Roberts (1956) showed that:
),1,0(N~)]1(31)[1(n2
)1(22
1N
zruns
where the value one-half in the numerator is a continuity correction. Applying this to the data, the total number of runs is computed as 1,411 as against the expected number of 1,720. The computed z-value is –10.50 which again has a p-value of one for a two-tailed test. This is again a resounding rejection of the random walk hypothesis on the daily returns.
4.1.3 Tests Based on Autocorrelation Coefficients
To accommodate the possibility of heteroscedasticity4, a weaker form of the random walk hypothesis RW3 is that stock returns are uncorrelated at all leads and lags. A related but not equivalent hypothesis is the unit root null hypothesis which contains the random walk null hypothesis (see Campbell et al, 1997). Table 4 summarizes the unit root tests for stock prices, the logarithm of stock prices and stock returns. The results suggest that prices and their logarithms are nonstationary but stock returns are stationary. This is one indication of weak-form market efficiency but this evidence alone is not conclusive.
Table 4 – Unit Root Tests of Prices and Returns: Daily
None With Intercept With Intercept & Trend
ADF Lag ADF Lag ADF Lag
Phisix -0.3847 3 -1.6936 3 -1.0353 3
Log(Phisix) 0.6033 3 -2.2831 3 -1.4324 3
Returns -31.28583* 2 -31.29333* 2 -31.35397* 2
Returns -46.6283* 3 -46.62158* 3 -46.61498* 3
4 Although the homoscedasticity hypothesis is not rejected by White’s heteroscedasticity test on a time
trend, visual inspection of the returns chart (Chart 2) indicates probably higher than normal volatility right after the 1986 change in government, the period during the series of coup attempts against the Aquino government, and after the 1997 Asian financial crisis.
16
Weak-form efficiency means that the increments or first differences of the level of the random walk, i.e., rt = st – st-1, are uncorrelated at all leads and lags. This implies an AR (k) model represented by:
(14) t
T
1iitit rr~r
where t represents a serially uncorrelated error process. This means that i = 0 for all i = 1, 2,…, T. Table 5 below shows the autocorrelation coefficients and the Box-Pierce Q-statistic for the data:
Table 5 – Autocorrelation Results: Daily Returns
Lag Autocorrelation p-value Q-Statistic p-value
1 0.185 0.008 117.52 0.000
2 -0.026 0.632 119.78 0.000
3 0.033 0.334 123.47 0.000
4 0.046 0.276 130.65 0.000
5 -0.044 0.716 137.47 0.000
6 -0.028 0.642 140.10 0.000
7 0.047 0.271 147.82 0.000
8 0.084 0.138 172.04 0.000
9 -0.003 0.516 172.08 0.000
10 -0.024 0.622 174.06 0.000
From the above results, only the first-order autocorrelation is statistically different from zero suggesting an AR (1) model is appropriate for the data. One additional consideration is worth mentioning at this point. As indicated in a previous footnote, Chart 2 indicates probably higher than normal volatility right after the 1986 change in government, the period during the series of coup attempts against the Aquino government, and after the 1997 Asian financial crisis5. Thus, the AR model was run using a Generalized Autoregressive Conditional Heteroscedastic or GARCH (p, q) model (Enders, 1995) with various values of p (the number of lags in the conditional variance) and q (the number of lags in the squares of the error terms) and the residuals tested. The model with the best fit is a GARCH (1, 2) AR (1) model which is as follows:
rt = 0.00292 + 0.217063rt-1 + t
(0.3033) (0.0000)
21t
22t
21t
2t 86402.005967.018549.0 .
(0.000) (0.0015) (0.0000)
5 There appears to be no statistically significant change in the first-order autoregression coefficient
from before and after the onset of the Asian financial crisis. However, there appears to be a statistically significant increase in the coefficent from before and after the start of foreign exchange liberalization in 1992.
17
The first equation is the AR (1) model of the return process rt. The second equation is the
GARCH (1, 2) for the conditional variance 2t as a function of its lagged value and the
square of the lagged values of the error term 2t . The figures in parenthesis are the p–values
of the coefficient estimates. The correlogram and the Durbin Watson statistic of 2.0377 indicate that the residuals constitute a white noise process validating the AR (1) model. These results are consistent with the previous estimate assuming no heteroscedasticity and with Cayanan’s 1994 results which yielded first-order correlation coefficients ranging from 0.071689 to 0.225227 for the six stocks he examined.
The above results support the hypothesis that the stock market is not weak-form informationally efficient as far as daily return data are concerned. This means that past prices, at least for the last trading day, carry information that helps to predict current prices and returns. However, before it can be concluded that the market is operationally weak-form inefficient, transaction costs must be taken into consideration based on Malkiel’s third definition quoted above. Note that a first-order autocorrelation coefficient of 0.22865 implies that 5.23% of the variation in daily returns is predictable using the previous day’s index return.6 Daily nominal returns has a computed sample standard deviation of 1.9%. Two standard deviations multiplied by 5.23% equals 0.179% average excess returns. On the other hand, buying and selling will incur transaction cost of at least 1.05% to 3.8% of the stock price.7 Thus, with transaction costs taken into consideration, one cannot earn excess profits by just trading based on past price information. This suggests that the stock market is weak-form efficient with respect to daily price movements based on Malkiel’s third definition.
4.2 Monthly Returns
This section examines whether the findings on daily returns extend to monthly data. Table 6 summarizes the unit root tests for stock prices, the logarithm of stock prices and stock returns.
Table 6 – Unit Root Tests of Prices and Returns: Monthly
None With Intercept With Intercept & Trend
ADF Lag ADF Lag ADF Lag
Phisix -0.42477 1 -1.92585 2 -1.70393 1
Log(Phisix) 0.570394 1 -2.37105 2 -2.07721 1
Returns -9.19933* 1 -8.0887* 2 -8.24070* 2
Returns -11.28285* 3 -11.24767* 3 -11.2149* 3
*Critical at the 1% significance level.
The results for the monthly data are similar to those for the daily data, that is, prices and their logarithms are nonstationary but stock returns are stationary. This is not inconsistent
6 The R2 from regressing returns on a constant plus its first lag is equal to the square of the slope
coefficient which is also the first order autocorrelation (Campbell et al., 1997). 7 Buying and selling shares in the Philippine Stock Exchange is subject to brokerage commission ranging from 0.25-1.5% of the share price, 10% value added tax on the brokerage commission (equivalent to 0.025% of price), documentary stamp tax, and other related costs paid to the Philippine Central Depository. Selling is also subject to a sales tax of 0.5% of the price. The minimum cost cited is 0.25% brokerage commission plus 0.025% VAT (times two for buying and selling) plus 0.5% sales tax on price for selling.
18
with the hypothesis of weak-form market efficiency. Proceeding further, Table 7 below shows the autocorrelation coefficients and the Box-Pierce Q-statistics for the monthly data:
Table 7 – Autocorrelation Results: Monthly Returns
Lag Autocorrelation p-value Q-Statistic p-value
1 0.193 0.006 6.3624 0.012
2 -0.086 0.868 7.6395 0.022
3 -0.123 0.945 10.261 0.016
4 -0.056 0.766 10.802 0.029
5 0.017 0.413 10.852 0.054
6 -0.043 0.711 11.178 0.083
7 -0.033 0.666 11.377 0.123
8 0.009 0.454 11.392 0.180
9 -0.006 0.531 11.398 0.249
10 -0.023 0.617 11.497 0.320
Similar to the findings for daily returns, the results above show that only 1 is statistically significant indicating that the returns may be generated by an AR (1) process. Running AR (p) models under the assumption of conditional heteroscedasticity, an ARCH (1) AR (1) model with first-order correlation coefficient of 0.18866 is obtained. This implies that returns in period t-1 carry information that can help predict period t returns. This provides evidence that the stock market may not be weak-form informationally efficient. However, note that 1 is quite small at 0.18866 which means that only 3.56 % of the variation in monthly returns is predictable using the previous month’s index return. As in the daily data, to appreciate the magnitude of potential excess returns, note that the standard deviation of the returns data in monthly terms is 10.83%. Two standard deviations multiplied by 3.56% equal 0.77% - hardly enough to cover transaction costs and taxes. This may not be enough basis to reject the notion of weak-form stock market efficiency as a speculator is unlikely to earn excess profits after transaction costs and taxes using this information.
Lo and MacKinlay (1988) devised another test of the random walk hypothesis where the null is that the returns are independently and identically distributed (iid). This is based on the notion that if the rt’s are iid, then the variance of rt(q) = rt+rt-1+…+ rt-q, for integer q, must be equal to q times the variance of rt, or
(15) 1]r[Varq
)]q(r[Var)q(VR
t
t
.
For example, under the iid null hypothesis, the variance of the five-day returns must be five times the variance of daily returns. Thus, the ratio of the five-day day return variance to five times the variance of daily returns must be one. Lo and MacKinlay (1988) developed the following test statistic for the null hypothesis that equation (15) is true:
(16) 2
1
q3
)1q)(1q2(2)1)q(VR(nq)q(
19
and showed that it is distributed asymptotically as standard normal. If the test statistic thus computed is outside the critical range, then the null hypothesis that the returns are iid is rejected. Applying this to the data, the following results are obtained:
Table 8 – Variance Ratios for Monthly Phisix Index
Aggregation Period q 2 3 4 5 6
Variance Ratio VR(q) 1.199561 1.217087 1.17242 1.145218 1.098114
Test Statistic (q) 2.586606 1.887538 1.194562 0.538481 0.297005
p-value 0.004846 0.029544 0.116129 0.295122 0.383231
The results are consistent with the previous results. For example, VR(2) above demonstrates a first-order autocorrelation coefficient of 0.199561 which is consistent with the previous result. The null hypothesis of uncorrelated returns are rejected at fairly strict levels of significance for q = 2 and 3, providing additional support to the previous finding that the stock market is not weak-form informationally efficient.8 Beyond q = 3, however, the results support the hypothesis of market efficiency.
5 Semistrong-Form Market Efficiency
5.1 Cointegration Test
As indicated above, if the return rt is cointegrated with a set or vector of variables xt relevant to the pricing of stocks, then it is possible to define the following equilibrium relationship in real terms
(17) ttt xr
where t is a stationary disturbance term Within this framework, stock market efficiency can be examined with respect to macroeconomic fundamentals of the Philippine economy. If the stock market is long-term efficient, then stock prices and the variables selected in xt cannot be cointegrated and no one variable can be used to forecast another.
In selecting the variables to be included in xt, note that stock prices can be written as expected discounted dividends. Simplistically assuming that expected dividends are constant through time (which is implied if earnings are all declared as dividends and none are retained to flow back into investments), then (Chen, Roll and Ross, 1986)9:
R
]D[EPt
where Pt is stock price at end of period t, D is dividends and R is the discount rate. Differentiation gives:
(18) R
dR
]D[E
]D[dE
P
dP
t
t
Thus, it follows that the economic forces that influence prices and returns are those that influence expected cash flows (dividends) and the discount factor. Following Leigh (1997),
8 The tests were repeated using a test with correction for the possible presence of heteroscedasticity in
the return data with similar results. 9 A more rigorous decomposition is available in Campbell and Shiller (1988). However, this suffices
for the current requirements.
20
two vector autoregressive (VAR) systems and sets of xt’s are postulated. For the first system, set 'rerexincrx tttttt where
rt – aggregate stock returns in real terms (in %)
ct – aggregate consumption in real terms
int – gross capital formation in real terms
ext – aggregate exports in real terms
rert – real exchange rate.
Leigh referred to the above as the aggregate demand system. In the formulation of equation (18), these would be the factors that influence expected cash flows. Fama and French (1989), for instance, concluded that there appears to be a causal relationship between stock returns and components of aggregate demand.
The second system is the discount factor system (Leigh referred to this as a money demand system) where 'rfrdymsx tttttt and
mt – real money balances based on domestic liquidity divided by the price level
yt – real income represented by the gross domestic product in real terms
rdt – real domestic interest rate represented by the average rate of the 91-day treasury bills minus the average inflation rate
rft – real foreign interest rate represented by the 90-day LIBOR minus the inflation rate
The relevant factors are those relating to monetary policy and returns to competing financial assets. The above systems are further justified by findings by Fama (1981) and Fama and Gibbons (1982) of a significant relationship between stock returns, inflation, money, and real variables.
Table 9 shows the ADF statistics for the different variables.
Table 9 – Unit Root Tests of Quarterly Economic Data
None With Intercept With Intercept & Trend
ADF Lag ADF Lag ADF Lag
Log Phisix-real -0.5528 2 -1.6367 2 -1.5710 2 Returns-real -2.6362* 7 -2.6258*** 7 -2.8493 7 Consumption 1.7607 1 -0.8121 1 -6.7150* 1 Investment 0.1327 1 -2.7074*** 1 -4.1270** 1 Exports 0.9635 1 -0.9480 1 -3.2122*** 1 REER -0.2523 3 -1.7803 3 -1.2381 3 Money Balances 5.1774 1 2.2998 1 -1.2572 1 GDP 1.1266 1 -0.9776 1 -5.4485* 1 Domestic Int. Rate -1.9173 1 -5.3517* 2 -5.4844* 2 Foreign Int. Rate -2.5933 4 -2.9140 4 -2.8746 4 * Critical at the 1% significance level. ** Critical at the 5% significance level ***Critical at the 10% significance level
The evidence from the unit root tests cannot reject the unit root hypothesis for the variables included in the two systems.
21
For the aggregate demand system, a system with four lags is tested for cointegration using the Johansen methodology (see Johansen, 1988 and Enders, 1995). The number of lags is selected using the Akaike Information Criterion and the Schwarz Criterion. The test statistics are the trace statistic and the maximum eigenvalue statistic computed, respectively, as:
)1ln(T)1r,r(
)1ln(T)r(
1rmax
n
1riitrace
for r = 0, 1, …, n-1 where i is the ith largest eigenvalue, T is the number of usable observations after taking into account lags, and n is the number of variables in the system.
The table below summarizes the results of the cointegration tests for the aggregate demand system.
Table 10 – Cointegration Tests of Aggregate Demand System Four Lags with Intercept and Trend
Null Alternative Test 95% 99% Hypothesis Hypothesis Statistic Critical
Value Critical Value
trace tests r=0 r>0 88.48* 69.98 77.91 r1 r>1 52.81** 48.42 55.55 r2 r>2 28.01 31.26 37.29 r3 r>3 9.50 17.84 18.78 r4 r>4 0.05 8.80 11.58 max tests r=0 r=1 33.00 33.26 38.86 r1 r=2 26.01 27.34 32.62 r2 r=3 18.53 21.28 26.15 r3 r=4 9.45 14.60 18.78 r4 r=5 4.05 8.80 11.58 * Critical at the 1% significance level. **Critical at the 5% significance level.
The results of the tests are not clear-cut. The results of the trace test indicate the existence of one, possibly two, cointegrating vectors but the maximum eigenvalue test cannot reject the hypothesis of no cointegrating vector. The cointegrating equation indicated for r = 1 is as follows:
(19) 1.0rt – 3.2184ct – 1.902int + 3.2785ext – 2.88707rert + 372.65 = 0
(0.7588) (1.3385) (0.8889) (0.98905)
The figures in parenthesis are the asymptotic standard errors which, using the t-tests, indicate that all coefficients, except that of investment, are statistically significant. When only one cointegrating equation is determined (i.e., r = 1), the usual t-statistic can be used to test significance of the cointegrating coefficients (Enders, 1995). The equation says that stock returns move in the same direction as consumption and the real exchange rate and in the opposite direction as exports. Thus, on the basis of the above, the hypothesis that the Philippine stock market is semistrong-form efficient in terms of quarterly time horizons is not supported.
Table 11 summarizes the results of the cointegration test for the discount factor system.
22
Table 11 – Cointegration Tests of Discount Factor System Four Lags With Intercept and Trend
Null Alternative Test 95% 99% Hypothesis Hypothesis Statistic Critical
Value Critical Value
trace tests r=0 r>0 140.21* 69.98 77.91 r1 r>1 81.38* 48.42 55.55 r2 r>2 41.09* 31.26 37.29 r3 r>3 15.90 17.84 18.78 r4 r>4 0.58 8.80 11.58 max tests r=0 r=1 58.88* 33.26 38.86 r1 r=2 40.28* 27.34 32.62 r2 r=3 25.20** 21.28 26.15 r3 r=4 15.32** 14.60 18.78 r4 r=5 0.58 8.80 11.58 * Critical at the 1% significance level. ** Critical at the 5% significance level.
The results are stronger than the previous results. The results of the trace test suggest the existence of three cointegrating vectors but the maximum eigenvalue test indicates the existence of two to four. When the hypothesis of only one cointegrating vector is accepted, the cointegrating equation is:
(20) 1.0rt – 0.27312mt - 3.54594yt + 11.57539rdt – 8.51384rft + 466.87 = 0
(0.08359) (1.18306) (2.31798) (2.40907)
Based on the standard errors and using the t-statistics, all the coefficients are significant at the 99% confidence level.
Based on the above results on the aggregate demand and discount factor systems, there is strong support to the proposition that the local stock market is not semistrong-form informationally inefficient.
5.2 MRE Tests
5.2.1 Econometric Methodology
The results in the cointegration tests in the previous section indicate that the local stock market is not long-term efficient using quarterly data. In this section, the short-term semistrong-form efficiency of the stock market is tested using monthly data and Macro Rational Expectations (MRE) tests developed by Mishkin (1983). This procedure enables the separate testing of the effects of anticipated and unanticipated variables. Originally developed to address the issue of the neutrality of anticipated monetary or aggregate demand policies and the hypothesis of rational expectations, the MRE procedure can be used to “analyze the differential effects of anticipated versus unanticipated movements in explanatory variables (Mishkin, 1983).”
This study follows the approach suggested by Mishkin. First, the joint hypothesis that anticipated movements in the macro variables are not correlated with stock returns and that expectations are rational is tested. Next, the hypothesis that anticipated movements in the macro variables are not correlated with stock returns is tested. Finally, the rationality conditions alone are tested.
23
5.2.2 Empirical Application
In addition to past prices, all public information available to market participants (semistrong-form efficiency) are considered. From the results of the cointegration tests in the previous section, the candidate macroeconomic variables that seem to have predictive power on stock returns are aggregate consumption and exports. However, these variables are only reported quarterly but monthly variables are needed in the application. Regressing aggregate consumption and exports against monthly reported macro variables, real money balances, nominal exchange rate, real exchange rate, and an index of industrial production are found to be highly significant (most at the 1% and all at least at the 5% significance levels). Exports are also found to be correlated with the consumer price index but that effect could also be explained in terms of the effects of the real and nominal exchange rate variables. For completeness, output represented by real GDP was also found to be highly significant with respect to real money balances and the 91-day treasury bill rates. Thus, in this first model,
ttttt rmorerex is the vector of additional predictor variables where
et – the end of month nominal exchange rate
rert – the end of month real exchange rate
ot – the index of the value of industrial production
rmt – real money balances (M2).
Then, on this basis, (10) and (12) become:
(21)
N
1i
N
1i
N
1iiti4iti3
N
1iIti2iti110t
N
1i
N
1i
N
1iiti4iti3
N
1iiti2iti110t
N
1i
N
1i
N
1iiti4iti3
N
1iiti2iti110t
N
1i
N
1i
N
1iiti4iti3
N
1iiti2iti110t
rmorerei
rmorereo
rmorererer
rmoreree
(22)
N
1i
N
1i
N
1iit
*i4it
*i3
N
1iit
*i2it
*i1
*104
N
1i
N
1i
N
1iIt
*i4it
*i3
N
1iit
*i2it
*i1
*103
N
1i
N
1i
N
1iit
*i4it
*i3
N
1iit
*i2it
*i1
*102
N
1i
N
1i
N
1iit
*i4it
*i3
N
1iit
*i2it
*i1
*101
N
1i
N
1i
N
1iit
*i4it
*i3
N
1iit
*i2it
*i1
*10t4
N
1i
N
1i
N
1iit
*i4it
*i3
N
1iit
*i2it
*i1
*10t3
N
1i
N
1i
N
1iit
*i41t
*i3
N
1i1t
*i21t
*i1
*10t2
N
1i
N
1i
N
1iit
*i4it
*i3
N
1iit
*i2it
*i110t1
N
1tittt
)rmorere(
)rmorere(
)rmorere(
)rmorere(
)rmorere(rm
)rmorere(o
)rmorere(rer
)rmorere(e
rr~r
24
First, the joint hypothesis that anticipated movements in the macroeconomic variables have no predictive value on returns and that expectations of market players are rational is tested. This is equivalent to the hypothesis that i = 0 for all i’s and
*kiki
*kiki
*kiki
*kiki and ,,, for all k’s and i’s. Nonlinear generalized least
squares (GLS) estimates are obtained10 for the constrained and unconstrained equations. The likelihood ratio test statistic is:
u
cLnT)k(LR
which is distributed as a 2 with k degrees of freedom. The values uc and are the
determinants of the residual covariance matrices of the constrained and unconstrained equations, respectively, T is the number of usable observations, and k is the number of cross equation constraints. The likelihood ratio statistic cannot reject the joint null hypothesis, The test statistic is 7.8212 with a corresponding p-value of 0.79894 for a chi-square distribution with 12 degrees of freedom (the number of cross-equation constraints).
Next, only the restriction that i = 0 for all i’s is tested. The likelihood ratio test also cannot reject the null hypothesis that the ’s are zeroes. The likelihood ratio statistic is 0.00948 with a corresponding p-value for the chi-square distribution with four degrees of freedom is 0.99999. Lags greater than one are no longer tested because the R2’s for the set of equations in (19) where the predictor variables are the dependent variables are already very close to one. Additional lags can no longer add predictive value to the estimation equations, i.e., the coefficients become zero for i = 2. On the basis of the above, it can be concluded that anticipated movements in the predictor macro variables are already factored into stock returns.
This portion presents the test of the rationality assumption.11 The cross equation
restrictions for the rationality hypothesis are that *kiki
*kiki
*kiki
*kiki and ,,, .
The results are summarized in Table 12 below together with the multivariate forms of the Akaike Information Criterion (AIC) and the Schwarz Criterion. Based on the AIC and the Schwarz Criterion an optimal lag of three is indicated.
Table 12 – Semistrong-Form Efficiency Test Results (Constant Expected Returns Model)
One Lag Two Lags Three Lags
c 10,415,443 5,028,184 4,182,538
u 9,985,165 4,623,699 3,459,715
T 167 166 165k 8 12 16LR(k) 7.0456 13.9214 31.3058p-value 0.53172 0.30575 0.01230AIC 2751.4740 2627.5531 2584.3550Schwarz Criterion 2845.0139 2752.0326 2739.6522
From these results, the null hypothesis of rationality or semistrong market efficiency cannot be rejected for lags of one to two. However, at three lags, the null hypothesis is
10 Using EViews. 11 See Bautista (1996) for an application in the 91-day treasury bill market.
25
rejected. Thus, as in the previous section, the evidence cannot support the hypothesis that the local stock market is efficient.
The result that the local stock market is semistrong-form inefficient adds to the previous finding that it is also weak-form inefficient. However, the question whether abnormal profits are possible trading on public information must still be addressed. In the unconstrained regression of stock returns against three lags of the information set, R2 is found to be 0.15734 meaning that 15.734% of next month’s variation in monthly returns is predictable using three lagged values of the macroeconomic variables used. Given the sample standard deviation of monthly returns of 10.83%, this translates into 1.7% for one standard deviation and 3.4% for two standard deviations in average excess returns. As mentioned previously, the cost of a round-trip transaction is about 1.05-3.8%. Thus, there may be opportunities for above-average profits after transaction cost (and information gathering cost) for a trading strategy using public information. Note that the information set can be expanded beyond macroeconomic variables to include firm-level information such as earnings and dividend announcements, mergers, company fundamentals and others, increasing the opportunities for predictability and (provided again that the additional information gathering and analysis costs are covered) excess profits.
5.2.3 Equity Risk Premium
Instead of assuming that the expected return on stocks is a constant, it can be assumed that the market equates expected one-period, holding returns across securities to a riskless rate, after allowing for an equity risk premium which is the one assumed to be constant over
time. Thus, the expected equity return etr is:
(23) di)r(Er t1ttet
or, in terms of expected excess returns ttt
et irz :
(24) d)z(Ez 1ttet
where it is the riskless return represented here by the 91-day treasury bill rate and d is the constant equity risk premium. These imply that:
(25) 0)dir(E)rr(E 1ttt1te
1tt
Then, on this basis and assuming the previous result that anticipated variables are already incorporated into the equilibrium rate, (21) and (22) become:
(26)
N
1i
N
1i
N
1iiti4iti3
N
1iiti2iti110t
N
1i
N
1i
N
1iiti4iti3
N
1iiti2iti110t
N
1i
N
1i
N
1iiti4iti3
N
1iiti2iti110t
N
1i
N
1i
N
1iiti4iti3
N
1iiti2iti110t
rmorererm
rmorereo
rmorererer
rmoreree
26
(27)
N
1i
N
1i
N
1iit
*i4it
*i3
N
1iit
*i2it
*i1
*10t4
N
1i
N
1i
N
1iit
*i4it
*i3
N
1iit
*i2it
*i1
*10t3
N
1i
N
1i
N
1iit
*i4it
*i3
N
1iit
*i2it
*i1
*10t2
N
1i
N
1i
N
1iit
*i4it
*i3
N
1iit
*i2it
*i110t1t
)rmorere(rm
)rmorere(o
)rmorere(rer
)rmorere(edz
As before, the rationality restrictions *kiki
*kiki
*kiki
*kiki and ,,, can
then be subjected to statistical testing. The results are summarized in Table 13 below together with the multivariate Akaike Information Criterion (AIC) and Schwarz Criterion results. Based on the AIC and the Schwarz Criterion, the optimal lag is three.
Table 13 – Semistrong-Form Efficiency Test Results (Constant Risk Premium Model)
One Lag Two Lags Three Lags
c 10,791,361 5,244,479 5,244,479
u 10,286,009 4,744,216 3,536,809
T 167 166 165k 8 12 16LR(k) 8.0095 16.6415 65.0019p-value 0.43254 0.16359 0.00000AIC 2756.4313 2631.8245 2587.9914Schwarz Criterion 2849.9711 2756.3040 2743.2886
As in the constant return model, the null hypothesis of rationality or semistrong market efficiency cannot be rejected at lags one to two. However, at three lags, the null hypothesis is rejected.
6 Conclusion
The results of the previous sections can be summarized as follows:
The market is weak-form informationally inefficient in terms of daily and monthly trading horizons but it is not possible to make abnormal profits trading based only on past price information when transactions costs are taken into consideration.
The market is not semistrong-form efficient in terms of both long-term and short-term horizons. In addition, there seems to be opportunities to develop profitable trading strategies based on information known to the public even when transactions costs are taken into consideration.
It is possible to state the results in one sentence: the local stock market is at best weak-form efficient when transactions costs are taken into consideration.
These results seem to be consistent with the results in other countries in similar stage of development, as discussed in Section 3. The country’s stock market is probably more efficient than those of China, Egypt and Bangladesh but less efficient than those of New Zealand, Taiwan and certainly other more developed countries.
Since market efficiency is desirable, both from the viewpoint of ordinary investors and the general economy, the sources of inefficiency must be identified and addressed. While
27
the list is not exhaustive, the following conditions appear to be the major causes of market inefficiency:
Ownership in publicly listed company is highly concentrated. Saldaña (2001) reported that most publicly listed companies issue only up to 20% of their total shares to the public, the minimum required to qualify as a public corporation Thus, most listed companies are controlled by their five largest shareholders. As a result, their shares are thinly traded and illiquid and stock prices are sensitive to movements of foreign funds.
Institutional investors have only limited participation in the stock market. As a result, Saldaña claimed that there was no real market for investment information. Thus, the active investment community of investment professionals “with similar training who examine mainly similar information and compete vigorously in a free market atmosphere” that was the basis for Clemente’s (1995) claim that the stock market was reasonably efficient did not exist.
Financial disclosure standards and their implementation by regulatory agencies are not rigorous enough for public investors12. Publicly available financial information are often of low quality. Saldaña attributed this to the highly concentrated ownership of large corporations wherein large shareholders already have access to all information about the companies they control. This asymmetry in access to information is a major source of market inefficiency.
12 A study of the financial reporting practices of listed Philippine firms (1997-1998) by Cayanan and
Valderrama found that majority of the listed firms they surveyed were inclined to follow only the minimum disclosure required by generally accepted accounting principles (GAAP). The authors cited significant violations of GAAP that have the potential of resulting in damage to investors and other users who rely on the information in the financial reports.
28
References
Barro, R. J. (1997). “Unanticipated Money Growth and Unemployment in the United States,”
American Economic Review 67: 101-115.
Bautista, C. (1996). “Testing for Forecast Rationality in Financial Markets: The Case of the Philippines,” Philippine Review of Economics and Business 33 No. 2: 232-252.
Campbell, John Y. and R. Shiller (1988). “The Dividend-Price Ratio and Expectations of Future Dividends and Discount factors,” Review of Financial Studies 1: 195-227.
Campbell, John Y., Andrew W. Lo and A. Craig MacKinlay (1997). The Econometrics of Financial Markets, New Jersey: Princeton University Press.
Cayanan, Arthur S. (1995). “An Empirical Study on the Weak-Form Efficiency of the Philippine Stock Market,” Philippine Management Review 5 1: 72-82.
---- and H. Valderrama (1997-1998). “Financial Reporting Practices of Listed Philippine Firms,” Philippine Management Review 7 1: 1-17.
Chortareas, G. E., T. E. Ritsatos and J. M. Sfiridis (2000). “Capital Outflow Liberalization and Stock Market Reaction in an Emerging Market: Experience from Greece,” Journal of Economics and Finance 24 1: 77-89.
Clemente, L. C. (1995). “Investment Management and a Case Study: Managing the First Philippine Fund,” in Ilano, A. R. and R. S. Mariano, eds., Investment Management and the Philippine Stock Market, Development Center for Finance and FINEX Research and Development Foundation, Inc.
Copeland, T. E. and J. F. Weston (1983). Financial Theory and Corporate Policy, 2nd ed., Massachusetts: Addison-Wesley.
Cornelius, P. K. (1993) “A Note on the Informational Efficiency of Emerging Stock Markets,” Weltwirtschaftliches Archiv October/December: 820-828.
Cuthberston, K. (1996). Quantitative Financial Economics: Stocks, Bonds and Foreign Exchange, New York: Wiley.
Elton, Edwin J. and Martin J. Gruber (1994). Modern Portfolio Theory and Investment Analysis, 4th ed., New York: Wiley.
Estalilla, Ma. Georgiana O. (1995). Calendar Anomalies and the Behavior of Stock Prices in the Philippine Stock Market: A Test of the Efficient Markets Hypothesis, unpublished DBA dissertation, College of Business Administration, University of the Philippines, Quezon City, Philippines.
Fama, E. (1970). “Efficient Markets: A Review of Theory and Empirical Work,” Journal of Finance 25: 383-417.
----- (1975). “Short-Term Interest Rates as Predictors of Inflation,” American Economic Review 65: 269-283.
----- (1981). “Stock Returns, Real Activity, Inflation and Money,” American Economic Review 71:545-565.
----- (1991). “Efficient Capital Markets II,” Journal of Finance 46: 1575-1618.
Gujarati, D. N. (1995). Basic Econometrics, 3rd ed., New York: McGraw-Hill.
Hancock, D. G. (1989). “Fiscal Policy, Monetary Policy and the Efficiency of the Stock Market,” Economic Letters 31: 65-69.
Hernandez Perales, N. A. and R. Robbins (2001). “The Relationships Between Stock Market Returns and Real, Monetary and Economic Varaiables,” ITESM Unpublished Paper.
29
Leigh, Lamin. (1997). “Stock Market Equilibrium and Macroeconomic Fundamentals,” IMF Working Paper.
Li, Wen Sui (2001). “Informational Efficiency of Taiwan Stock Market,” Unpublished Paper.
Li, Xiaoming (2001). “A Note on New Zealand Market Efficiency,” Massey University Working Paper.
Lo, A. and A. C. MacKinlay (1988). “Stock Market Prices Do Not Follow Random Walks: Evidence From a Simple Specification Test,” Review of Financial Studies 1: 41-66.
Malkiel, Burton G. (1989), “Efficient Market Hypothesis,” in John Eatwell, Murray Milgate and Peter Newman, eds , New Palgrave Dictionary of Money and Finance, New York: W. W. Norton.
Mecagni, M. and M. S. Sourial (1999). “The Egyptian Stock Market: Efficiency Tests and Volatility Effects,” NBER Working Paper.
Mishkin, F. (1983), A Rational Expectations Approach to Macroeconometrics: Testing Policy Ineffectiveness and Efficient-Markets Models, National Bureau of Economic Research.
Modigliani, F. and R. Shiller (1973). “Inflation, Rational Expectations, and the Term Structure of Interest Rates,” Economica 40: 12-43.
Maddala, G. S. and I. Kim (1998). Unit Roots, Cointegration and Structural Change, Cambridge: Cambridge University Press.
Mobarek, A. and K. Keasey (2000). “ Weak-form Market Efficiency of an Emerging Market: Evidence from the Dhaka Exchange of Bangladesh,“ University of Leeds Paper.
Mookerjee, R. and Q. Yu (1999). “An Empirical Analysis of the Equity Markets in China,” Review of Financial Economics 8: 41-60.
Pindyck, Robert S. and Daniel L. Rubinfeld, 1998. Econometric Models and Economic Forecasts, 4th ed., Boston, Irwin McGraw Hill.
Sloan, R. G. (1996). “Do Stock Price Fully Reflect Information in Accruals and Cash Floes About Future Earnings?” The Accounting Review 71 3:289-316.
Wallis, W. and H. Roberts (1956). Statistics: A New Approach, New York: Free Press.
Ybañez, R. (2001). “Rates of Return on Stocks, T-Bills and Deposits in the Philippines, 1987-2000,” U. P. College of Business Administration Discussion Paper.
Yilmaz, K. (1999). “Market Development and Efficiency in Emerging Stock Markets,” Koc University Paper.
Yuhn, Ky-Hyang (1997). “Financial Integration and Market Efficiency: Some International Evidence from Cointegration Tests,” International Economic Journal 11 2: 103-116.
Related Documents
![[OPPORTUNITIES BOOKLET] AIESEC University of the Philippines - DIliman](https://static.cupdf.com/doc/110x72/579079dc1a28ab6874c93bb2/opportunities-booklet-aiesec-university-of-the-philippines-diliman.jpg)
