This paper aims to test for weak form efficiency three company stocks and two indices. For this purpose and with a view to compare and contrast their results a number of tests have been employed: autocorrelation, variance ratio, runs and delay tests. The analysis finds evidence that some stocks and indices follow a random walk, while others do not.
Recent financial theory is based a great deal in the Efficient Market Hypothesis (EMH). According to Fama (1970) in an efficient market, prices fully reflect all known and available information and are affected in a precise and instant way. Such information could refer for example to future earnings, dividends, expected dividend growth or expected return. Therefore, market securities trade at prices that equal their intrinsic values. There are no undervalued or overvalued stocks and investors behave rationally.
In an efficient market, today's price change can only be accounted for today's unexpected news. Information of the past has no more value since has already incorporated in past prices. As news come in a random way, random and unexpected shall be the price change (Malkiel, 2003). This means that today's price is unrelated to previous day price change suggesting that they follow a random walk. The price independency will not allow for predictability patterns to persist (Schwert, 2002).
Fama (1970) provided three classifications of market efficiency. The weak form efficiency suggests that current prices fully and instantaneously incorporate the information implied by historical prices and investors cannot enhance their stock picking skills simply by having a historical record of prices. The semi-strong form efficiency states that publicly available information as well as historic trading data is incorporated in today's prices. Finally, the strong form efficiency states that all information, public or private, cannot be used by investors to forecast future prices and achieve abnormal returns.
This report aims to test the weak-form efficiency of three company stocks (Vicor Corporation, ViaSat Incorporated and Vical Incorporated) and two decile indices (the Nyse/Amex/Nasdaq index capitalization-based Deciles 1 and 10).
The report is structured in five sections. Section I summarizes the selected companies. Section II provides a description of the data and the methods used to test for weak-form market efficiency. Section III contains the descriptive statistics. Section IV presents results of the tests and section V concludes.
Vicor's Corporation main focus is on the design, production and promotion of its modular power components and to complete power systems as well as license its technology. Its distribution network captures North and South America, US, France, Germany, Italy, Hong Kong, UK, Netherlands and Japan.
ViaSat's Incorporated main focus is on the design, manufacture and promotion of satellite and wireless communication or networking systems both for governmental and commercial purposes such as consumers, companies and mobile broadband customers.
Vical's Incorporated main focus is on the research and development of biopharmaceutical products. The company has patented DNA delivery technologies for the use of preventing and treating diseases. Its services include gene therapies, DNA vaccines and DNA therapeutic protein delivery.
For the purposes of the empirical analysis, this reports uses as a sample three Nasdaq stocks and two deciles of the Nyse/Amex/Nasdaq index, that is the 10% smallest and 10% largest companies by market capitalization. The data employed is over the period January 2000 to December 2005, giving a total of 1507 observations for daily data and 71 observations for monthly data.
The daily and monthly data used for the study was extracted from the Center for research in Securities Prices database (CRSP) through the Wharton Research Data Services (WRDS) database. Throughout the report logarithmic returns are used with the exception of descriptive statistics section, where results are based on simple returns. The input data used to calculate the variance ratio results is logarithmic prices. Finally for conducting the delay test, the Standard & Poor 500 index is acquired as a proxy for the market.
Simple returns are calculated as:
and logarithmic returns are calculated as:
where Pt and Pt-1 represent the stock prices or index levels at times t and t-1, respectively.
Cambell, Lo and MacKinlay (1997) suggested three additional hypotheses to the EMH. In specific, the strongest form of random walk (RW1) represents the case where the increments are independently and independently distributed (IID). Increments are uncorrelated but also any other nonlinear function of them is uncorrelated too. The dynamics of price are shown in the above equation:
Pt=μ+Pt-1+εt , εt~IID0,σ2 3
where μ is the expected price change and IID(0,σ2) stands for the independently and identically distributed increments with zero mean and σ2 variance. RW2 is a weaker form than RW1. RW2 relaxes the assumption of IID increments and therefore represents the case of independent and not IID increments (INID). Finally by further relaxing the assumption of RW2 we conclude to the weakest form of random walk, RW3. RW3 represents the case of dependent and uncorrelated increments.
The report will initially employ autocorrelation test to examine RW3. Next the report employs the run test and the variance ratio test to examine for RW1. Finally, the last test used is the Griffin, Kelly and Nardari Delay test and that will document how sensitive are returns to historical information.
Fama (1965) suggested that a simple way to test for a random walk is to check for serial correlation. For any lag of a random walk on stock prices, the returns should be uncorrelated. As stated above, RW3 means dependent and uncorrelated increments and tests whether random variables within the series are dependent. Testing for RW3 is done by having a null hypothesis that autocorrelation coefficients (AC) at multiple lags are zero. We will reject the null hypothesis if autocorrelation is found to be significant at 5% level. For all lags, the autocorrelation formula is the following:
where ρk is the autocorrelation at lag k; ri,t is the log return on stock i at the time t; and r i,t-k is the log-return on stock i at time t-k.
The partial autocorrelation coefficients (PAC) depict the autocorrelation effect without the influence of shorter lags to longer lags.
The report presents results of daily and monthly data of 5 and 3 lags respectively. Finally, the Ljung-Box test is employed to test the hypothesis of autocorrelation coefficients jointly significance for the same lags. The above analysis is made for logarithmic returns, absolute returns and squared returns.
The report runs the variance ratio test proposed by Lo and MacKinlay (1988) as an alternatively way of testing RW1. Thus it is tested whether increments are identically distributed so that our data is stationary with a constant variance through time. The test suggests that the increments of a random walk must be linear function of time. For a random walk series of equal intervals the following equation holds:
The variance ratio equation that holds is:
where VR(q) is the variance ratio for q periods, σ2(q) is 1/q times the variance of (Pt-Pt-1) and σ2(1) is the variance of (Pt-Pt-q).
As the null hypothesis, we accept VR(q)=1. Therefore if stock returns have negative serial correlation, it would be smaller than one suggesting a mean reverting process and accordingly in the case of positive serial correlation then larger than one. Lo and MacKinlay (1988) report two tests. First, Zq statistic for RW1, assuming homoskedasticity in the increments. Second, Zq* statistic for RW3, assuming heteroskedasticity in the increments. In our report the variance ratio test will be applied for daily and monthly log returns for q periods of 2, 4, 8 and 16.
Bradley's (1968) non parametric run test was used to test for the random walk hypothesis and for the weak form hypothesis by figuring out whether there is independency in successive prices, without returns needed to be normally distributed. The test will seek for positive and negative changes looking at the sequence of successive prices. The weakness of the test stands for that it does not focus on the variance of the price change, but simply to the sign of the change. We will reject the null hypothesis of RW1 when the expected number of runs will different significantly from the number of runs provided from our sample. The run test procedure works as follows: First we compute the number of runs in the series and make the null hypothesis of independence. Then we calculate the expected number of runs and the variance:
where na is the number of positive runs and nb is the number of negative runs and Z(r) is the z-statistic. Finally if the following imparity does not stand, then we reject the null hypothesis of independence.
Er-1.96σr≤r≤Er+1.96σr , a=0.05 (10)
The last test used in this report is the DELAY test. Through Griffin, Kelly and Nardari DELAY test (2006) we will examine the sensitivity of current returns to historic market wide information. At the same time we will use the S&P 500 index as a proxy for a market portfolio. With the use of the DELAY test it would be possible to see how more lags in the regression of the stock returns can improve the fit. Therefore throughout the period of our sample (January 2000 till December 2005) we will provide accordingly restricted and unrestricted models for the all stocks and indices. The unrestricted daily model shall be:
and the monthly model:
The restricted model shall be:
where ri,t is the stock return at time t, rm,t is the log return of the S&P 500 index at time t, rm,t-n is the lagged market return, ai is intercept, β is the coefficient on the lagged market return and εi,t is the error term.
We will use for daily data 1, 2, 3 and 4 lags whereas for monthly data 1, 2 and 3 lags.
The DelayGKN, DelayA and F-statistic is measured by first estimating the adjusted R2 and the sum of the squared residuals. The DelayGKN will be the difference between the restricted and unrestricted adjusted R2.
Mech (1993) and Hou and Moskowitz (2005) proposed an DelayGKN as follows:
To conclude, the delay in market news is stronger, for larger values of DelayGKN or of DelayA. We will then calculate the F-statistic as follows:
where SSRRR is the restricted sum of squared residuals, SSRUR is the unrestricted sum of squared residuals, T is number of observations, K is number of regressors and n is number of lag restrictions.
The descriptive statistics for daily and monthly data are depicted on Tables I and II. There is a distinction between logarithmic (r) and simple (R) returns. The main underlying assumption is that returns are distributed normally.
Concerning logarithmic returns, VICR and VICL have the lowest mean of (-0.001). The highest mean is of NAN D1 (0.001). The lowest median is again for VICR and VICL with (-0.002) and the highest for NAN D1 with (0.001). The lowest maximum return is for NAN D1 with (0.077) and NAN D10 with (0.054). In contrast, the highest maximum return is of VICL with (0.329). Finally, the lowest minimum return holds for VSAT with (-0.660) and the highest for NAN D10 with (-0.068).
As for dispersion, the standard deviation of NAN D1 and NAN D10 is the lowest with (0.011) and (0.012), being the least volatile. The highest standard deviation is of VICL with (0.053) being the most volatile. As for asymmetry, the highest positive holds for NAN D10 with (0.096) suggesting more possible to earn positive returns. In contrast the least negative holds for VSAT with (-1.573). The kurtosis of all stocks and indices are positive suggesting more peaked distribution compared to the normal on the tails and around the mean, giving more possibilities for extreme events to happen. Accounting for the Jarque-Bera, the null hypothesis of having normal distribution is rejected for all stocks and indices at a 5% significance level, since they have a 0.000 p-value.
Concerning simple returns, the results show higher mean, median, maximum and minimum for all stocks and indices. As for skewness, VICR and VICL from negative become positive.
Table I depicts the descriptive statistics of daily returns for three stocks and two decile indices over the period January 2000 to December 2005. The lower-case letter r denotes logarithmic return. The upper-case letter R denotes simple return. VICR - Vicor Corp., VSAT - Viasat Inc., VICL - Vical Inc., NAN D1 - Nyse/Amex/Nasdaq Decile 1 and NAN D10 - Nyse/Amex/Nasdaq Decile 10, Max. stands for Maximum, Min. stands for Minimum, Std. Dev. stands for Standard Deviation, JB stands for Jarque-Bera, Obs. stands for Observations.
In general daily and monthly results are almost consistent. As for logarithmic returns, NAN D10 has the lowest and NAN D1 has the highest mean with (0.000) and (0.016) respectively. The lowest median holds for VICR with (-0.005) and the highest for VICL and NAN D10 with (0.008). VSAT has again the lowest minimum return with (-0.984) and as in daily frequencies NAN D1 has the highest maximum return with (0.434).
As for dispersion, the standard deviation of NAN D10 is the lowest with (0.046) and VICL is the highest with (0.234), like the daily frequencies. The skewnesses are all negative except for NAN D1 with (1.294). NAN D1 is more probable to have positive returns than negative. Kurtosis figures suggest again more peaked distribution compared to the normal on the tails and around the mean. Finally as for the Jarque-Bera, VICR with (5.607) and NAN D10 with (2.465) cannot reject the null hypothesis of normal distribution at a 5% significance level.
Table II depicts the descriptive statistics of monthly returns for three stocks and two decile indices over the period January 2000 to December 2005. The lower-case letter r denotes logarithmic return. The upper-case letter R denotes simple return. VICR - Vicor Corp., VSAT - Viasat Inc., VICL - Vical Inc., NAN D1 - Nyse/Amex/Nasdaq Decile 1 and NAN D10 - Nyse/Amex/Nasdaq Decile 10, Max. stands for Maximum, Min. stands for Minimum, Std. Dev. stands for Standard Deviation, JB stands for Jarque-Bera, Obs. stands for Observations.
Concerning the daily logarithmic returns, in Table III Panel A both AC and PAC coefficients are statistically insignificant for VICR, VSAT and N/A/N D10. VICL has negative statistically significant coefficients for the 1st lag of AC and the 1st and 2nd lag of PAC. All coefficients are positively significant for N/A/N D1 for all lags of AC and PAC, except of the 4th lag of PAC.
The Ljung-Box test, accounting for the joint hypothesis of statistical significance shows that VICL and N/A/N D10 have jointly significant coefficients for all 5 lags. Consequently, the null hypothesis of no serial correlation is rejected at a 5% significance level. In contrast, the Ljung-Box statistics for VICR, VSAT and N/A/N D10 are insignificant meaning no serial dependency.
Concerning the monthly logarithmic returns in Panel B, only VICL has significant coefficients on the 2nd lag of both AC and PAC. The rest lags for all other stocks and indices have insignificant coefficients. The Ljung-Box test gives significance only for lags 2 and 3. All the rest are insignificant.
Concerning the squared daily logarithmic returns in Table IV Panel A every stock or index has at least one AC and PAC coefficient significant meaning that they do not follow a random walk. Specifically, VICR has its 1st lag of AC and PAC significant. VSAT has for the AC the 1st, 3rd and 4th lags significant, whereas for the PAC has the 1st and 3rd lags significant. VICL has for the AC the 1st and 2nd lag significant and only the 1st for PAC. Finally, most of the lags for both AC and PAC there is significance N/A/N D1 and N/A/N D10. As for the Ljung-Box statistics, they are all significant for all stocks and indices, therefore the null hypothesis of no serial correlation is rejected which indicates serial correlation.
Concerning the squared monthly logarithmic returns in Panel B, there is significance only to the 2nd lag of VSAT and to the 3rd lag of N/A/N D10 for both AC and PAC coefficients. As for the Ljung-Box statistics they is significance only to the 1st lag of VICL and to the 3rd lag of N/A/N D10. Therefore in all other lags the null hypothesis cannot be rejected.
Concerning the absolute daily logarithmic returns in Table V Panel A, all the coefficients of AC and PAC are statistically significant for all lags. Not significant coefficients are spotted for VICR in the 3rd lag of AC and in the 2nd and 3rd lag of PAC. As for the Ljung-Box statistics, they are all significant for all stocks and indices, therefore the null hypothesis of no serial correlation is rejected which indicates serial correlation.
Concerning the absolute monthly logarithmic returns in Panel B, statistical significances are spotted at the 2nd lag of VSAT and at the 1st lag of VICL for both AC and PAC coefficients. All the other lags of VSAT and VICL are not significant. The VICR, N/A/N D1 and N/A/N D10 have insignificant coefficients meaning that there is no serial dependency. As for the Ljung-Box statistics, VICR, VSAT and N/A/N D10 are insignificant and therefore the null hypothesis of no serial correlation cannot be rejected at a 5% significance level, which indicates serial correlation. Jointly significances appear for VICL and NAN D1 for lags 1 and 3 respectively.
Table III depicts the autocorrelation and partial autocorrelation coefficients up to 5 lags for logarithmic returns and up to 3 lags for monthly data. AC stands for autocorrelation and PAC for partial autocorrelation and L-B for Ljung-Box test statistics. VICR - Vicor Corp., VSAT - Viasat Inc., VICL - Vical Inc., N/A/N D1 - Nyse/Amex/Nasdaq Decile 1 and N/A/N D10 - Nyse/Amex/Nasdaq Decile 10. Figures in italics depict p-values of the L-B test statistics. Asterisk indicates statistical significance of a 5% level.
Table IV depicts the autocorrelation and partial autocorrelation coefficients up to 5 lags for squared logarithmic returns and up to 3 lags for monthly data. AC stands for autocorrelation and PAC for partial autocorrelation and L-B for Ljung-Box test statistics. VICR - Vicor Corp., VSAT - Viasat Inc., VICL - Vical Inc., N/A/N D1 - Nyse/Amex/Nasdaq Decile 1 and N/A/N D10 - Nyse/Amex/Nasdaq Decile 10. Figures in italics depict p-values of the L-B test statistics. Asterisk indicates statistical significance of a 5% level.
Table V depicts the autocorrelation and partial autocorrelation coefficients up to 5 lags for absolute logarithmic returns and up to 3 lags for monthly data. AC stands for autocorrelation and PAC for partial autocorrelation and L-B for Ljung-Box test statistics. VICR - Vicor Corp., VSAT - Viasat Inc., VICL - Vical Inc., N/A/N D1 - Nyse/Amex/Nasdaq Decile 1 and N/A/N D10 - Nyse/Amex/Nasdaq Decile 10. Figures in italics depict p-values of the L-B test statistics. Asterisk indicates statistical significance of a 5% level.
The correlations shown in Table VI are all positive regarding the daily log returns. The correlation values vary from (0.1778) of VICL-VICR to (0.5052) of NAN D10-NAN D1. Concerning the lowest stock-stock correlation appears to be the VICL-VICR whereas the highest is for VSAT-VICR with (0.2272).
Panel B represents the correlation results for monthly logarithmic returns. It appears that again all correlations are positive. The correlation values vary from (0.1907) of VSAT-VICR to (0.5552) of NAN D10-VICL. As for stock-stock correlations, the lowest is for VSAT-VICR and the highest for VICL-VSAT with (0.2877).
Table VI depicts the correlation matrix of logarithmic returns over the period January 2000 to December 2005. VICR - Vicor Corp., VSAT - Viasat Inc., VICL - Vical Inc., N/A/N D1 - Nyse/Amex/Nasdaq Decile 1 and N/A/N D10 - Nyse/Amex/Nasdaq Decile 10.
Table VII and specifically Panel A shows that under homoscedasticity the null hypothesis of random walk is rejected for VICL in lags 2, 4 and 8 and for N/A/N D1 in all lags. Concerning VICL the variance ratio estimate is smaller than the unit, meaning that there is negative correlation. In contrast, N/A/N D1 variance ratio estimates are greater than one meaning positive correlation. For VICR, VSAT and N/A/N D10 estimates are lower that the unit. Under heteroscedasticity there is evidence of significance only every lag of N/A/N D1, thus rejecting the null hypothesis of random walk and having positive correlation. As for Panel B that accounts for monthly data, interestingly enough it looks that the significances of the daily data do not hold. Both under homoscedasticity and heteroscedasticity we cannot reject the null hypothesis of random walk.
In addition in Table VIII the variance ratio test is run again but by first having trimmed the data at a 5% level. In Panel A for daily logarithmic returns, interestingly VSAT appears to have significances for all lags concerning homoscedasticity. The same holds for VICL and N/A/N D1. However, under heteroscedasticity there are significances in lag 4 of VICL, in lag 4 and 8 of NAN D10 and in all lags of NAN D1. As for monthly data of Panel B, it seems that trimming the data corrects in some degree for the insignificances that were not spotted for VICL and NAN D1 of Table VII. Therefore under heteroscedasticity lag 4 of VICL appears to be significant and under both homoscedasticity and heteroscedasticity lag 16 of N/A/N D10 are significant, thus rejecting the null hypothesis of random walk, and having positive correlation like the case of Table VII.
Table VII depicts the variance ratio results over the period January 2000 to December 2005 based on Lo and MacKinley (1988). VICR - Vicor Corp., VSAT - Viasat Inc., VICL - Vical Inc., N/A/N D1 - Nyse/Amex/Nasdaq Decile 1 and N/A/N D10 - Nyse/Amex/Nasdaq Decile 10. The analysis below accounts for lag orders 2, 4. 8 and 16. The italic figures depict homoscedastic test-statistics and figures in brackets depict heteroskedastic test tatistics. Asterisk indicates statistical significance of a 5% level.
Table VIII depicts the variance ratio results for trimmed data over the period January 2000 to December 2005 based on Lo and MacKinley (1988). In specific, 5% of the tails is removed. VICR - Vicor Corp., VSAT - Viasat Inc., VICL - Vical Inc., N/A/N D1 - Nyse/Amex/Nasdaq Decile 1 and N/A/N D10 - Nyse/Amex/Nasdaq Decile 10. The analysis below accounts for lag orders 2, 4. 8 and 16. The italic figures depict homoscedastic test-statistics and figures in brackets depict heteroskedastic test-statistics. Asterisk indicates statistical significance of a 5% level.
The results of the Runs Tests employed for the stocks and indices are shown in Table IX. Concerning Panel A of daily logarithmic returns only VICL and N/A/N D1 prove to have significances at a 5% level and thus reject the hypothesis of random walk. VICR, VSAT and N/A/N D10 fail to reject the null hypothesis that the number of expected and actual returns is not significantly different.
Concerning Panel B of monthly logarithmic returns all three stocks and two indices prove not to be significant at a 5% level. Therefore the null hypothesis of random walk cannot be rejected and the differences between the number of expected and actual returns are not statistically significant.
The resulting sensitivity of current logarithmic returns to past wide market information is measured in Table X through the Griffin-Kelly-Nardari DELAY tests. As shown in Panel A only VICR is insignificant. Concerning significances, the lowest is spotted for N/A/N D10 with (0.000) whereas the highest is for N/A/N D1 with (0.070). Concerning, DelayA measure it appears that the lower and highest estimates are again NAN D10 and NAN D1 with (0.000) and (0.238) respectively.
As for Panel B, the results of monthly logarithmic returns give significance for VICR and insignificance for VSAT. VICL, NAN D1 and NAN D10 are statistically significant at a 5% level. The lowest significant delay estimates are for NAN D10 with (0.021) and the highest for VICL with (0.117).
Comparing the results drown with DelayA to DelayDKN it appears that all estimates are higher for the former and the reason is the high unrestricted R-square (Griffin et al., 2007). In addition, Griffin et al. (2007) suggested that large capitalization stocks are likely to be more efficient than small capitalization stocks. Consequently, by construction and based on their capitalization deciles the delay should be lower for N/A/N D10 than N/A/N D1. The evidence shown in Table X supports that for both monthly and daily data.
Table IX depicts the results after employing the runs tests over the period January 2000 to December 2005. VICR - Vicor Corp., VSAT - Viasat Inc., VICL - Vical Inc., N/A/N D1 - Nyse/Amex/Nasdaq Decile 1 and N/A/N D10 - Nyse/Amex/Nasdaq Decile 10. E(r) stands for the expected number of runs. r stands for the observed number of runs. The italic figures depict Z-statistics. Asterisk indicates statistical significance of a 5%level.
Table X depicts the results after employing the delay tests over the period January 2000 to December 2005. VICR - Vicor Corp., VSAT - Viasat Inc., VICL - Vical Inc., N/A/N D1 - Nyse/Amex/Nasdaq Decile 1 and N/A/N D10 - Nyse/Amex/Nasdaq Decile 10. DelayGKN equals Adj.R2unrestricted - Adj.R2restricted. DelayA equals 1 - Adj.R2restricted/Adj.R2restricted. The italic figures depict F-test statistics. Asterisk indicates statistical significance of a 5%level.
The weak form market efficiency hypothesis was tested via employing four tests in our sample of three NASDAQ company stocks and two decile indices over the period January 2000 till December 2005. First, autocorrelation tests of logarithmic, squared logarithmic and absolute logarithmic returns are provided on daily and monthly basis. Next, the report provides the daily and monthly estimates of variance ratio tests accounting for homoscedasticity and heteroscedasticity and also their results after trimming the data. Following, runs and delay tests are conducted again on a daily and monthly basis.
In general it seems that the results provided from these tests have consistency for most of the sample. Throughout the report it seems that VICL and N/A/N D1 have statistical significances supported by all the tests. This means that they are likely to reject the null hypothesis of a random walk.
In particular, autocorrelation test provide different results in the cases of regular, squared and absolute logarithmic returns. For absolute logarithmic returns autocorrelations proves to be much stronger. Also monthly results tend to be more stationary than those of daily, suggesting that the market is more efficient for longer than shorter periods. That is obvious and by the results of the variance ratio tests. However after trimming the daily data, even though significances of VICL and NAN D1 are spotted in more lags, it appears certain significances for VSAT and NAN D10 that previously were insignificant. However, monthly trimmed data appears to be consistent to our primary findings of significant VICL and NAN D1. Following the analysis, the runs test clearly support the VICL and N/A/N D1 significances. Finally, the delay tests even thought evident significances for all stocks and indices it provides results consistent to the idea that smaller capitalization stocks are less efficient than larger.
To conclude, this report depicts results accounting for a specific sample and therefore the evidence provided is not catholic. Different sample characteristics could generate significantly different results. Rejection of weak form efficiency does not mean that investors could earn abnormal returns, since market frictions can usually eliminate them.
Source: Essay UK - http://turkiyegoz.com/free-essays/finance/weak-form-efficiency.php
If this essay isn't quite what you're looking for, why not order your own custom Finance essay, dissertation or piece of coursework that answers your exact question? There are UK writers just like me on hand, waiting to help you. Each of us is qualified to a high level in our area of expertise, and we can write you a fully researched, fully referenced complete original answer to your essay question. Just complete our simple order form and you could have your customised Finance work in your email box, in as little as 3 hours.
This Finance essay was submitted to us by a student in order to help you with your studies.
This page has approximately words.
If you use part of this page in your own work, you need to provide a citation, as follows:
Essay UK, Weak form efficiency . Available from: <http://turkiyegoz.com/free-essays/finance/weak-form-efficiency.php> [19-12-18].
If you are the original author of this content and no longer wish to have it published on our website then please click on the link below to request removal: