In this paper. the random walk hypothesis based on monthly stock market returns is tested by comparing discrepancy ratios. The random walk theoretical account is non rejected for the full sample period ( 1926-2007 ) and for its subperiods when utilizing value-weighted stock returns. However. the theoretical account is rejected on equal-weighted stock returns when utilizing low collection values q. Generally. the random walk theoretical account is non rejected when utilizing monthly informations.
It was widely believed that the market is efficient in reflecting all available information that no unnatural returns can be earned by analyzing the historical monetary values.
However. some recent documents suggest that stock monetary values are partly predictable. In this paper. I test the weak signifier efficiency of the market utilizing the discrepancy ratio trial by Lo and Mackinlay ( 1988 ) . And the consequence outputs that the market by and large follows the random walk for monthly stock returns. The remainder of the paper is organized as follows. In subdivision 1. the old chief findings on the Efficient Market Hypothesis are reviewed.
The information and sample period are described in subdivision 2. The chief consequences are given in subdivision 3. where trials for both homoscedastic and heteroscedastic random walks are conducted. Section 4 is the decision of this paper.
1. Related literature on Efficient Market Hypothesis
Harmonizing to Eugene Fama’s ( 1970 ) study article. “Efficient Capital Market” . the huge bulk of academic fiscal economic expert failed to reject the efficient market hypothesis in their surveies. Malkiel ( 2003 ) in his recent survey “the Efficient Market and Its Critics” besides concludes that “the stock markets are far more efficient and far less predictable” . However. Kiem and Stambaugh ( 1986 ) suggest that stock returns contain predictable constituents that are statistically important. Furthermore. Lo and Mackinley ( 1988 ) province in their survey that stock monetary values do non follow random walk by comparing discrepancy calculators. they besides find a positive autocorrelation for hebdomadal stock returns.
2. Datas and Sample Period
Since the trial is based on asymptotic estimates. a big figure of informations is chosen for this survey. The sample period is from 1926 to 2007. and a sum of 984 monthly observations are derived from the CRSP index. Two different indexes are used in this survey: equalweighted CRSP index and value-weighted CRSP index. Besides. observations from both index are divided into two subperiods. The first subperiod starts from 1926 and ends in 1964 ; the 2nd subperiod starts from 1965 and ends in 2007.
3. Empirical Consequences
Table 1 provides the consequences based on the methodological analysis of discrepancy ratio trial by Lo and MacKinlay ( 1988 ) . It demonstrates that discrepancy ratio estimations and trial statistics of the Random Walk Hypothesis for the full survey period and two subperiods.
Table 1 Market Index consequences for one-month base observation period Number nq of Time period A. Equal-weighted CRSP index 1/1/1926-12/1/2007 1/1/1926-12/1/1964 1/1/1965 – 12/1/2007 B. Value-weighted CRSP index 1/1/1926-12/1/2007 1/1/1926-12/1/1964 1/1/1965 – 12/1/2007 984 468 516 1. 0952 ( 1. 6822 ) 1. 1218 ( 1. 5087 ) 1. 0490 ( 0. 9310 ) 1. 0776 ( 0. 7421 ) 1. 1146 ( 0. 7687 ) 1. 0242 ( 0. 2493 ) 1. 1013 ( 0. 6238 ) 1. 1541 ( 0. 6666 ) 1. 0403 ( 0. 2702 ) 1. 2361 ( 0. 9853 ) 1. 4067 ( 1. 1904 ) 1. 0077 ( 0. 0361 ) 984 468 516 1. 1691 ( 2. 4694 ) 1. 1639 ( 1. 6903 ) 1. 1888 ( 3. 8454 ) 1. 2157 ( 1. 9250 ) 1. 2182 ( 1. 3120 ) 1. 235 ( 2. 5590 ) 1. 1484 ( 0. 8588 ) 1. 1445 ( 0. 5980 ) 1. 2105 ( 1. 4532 ) 1. 2328 ( 0. 9219 ) 1. 3337 ( 0. 9470 ) 1. 1248 ( 0. 5810 ) base observations Number Q of base observations aggregated to organize discrepancy ratio 2 4 8 16
For the equal-weighted CRSP index. the random walk void hypothesis is merely rejected with an collection value q equal to 2. Since a discrepancy ratio with Q of 2 is about equal to 1 plus the first-order autocorrelation coefficient calculator of monthly stock returns. the consequence 1. 1691 indicates that the first-order autocorrelation for monthly returns is around 17 per cent.
And the trial statistic suggests rejections of the Random Walk Hypothesis at 5 per cent of significance. As the value of Q additions. the trial statistics lessenings. and this leads to the fail of rejections of the random walk hypothesis. For the value-weighted CRSP index. the void hypothesis is non rejected at the significance degree of 5 per cent for all different value of Q. Since the value-weighted index put more weight on the big capital houses. and the Random Walk Hypothesis is more likely to keep for big capital stocks. the empirical determination in this paper is consistent with such theory that the random walk is non rejected for the valueweighted CRSP index. For the equal-weighted index. the hypothesis is rejected due to the fact that the index put more weight on the little capital socks comparatively to the value- weighted index. And it is more likely to happen some predictability in little capital houses. This consequence is consistent with Lo and Mackinlay’s ( 1988 ) happening that “the rejection of the random walk hypothesis is much weaker for the value-weighted index” .
For both indexes. the discrepancy ratios for their subperiods are rather stable and consistent with the discrepancy ratio of the full sample period. The Random Walk Hypothesis is non rejected for both subperiods for the value-weighted index. However. for the equal-weighted index. the void hypothesis is non rejected for the first subperiod from 1926 to 1964. But for the 2nd subperiod from 1965 to 2007. the random walk hypothesis is rejected when the collection value Q peers to 2 and 4. The rejection of RWH in this subperiod ( 1965-2007 ) is likely due to the fact that the US economic system fluctuated more frequently in this period. The OPEC recession. the market clang of October 1987. the 1990-91 recession. the dot-com bubble and the recent fiscal crisis may all take to some extend of unreason of the market. For both indexes. all of the discrepancy ratios are greater than 1 and a form that the ratios increases as the collection value Q additions while the trial statistics by and large decreases as Q additions can be found. Besides. the returns are positively correlated for both indexes.
This is consistent with Lo and Mackinlay’s ( 1988 ) happening but differ from Fama’s ( 1987 ) happening that a negative consecutive correlativity can be found in long keeping period returns. In this paper. merely monthly returns are tested. and by and large. the Random Walk Hypothesis is non rejected for both equal-weighted and value-weighted index. This is consistent with old surveies that the hypothesis is by and large non rejected when utilizing monthly returns. However. harmonizing to Lo and Mackinlay ( 1988 ) . it is much more likely to reject the random walk when utilizing a basal observation period of one hebdomad. In their survey. the Random Walk Hypothesis is rejected at all usual significance degrees for the whole sample period from 1962 to 1985 utilizing hebdomadal informations.
By and large. the Random Walk Hypothesis is non rejected for monthly stock market returns by utilizing the Lo and Mackinlay ( 1988 ) discrepancy ration trial. The trial consequences for the valueweighted CRSP index indicate that none of the trial for heteroscedasticity at any different value of Q is important. Therefore. the RWH can non be rejected for the value-weighted index. For the equal-weighted CRSP index. the RWH is rejected merely when the collection value Q peers to 2. Such difference in the two indexes indicates that the rejections of the Random Walk Hypothesis may mostly due to the predictability of little capital stocks.
1. Lo. A. W. and A. C. MacKinlay. 1988. Stock Market Monetary values Do Not Follow Random Walks: Evidence from a Simple Specification Test. The Review of Financial Study 1. 41-66. 2. Fama. E. . 1970. “Efficient Capital Markets: A Review of Theory and Empirical Work. ” Journal of Finance 25. 383-417 3. Keim. Donald B. and Robert T. Stambaugh. 1986. “Predicting Returns in Stock and Bond Markets. ” Journal of Financial Economics. December. 17. pp. 357–90. 4. Malkiel. Burton G. 1973. A Random Walk Down Wall Street. New York: W. W. Norton & A ; Co.
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