Tests of Random Walk Hypothesis
In this paper, the random walk hypothesis based on monthly stock market returns is tested by comparing variance ratios. The random walk model is not rejected for the entire sample period (1926-2007) and for its subperiods when using value-weighted stock returns. However, the model is rejected on equal-weighted stock returns when using low aggregation values q. Generally, the random walk model is not rejected when using monthly data.
It was widely believed that the market is efficient in reflecting all available information that no abnormal returns can be earned by studying the historical prices. However, some recent papers suggest that stock prices are partially predictable. In this paper, I test the weak form efficiency of the market using the variance ratio test by Lo and Mackinlay (1988). And the result yields that the market generally follows the random walk for monthly stock returns. The rest of the paper is organized as follows. In section 1, the previous main findings on the Efficient Market Hypothesis are reviewed. The data and sample period are described in section 2. The main results are given in section 3, where tests for both homoscedastic and heteroscedastic random walks are conducted. Section 4 is the conclusion of this paper.
1. Related literature on Efficient Market Hypothesis
According to Eugene Fama's (1970) survey article, "Efficient Capital Market", the vast majority of academic financial economist failed to reject the efficient market hypothesis in their studies. Malkiel (2003) in his recent study "the Efficient Market and Its Critics" also concludes that "the stock markets are far more efficient and far less predictable". However, Kiem and Stambaugh (1986) suggest that stock returns contain predictable components that are statistically significant. Furthermore, Lo and Mackinley (1988) state in their study that stock prices do not follow random walk by comparing variance estimators, they also find a positive autocorrelation for weekly stock returns.
2. Data and Sample Period
Since the test is based on asymptotic approximations, a large number of data is chosen for this study. The sample period is from 1926 to 2007, and a total of 984 monthly observations are derived from the CRSP index. Two different indexes are used in this study: equalweighted CRSP index and value-weighted CRSP index. Also, observations from both index are divided into two subperiods. The first subperiod starts from 1926 and ends in 1964; the second subperiod starts from 1965 and ends in 2007.
3. Empirical Results
Table 1 provides the results based on the methodology of variance ratio test by Lo and MacKinlay (1988). It demonstrates that variance ratio estimates and test statistics of the Random Walk Hypothesis for the entire study period and two subperiods.
Table 1 Market Index results 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 form variance ratio 2 4 8 16
For the equal-weighted CRSP index, the random walk null hypothesis is only rejected with an aggregation value q equal to 2. Since a variance ratio with q of 2 is approximately equal to 1 plus the first-order autocorrelation coefficient estimator of monthly stock returns, the result 1.1691 indicates that the first-order autocorrelation for monthly returns is around...
References: 1. Lo, A. W. and A. C. MacKinlay, 1988, Stock Market Prices Do Not Follow Random Walks: Evidence from a
Simple Specification Test, The Review of Financial Study 1, 41-66
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